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Provide tags and a correct Python 3 solution for this coding contest problem.
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you."
<image>
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
If we sort all lucky numbers in increasing order, what's the 1-based index of n?
Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.
Input
The first and only line of input contains a lucky number n (1 β€ n β€ 109).
Output
Print the index of n among all lucky numbers.
Examples
Input
4
Output
1
Input
7
Output
2
Input
77
Output
6
Tags: bitmasks, brute force, combinatorics, implementation
Correct Solution:
```
import sys
s = input()
ans = 0
for i in s:
if i == '4':
ans = ans * 2
else:
ans = ans * 2 + 1
ans += 1
ans += (1<<len(s))-2
print ("%d"%(ans))
```
| 400
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you."
<image>
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
If we sort all lucky numbers in increasing order, what's the 1-based index of n?
Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.
Input
The first and only line of input contains a lucky number n (1 β€ n β€ 109).
Output
Print the index of n among all lucky numbers.
Examples
Input
4
Output
1
Input
7
Output
2
Input
77
Output
6
Tags: bitmasks, brute force, combinatorics, implementation
Correct Solution:
```
s = input()
s = '7' + s
s = s.replace("4", "0")
s = s.replace("7", "1")
print(int(s,2)-1)
```
| 401
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you."
<image>
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
If we sort all lucky numbers in increasing order, what's the 1-based index of n?
Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.
Input
The first and only line of input contains a lucky number n (1 β€ n β€ 109).
Output
Print the index of n among all lucky numbers.
Examples
Input
4
Output
1
Input
7
Output
2
Input
77
Output
6
Tags: bitmasks, brute force, combinatorics, implementation
Correct Solution:
```
n = input()
x = 1
ans = 0
for i in range(len(n) - 1):
x <<= 1
ans += x
x = 0
for i in range(len(n)):
if n[len(n) - 1 - i] == '4':
continue
else:
x |= 1<<i
ans += x
print(ans+1)
```
| 402
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you."
<image>
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
If we sort all lucky numbers in increasing order, what's the 1-based index of n?
Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.
Input
The first and only line of input contains a lucky number n (1 β€ n β€ 109).
Output
Print the index of n among all lucky numbers.
Examples
Input
4
Output
1
Input
7
Output
2
Input
77
Output
6
Tags: bitmasks, brute force, combinatorics, implementation
Correct Solution:
```
s=input()
l=len(s)
n = (1<<l)
num = n-1
sum=0
for i in range(l):
n=n//2
if s[i]== '7':
num+=n
print(num)
```
| 403
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you."
<image>
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
If we sort all lucky numbers in increasing order, what's the 1-based index of n?
Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.
Input
The first and only line of input contains a lucky number n (1 β€ n β€ 109).
Output
Print the index of n among all lucky numbers.
Examples
Input
4
Output
1
Input
7
Output
2
Input
77
Output
6
Submitted Solution:
```
def DFS(number):
if (number > 1e9):
return []
return DFS(number * 10 + 4) + DFS(number * 10 + 7) + [number]
def main():
res = DFS(0)
res.sort()
n = int(input())
return res.index(n)
if __name__ == '__main__':
print(main())
```
Yes
| 404
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you."
<image>
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
If we sort all lucky numbers in increasing order, what's the 1-based index of n?
Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.
Input
The first and only line of input contains a lucky number n (1 β€ n β€ 109).
Output
Print the index of n among all lucky numbers.
Examples
Input
4
Output
1
Input
7
Output
2
Input
77
Output
6
Submitted Solution:
```
'''
for i in range(1,10000):
if str(i).count('4')+str(i).count('7')==len(str(i)):
print(i)
'''
n=int(input())
if n==4:
print(1)
elif n==7:
print(2)
else:
count=len(str(n))
sum=0
for i in range(1,count):
sum+=pow(2,i)
l=[]
for i in str(n):
if i=='7':
l.append('1')
else:
l.append('0')
n=''.join(l)
ans=0
for i in range(len(n)-1,-1,-1):
ans+=int(n[i])*pow(2,len(n)-i-1)
print(ans+sum+1)
```
Yes
| 405
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you."
<image>
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
If we sort all lucky numbers in increasing order, what's the 1-based index of n?
Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.
Input
The first and only line of input contains a lucky number n (1 β€ n β€ 109).
Output
Print the index of n among all lucky numbers.
Examples
Input
4
Output
1
Input
7
Output
2
Input
77
Output
6
Submitted Solution:
```
from sys import stdin
#####################################################################
def iinput(): return int(stdin.readline())
def minput(): return map(int, stdin.readline().split())
def linput(): return list(map(int, stdin.readline().split()))
#####################################################################
n = input()
d = {'4':'0', '7':'1'}
x = 2**len(n) - 1
b = ''
for e in n:
b += d[e]
m = int(b, 2)
print(x+m)
```
Yes
| 406
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you."
<image>
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
If we sort all lucky numbers in increasing order, what's the 1-based index of n?
Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.
Input
The first and only line of input contains a lucky number n (1 β€ n β€ 109).
Output
Print the index of n among all lucky numbers.
Examples
Input
4
Output
1
Input
7
Output
2
Input
77
Output
6
Submitted Solution:
```
'''
Get the number n and turn it into a list l of its digits.
'''
n = int(input())
l = list(int(i) for i in str(n))
def index_of(l):
idx = 0
zero = [0 for i in range(len(l))]
# We turn a digit into 0 when we change to a lucky number with fewer
# digits.
while l != zero:
# We run through the digits starting from right to left turning 7's into
# 4's and 4's into 7's (and when we turn 4's into 7's it's a bit more
# complicated because you have to change the next digit to something)
for i in range(len(l) - 1, -1, -1):
if l[i] == 0:
break
# hard case
elif l[i] == 4:
# When the current digit is 4, we change it into 0 if:
# the digit 4 is the leftmost digit, for example if l is
# [4, 4], the next lucky number is [0, 7] and the series of
# changes we do is [4, 4] -> [4, 7] -> [0, 7].
#
# the digit to the left of 4 is 0, for example if l is
# [0, 4, 4], the next lucky number would be [0, 0, 7] and the
# series of changes we do is [0, 4, 4] -> [0, 4, 7] ->
# [0, 0, 7].
#
# Note that it is important that we put i == 0 as our first
# condition as otherwise it's possible that i - 1 < 0.
if i == 0 or l[i - 1] == 0:
l[i] = 0
else:
l[i] = 7
# easy case
elif l[i] == 7:
l[i] = 4
break
idx += 1
return idx
print(index_of(l))
```
Yes
| 407
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you."
<image>
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
If we sort all lucky numbers in increasing order, what's the 1-based index of n?
Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.
Input
The first and only line of input contains a lucky number n (1 β€ n β€ 109).
Output
Print the index of n among all lucky numbers.
Examples
Input
4
Output
1
Input
7
Output
2
Input
77
Output
6
Submitted Solution:
```
def lucky(n):
if(n==4):
print(1)
if(n==7):
print(2)
else:
x=len(str(n))
s=0
for i in range(1,x):
s+=2**i
for i in range(len(str(x))):
if str(n)[i]=="4":
pass
else:
s+=2**(x-1-i)
if str(n)[-1]=="7":
s+=1
print(s+1)
lucky(int(input()))
```
No
| 408
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you."
<image>
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
If we sort all lucky numbers in increasing order, what's the 1-based index of n?
Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.
Input
The first and only line of input contains a lucky number n (1 β€ n β€ 109).
Output
Print the index of n among all lucky numbers.
Examples
Input
4
Output
1
Input
7
Output
2
Input
77
Output
6
Submitted Solution:
```
import sys
lucky = str(input())
position = 0
multiplicador=1
for char in lucky:
if char == '4':
position+=multiplicador*1
else:
position+=multiplicador*2
multiplicador*=2
print (position)
```
No
| 409
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you."
<image>
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
If we sort all lucky numbers in increasing order, what's the 1-based index of n?
Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.
Input
The first and only line of input contains a lucky number n (1 β€ n β€ 109).
Output
Print the index of n among all lucky numbers.
Examples
Input
4
Output
1
Input
7
Output
2
Input
77
Output
6
Submitted Solution:
```
def main(n):
x = len(str(n))
res1 = (1<<x)-2
i = 0
res2 = 0
while i<x:
if str(n)[i] == 7:
res2 += (1<<(x-i))
i+=1
return res1 + res2 +1
```
No
| 410
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: "If you solve the following problem, I'll return it to you."
<image>
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
If we sort all lucky numbers in increasing order, what's the 1-based index of n?
Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.
Input
The first and only line of input contains a lucky number n (1 β€ n β€ 109).
Output
Print the index of n among all lucky numbers.
Examples
Input
4
Output
1
Input
7
Output
2
Input
77
Output
6
Submitted Solution:
```
def calc(n):
x = len(str(n))
res1 = (1<<x)-2
i = 0
res2 = 0
while i<x:
if str(n)[i] == 7:
index = x - i
res2 += (1<<(x-i))
i+=1
return res1 + res2 +1
```
No
| 411
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Volodya and Vlad play the following game. There are k pies at the cells of n Γ m board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy.
<image>
Input
First line contains 3 integers, separated by space: 1 β€ n, m β€ 100 β dimensions of the board and 0 β€ k β€ 100 β the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 β€ x β€ n, 1 β€ y β€ m β coordinates of the corresponding pie. There could be more than one pie at a cell.
Output
Output only one word: "YES" β if Volodya wins, "NO" β otherwise.
Examples
Input
2 2 1
1 2
Output
YES
Input
3 4 0
Output
NO
Input
100 50 2
50 25
50 25
Output
NO
Tags: games
Correct Solution:
```
n, m, k = [int(i) for i in input().split()]
flag = False
for j in range(k):
x, y = [int(z) for z in input().split()]
flag |= x < 6 or n - x < 5
flag |= y < 6 or m - y < 5
if flag:
print("YES")
else:
print("NO")
```
| 412
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Volodya and Vlad play the following game. There are k pies at the cells of n Γ m board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy.
<image>
Input
First line contains 3 integers, separated by space: 1 β€ n, m β€ 100 β dimensions of the board and 0 β€ k β€ 100 β the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 β€ x β€ n, 1 β€ y β€ m β coordinates of the corresponding pie. There could be more than one pie at a cell.
Output
Output only one word: "YES" β if Volodya wins, "NO" β otherwise.
Examples
Input
2 2 1
1 2
Output
YES
Input
3 4 0
Output
NO
Input
100 50 2
50 25
50 25
Output
NO
Tags: games
Correct Solution:
```
n, m, k = [int(x) for x in input().split()]
canwin = False
for i in range(k):
x, y = [int(x) for x in input().split()]
canwin |= x < 6 or n - x < 5
canwin |= y < 6 or m - y < 5
print("YES" if canwin else "NO")
```
| 413
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Volodya and Vlad play the following game. There are k pies at the cells of n Γ m board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy.
<image>
Input
First line contains 3 integers, separated by space: 1 β€ n, m β€ 100 β dimensions of the board and 0 β€ k β€ 100 β the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 β€ x β€ n, 1 β€ y β€ m β coordinates of the corresponding pie. There could be more than one pie at a cell.
Output
Output only one word: "YES" β if Volodya wins, "NO" β otherwise.
Examples
Input
2 2 1
1 2
Output
YES
Input
3 4 0
Output
NO
Input
100 50 2
50 25
50 25
Output
NO
Tags: games
Correct Solution:
```
n, m, k = map(int, input().split())
win = False
for i in range(k):
r, c = map(int, input().split())
dr = min(r - 1, n - r)
dc = min(c - 1, m - c)
if dr <= 4 or dc <= 4:
win = True
print("YES" if win else "NO")
```
| 414
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Volodya and Vlad play the following game. There are k pies at the cells of n Γ m board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy.
<image>
Input
First line contains 3 integers, separated by space: 1 β€ n, m β€ 100 β dimensions of the board and 0 β€ k β€ 100 β the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 β€ x β€ n, 1 β€ y β€ m β coordinates of the corresponding pie. There could be more than one pie at a cell.
Output
Output only one word: "YES" β if Volodya wins, "NO" β otherwise.
Examples
Input
2 2 1
1 2
Output
YES
Input
3 4 0
Output
NO
Input
100 50 2
50 25
50 25
Output
NO
Tags: games
Correct Solution:
```
[n,m,k]=[int(i) for i in input().split()]
isDone=False
for i in range(0,k):
[x,y]=[int(i) for i in input().split()]
if x<=5 or x>n-5 or y<=5 or y>m-5:
isDone=True
if isDone:
print("YES")
else:
print("NO")
```
| 415
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Volodya and Vlad play the following game. There are k pies at the cells of n Γ m board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy.
<image>
Input
First line contains 3 integers, separated by space: 1 β€ n, m β€ 100 β dimensions of the board and 0 β€ k β€ 100 β the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 β€ x β€ n, 1 β€ y β€ m β coordinates of the corresponding pie. There could be more than one pie at a cell.
Output
Output only one word: "YES" β if Volodya wins, "NO" β otherwise.
Examples
Input
2 2 1
1 2
Output
YES
Input
3 4 0
Output
NO
Input
100 50 2
50 25
50 25
Output
NO
Tags: games
Correct Solution:
```
n, m, k = map(int, input().split())
win = False
for i in range(k):
x, y = map(int, input().split())
if abs(x - 1) <= 4 or abs(y - 1) <= 4 or \
abs(n - x) <= 4 or abs(m - y) <= 4:
win = True
print('YES' if win else 'NO')
```
| 416
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Volodya and Vlad play the following game. There are k pies at the cells of n Γ m board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy.
<image>
Input
First line contains 3 integers, separated by space: 1 β€ n, m β€ 100 β dimensions of the board and 0 β€ k β€ 100 β the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 β€ x β€ n, 1 β€ y β€ m β coordinates of the corresponding pie. There could be more than one pie at a cell.
Output
Output only one word: "YES" β if Volodya wins, "NO" β otherwise.
Examples
Input
2 2 1
1 2
Output
YES
Input
3 4 0
Output
NO
Input
100 50 2
50 25
50 25
Output
NO
Tags: games
Correct Solution:
```
n,m,k=list(map(int,input().split()))
for i in range(k):
x,y=list(map(int,input().split()))
if min(x,n-x+1,y,m-y+1)<6:
print('YES')
break
else:
print('NO')
```
| 417
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Volodya and Vlad play the following game. There are k pies at the cells of n Γ m board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy.
<image>
Input
First line contains 3 integers, separated by space: 1 β€ n, m β€ 100 β dimensions of the board and 0 β€ k β€ 100 β the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 β€ x β€ n, 1 β€ y β€ m β coordinates of the corresponding pie. There could be more than one pie at a cell.
Output
Output only one word: "YES" β if Volodya wins, "NO" β otherwise.
Examples
Input
2 2 1
1 2
Output
YES
Input
3 4 0
Output
NO
Input
100 50 2
50 25
50 25
Output
NO
Tags: games
Correct Solution:
```
n, m, k = map( int , input().split() )
flag = False
while k > 0:
k -= 1
x, y = map( int , input().split() )
d = min( x , n - x + 1 , y , m - y + 1 )
if d <= 5: flag = True
print( "YES" if flag else "NO" )
```
| 418
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Volodya and Vlad play the following game. There are k pies at the cells of n Γ m board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy.
<image>
Input
First line contains 3 integers, separated by space: 1 β€ n, m β€ 100 β dimensions of the board and 0 β€ k β€ 100 β the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 β€ x β€ n, 1 β€ y β€ m β coordinates of the corresponding pie. There could be more than one pie at a cell.
Output
Output only one word: "YES" β if Volodya wins, "NO" β otherwise.
Examples
Input
2 2 1
1 2
Output
YES
Input
3 4 0
Output
NO
Input
100 50 2
50 25
50 25
Output
NO
Tags: games
Correct Solution:
```
n, m, k = [int(x) for x in input().split()]
canwin = False
for i in range(k):
x, y = [int(x) for x in input().split()]
canwin |= x < 6 or n - x < 5
canwin |= y < 6 or m - y < 5
print("YES" if canwin else "NO")
# Made By Mostafa_Khaled
```
| 419
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Volodya and Vlad play the following game. There are k pies at the cells of n Γ m board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy.
<image>
Input
First line contains 3 integers, separated by space: 1 β€ n, m β€ 100 β dimensions of the board and 0 β€ k β€ 100 β the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 β€ x β€ n, 1 β€ y β€ m β coordinates of the corresponding pie. There could be more than one pie at a cell.
Output
Output only one word: "YES" β if Volodya wins, "NO" β otherwise.
Examples
Input
2 2 1
1 2
Output
YES
Input
3 4 0
Output
NO
Input
100 50 2
50 25
50 25
Output
NO
Submitted Solution:
```
n, m, k = map(int, input().split())
win = False
for i in range(k):
row, col = map(int, input().split())
d = min(row - 1, n - row, col - 1, m - col)
if d <= 4:
win = True
if win:
print("YES")
else:
print("NO")
```
Yes
| 420
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Volodya and Vlad play the following game. There are k pies at the cells of n Γ m board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy.
<image>
Input
First line contains 3 integers, separated by space: 1 β€ n, m β€ 100 β dimensions of the board and 0 β€ k β€ 100 β the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 β€ x β€ n, 1 β€ y β€ m β coordinates of the corresponding pie. There could be more than one pie at a cell.
Output
Output only one word: "YES" β if Volodya wins, "NO" β otherwise.
Examples
Input
2 2 1
1 2
Output
YES
Input
3 4 0
Output
NO
Input
100 50 2
50 25
50 25
Output
NO
Submitted Solution:
```
n, m, k = map(int, input().split())
win = False
for i in range(k):
row, col = map(int, input().split())
d = max(row - 1, n - row, col - 1, m - col)
if d <= 4:
win = True
if win:
print("YES")
else:
print("NO")
```
No
| 421
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Volodya and Vlad play the following game. There are k pies at the cells of n Γ m board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy.
<image>
Input
First line contains 3 integers, separated by space: 1 β€ n, m β€ 100 β dimensions of the board and 0 β€ k β€ 100 β the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 β€ x β€ n, 1 β€ y β€ m β coordinates of the corresponding pie. There could be more than one pie at a cell.
Output
Output only one word: "YES" β if Volodya wins, "NO" β otherwise.
Examples
Input
2 2 1
1 2
Output
YES
Input
3 4 0
Output
NO
Input
100 50 2
50 25
50 25
Output
NO
Submitted Solution:
```
n, m, k = [int(x) for x in input().split()]
canwin = False
for i in range(k):
x, y = [int(x) for x in input().split()]
canwin |= x <= 9 or n - x <= 8
canwin |= y <= 9 or m - y <= 8
print("YES" if canwin else "NO")
```
No
| 422
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Volodya and Vlad play the following game. There are k pies at the cells of n Γ m board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy.
<image>
Input
First line contains 3 integers, separated by space: 1 β€ n, m β€ 100 β dimensions of the board and 0 β€ k β€ 100 β the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 β€ x β€ n, 1 β€ y β€ m β coordinates of the corresponding pie. There could be more than one pie at a cell.
Output
Output only one word: "YES" β if Volodya wins, "NO" β otherwise.
Examples
Input
2 2 1
1 2
Output
YES
Input
3 4 0
Output
NO
Input
100 50 2
50 25
50 25
Output
NO
Submitted Solution:
```
n, m, k = map(int, input().split())
win = False
for i in range(k):
row, col = map(int, input().split())
if row == 1 or col == 1 or row == n or col == m:
win = True
if win:
print("YES")
else:
print("NO")
```
No
| 423
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Volodya and Vlad play the following game. There are k pies at the cells of n Γ m board. Each turn Volodya moves one pie to the neighbouring (by side) cell. If the pie lies at the border of the board then Volodya can move it outside the board, get the pie and win. After Volodya's move, Vlad bans some edge at the border of the board of length 1 (between two knots of the board) so that Volodya is not able to move the pie outside the board through this edge anymore. The question is: will Volodya win this game? We suppose both players follow the optimal strategy.
<image>
Input
First line contains 3 integers, separated by space: 1 β€ n, m β€ 100 β dimensions of the board and 0 β€ k β€ 100 β the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 β€ x β€ n, 1 β€ y β€ m β coordinates of the corresponding pie. There could be more than one pie at a cell.
Output
Output only one word: "YES" β if Volodya wins, "NO" β otherwise.
Examples
Input
2 2 1
1 2
Output
YES
Input
3 4 0
Output
NO
Input
100 50 2
50 25
50 25
Output
NO
Submitted Solution:
```
n, m, k = [int(x) for x in input().split()]
canwin = False
for i in range(k):
x, y = [int(x) for x in input().split()]
canwin |= x <= 3 or n - x <= 2
canwin |= y <= 3 or m - y <= 2
print("YES" if canwin else "NO")
```
No
| 424
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasily has recently learned about the amazing properties of number Ο. In one of the articles it has been hypothesized that, whatever the sequence of numbers we have, in some position, this sequence is found among the digits of number Ο. Thus, if you take, for example, the epic novel "War and Peace" of famous Russian author Leo Tolstoy, and encode it with numbers, then we will find the novel among the characters of number Ο.
Vasily was absolutely delighted with this, because it means that all the books, songs and programs have already been written and encoded in the digits of Ο. Vasily is, of course, a bit wary that this is only a hypothesis and it hasn't been proved, so he decided to check it out.
To do this, Vasily downloaded from the Internet the archive with the sequence of digits of number Ο, starting with a certain position, and began to check the different strings of digits on the presence in the downloaded archive. Vasily quickly found short strings of digits, but each time he took a longer string, it turned out that it is not in the archive. Vasily came up with a definition that a string of length d is a half-occurrence if it contains a substring of length of at least <image>, which occurs in the archive.
To complete the investigation, Vasily took 2 large numbers x, y (x β€ y) with the same number of digits and now he wants to find the number of numbers in the interval from x to y, which are half-occurrences in the archive. Help Vasily calculate this value modulo 109 + 7.
Input
The first line contains string s consisting of decimal digits (1 β€ |s| β€ 1000) that Vasily will use to search substrings in. According to hypothesis, this sequence of digis indeed occurs in the decimal representation of Ο, although we can't guarantee that.
The second and third lines contain two positive integers x, y of the same length d (x β€ y, 2 β€ d β€ 50). Numbers x, y do not contain leading zeroes.
Output
Print how many numbers in the segment from x to y that are half-occurrences in s modulo 109 + 7.
Examples
Input
02
10
19
Output
2
Input
023456789
10
19
Output
9
Input
31415926535
10
29
Output
20
Submitted Solution:
```
a = [0] * 10 ** 4
ans = 0
for i in range(10 ** 2):
for i in range(10 ** 4):
ans += a[i]
print('2')
```
No
| 425
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Tags: implementation, math
Correct Solution:
```
#!/usr/bin/env python3
N, S = map(int, input().split())
stuff = [map(int, input().split()) for i in range(N)]
answer = S
for a, k in stuff:
answer = max(answer, a + k)
print(answer)
```
| 426
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Tags: implementation, math
Correct Solution:
```
n, m = map(int, input().split())
fl = []
ps = []
fl.append(0)
ps.append(0)
for i in range(0, n):
a, b = map(int, input().split())
fl.append(a)
ps.append(b)
lv = m
time = 0
for i in range(n, -1, -1):
time+=lv-fl[i]
if ps[i]>time:
time+=ps[i]-time
lv = fl[i]
print(time)
```
| 427
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Tags: implementation, math
Correct Solution:
```
import sys
import math
import collections
from pprint import pprint
mod = 1000000007
def vector(size, val=0):
vec = [val for i in range(size)]
return vec
def matrix(rowNum, colNum, val=0):
mat = []
for i in range(rowNum):
collumn = [val for j in range(colNum)]
mat.append(collumn)
return mat
n, s = map(int, input().split())
a = []
for i in range(n):
temp = list(map(int, input().split()))
a.append(temp)
a.sort(reverse=True)
t = 0
for x in a:
t += s - x[0]
s = x[0]
t += max(0, x[1] - t)
if s != 0:
t += s
print(t)
```
| 428
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Tags: implementation, math
Correct Solution:
```
n, s = map(int, input().split())
l = []
for i in range(n):
l.append(tuple(map(int, input().split())))
res = 0
for p, t in l[::-1]:
res += s - p
s = p
if t - res > 0:
res += t - res
res += l[0][0]
print(res)
```
| 429
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Tags: implementation, math
Correct Solution:
```
import sys
import math
from functools import reduce
import bisect
def getN():
return int(input())
def getNM():
return map(int, input().split())
def getList():
return list(map(int, input().split()))
def input():
return sys.stdin.readline().rstrip()
# input = sys.stdin.buffer.readline
def index(a, x):
i = bisect.bisect_left(a, x)
if i != len(a) and a[i] == x:
return i
return -1
#############
# MAIN CODE #
#############
n, s = getNM()
pasengers = []
for i in range(n):
pasengers.append(list(getNM()))
pasengers.sort(reverse=True)
ans = s
t = 0
for a, b in pasengers:
t += s - a
ans += b - t if b - t > 0 else 0
t += b - t if b - t > 0 else 0
s = a
print(ans)
```
| 430
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Tags: implementation, math
Correct Solution:
```
n, s = list(map(int, input().split()))
lp = list()
for i in range(n):
lp.append(tuple(map(int, input().split())))
lp.sort(reverse=True)
time = 0
current_floor = s
for i in range(n):
predicted_time = time + current_floor-lp[i][0]
passenger_atime = lp[i][1]
if passenger_atime > predicted_time:
time = passenger_atime
else:
time = predicted_time
current_floor = lp[i][0]
time += current_floor
print(time)
```
| 431
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Tags: implementation, math
Correct Solution:
```
if __name__ == '__main__':
n, s = map(int, input().split())
arr = [0 for _ in range(s + 1)]
for _ in range(n):
f, t = map(int, input().split())
arr[f] = max(arr[f], t)
arr.reverse()
cnt = arr[0]
for x in arr[1:]:
cnt = max(x, cnt + 1)
print(cnt)
```
| 432
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Tags: implementation, math
Correct Solution:
```
n, m = map(int, input().split())
ans = m
for x in range(n):
a, b = map(int, input().split())
ans = max(ans, a+b)
print(ans)
```
| 433
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Submitted Solution:
```
n,s=map(int,input().split())
ip=[]
count=0
for i in range(n):
a,b=map(int,input().split())
ip.append((a,b))
ip=sorted(ip,key=lambda l:l[0], reverse=True)
for i in range(n):
a,b=ip[i]
count+=s-a
if count<b:
count+=(b-count)
s=a
count+=a
print(count)
```
Yes
| 434
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Submitted Solution:
```
n, s = map(int, input().split())
ans = s
for _ in range(n):
f, t = map(int, input().split())
ans = max(ans, f + t)
print(ans)
```
Yes
| 435
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Submitted Solution:
```
n=list(map(int,input().split()))
lst=[]
for i in range(n[0]):
n1=list(map(int,input().split()))
lst.append(n1)
lst.sort()
lst.reverse()
w=n[1]-lst[0][0]
for j in range(len(lst)):
if(j==0):
if(w<lst[j][1]):
w=w+(lst[j][1]-w)
else:
w=w+(lst[j-1][0]-lst[j][0])
if(w<lst[j][1]):
w=w+(lst[j][1]-w)
m=lst[-1][0]-0
print(w+m)
```
Yes
| 436
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Submitted Solution:
```
n, up = map(int, input().split())
res = 0
for i in range(n):
fl, t = map(int, input().split())
res = max(res, max(t, up - fl) + fl)
print(res)
```
Yes
| 437
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Submitted Solution:
```
n,s = map(int,input().split())
a = []
z = []
d = {}
for i in range(n):
f,t = map(int,input().split())
d[f] = t
z.append(f)
s1 = 0
z.sort(reverse=True)
k = 0
for i in range(s,-1,-1):
if i in z:
if d[z[k]] > s1:
s1 = d[z[k]]
else:
s1 = s1 + 1
k = k + 1
else:
s1 = s1 + 1
print(s1)
```
No
| 438
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Submitted Solution:
```
n,m=map(int,input().split())
ls=[]
for i in range(n) :
f,t=map(int,input().split())
tp=f,t
ls.append(tp)
time=0
ls.sort()
ls=ls[::-1]
time=m-ls[0][0]
m=ls[0][1]
for i in ls:
time=time+m-i[0]
if time>=i[1]:
pass
else:
time=i[1]
m=i[0]
time=time+ls[n-1][0]
print(time)
```
No
| 439
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Submitted Solution:
```
n, s = map(int, input().split())
data = []
elapsed = 0
latest_floor = s
for i in range(n):
f, t = map(int, input().split())
data.append([f,t])
data.sort(reverse=True)
#print(data)
for pair in data:
elapsed += (latest_floor - pair[0]) # 2
if pair[1] <= elapsed: # y
latest_floor = pair[0] # 5
continue
else:
elapsed += (pair[1]-elapsed)
print(elapsed)
```
No
| 440
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Saitama accidentally destroyed a hotel again. To repay the hotel company, Genos has volunteered to operate an elevator in one of its other hotels. The elevator is special β it starts on the top floor, can only move down, and has infinite capacity. Floors are numbered from 0 to s and elevator initially starts on floor s at time 0.
The elevator takes exactly 1 second to move down exactly 1 floor and negligible time to pick up passengers. Genos is given a list detailing when and on which floor passengers arrive. Please determine how long in seconds it will take Genos to bring all passengers to floor 0.
Input
The first line of input contains two integers n and s (1 β€ n β€ 100, 1 β€ s β€ 1000) β the number of passengers and the number of the top floor respectively.
The next n lines each contain two space-separated integers fi and ti (1 β€ fi β€ s, 1 β€ ti β€ 1000) β the floor and the time of arrival in seconds for the passenger number i.
Output
Print a single integer β the minimum amount of time in seconds needed to bring all the passengers to floor 0.
Examples
Input
3 7
2 1
3 8
5 2
Output
11
Input
5 10
2 77
3 33
8 21
9 12
10 64
Output
79
Note
In the first sample, it takes at least 11 seconds to bring all passengers to floor 0. Here is how this could be done:
1. Move to floor 5: takes 2 seconds.
2. Pick up passenger 3.
3. Move to floor 3: takes 2 seconds.
4. Wait for passenger 2 to arrive: takes 4 seconds.
5. Pick up passenger 2.
6. Go to floor 2: takes 1 second.
7. Pick up passenger 1.
8. Go to floor 0: takes 2 seconds.
This gives a total of 2 + 2 + 4 + 1 + 2 = 11 seconds.
Submitted Solution:
```
n, s = [int(x) for x in input().split()]
lst = []
maxi =0
for i in range(n):
f, t = [int(x) for x in input().split()]
if t>maxi:
maxi = t
m1 = f
lst.append([f,t])
print(m1+maxi)
```
No
| 441
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alex was programming while Valentina (his toddler daughter) got there and started asking many questions about the round brackets (or parenthesis) in the code. He explained her a bit and when she got it he gave her a task in order to finish his code on time.
For the purpose of this problem we consider only strings consisting of opening and closing round brackets, that is characters '(' and ')'.
The sequence of brackets is called correct if:
1. it's empty;
2. it's a correct sequence of brackets, enclosed in a pair of opening and closing brackets;
3. it's a concatenation of two correct sequences of brackets.
For example, the sequences "()()" and "((()))(())" are correct, while ")(()", "(((((" and "())" are not.
Alex took a piece of paper, wrote a string s consisting of brackets and asked Valentina to count the number of distinct non-empty substrings of s that are correct sequences of brackets. In other words, her task is to count the number of non-empty correct sequences of brackets that occur in a string s as a substring (don't mix up with subsequences).
When Valentina finished the task, Alex noticed he doesn't know the answer. Help him don't loose face in front of Valentina and solve the problem!
Input
The first line of the input contains an integer n (1 β€ n β€ 500 000) β the length of the string s.
The second line contains a string s of length n consisting of only '(' and ')'.
Output
Print the number of distinct non-empty correct sequences that occur in s as substring.
Examples
Input
10
()()()()()
Output
5
Input
7
)(())()
Output
3
Note
In the first sample, there are 5 distinct substrings we should count: "()", "()()", "()()()", "()()()()" and "()()()()()".
In the second sample, there are 3 distinct substrings we should count: "()", "(())" and "(())()".
Submitted Solution:
```
n = int(input())
s = input()
e = 0
z = 0
for c in s:
if c == "(":
e += 1
else:
e -= 1
z += 1
if e < 0:
z -= 1
e = 0
print(z)
```
No
| 442
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alex was programming while Valentina (his toddler daughter) got there and started asking many questions about the round brackets (or parenthesis) in the code. He explained her a bit and when she got it he gave her a task in order to finish his code on time.
For the purpose of this problem we consider only strings consisting of opening and closing round brackets, that is characters '(' and ')'.
The sequence of brackets is called correct if:
1. it's empty;
2. it's a correct sequence of brackets, enclosed in a pair of opening and closing brackets;
3. it's a concatenation of two correct sequences of brackets.
For example, the sequences "()()" and "((()))(())" are correct, while ")(()", "(((((" and "())" are not.
Alex took a piece of paper, wrote a string s consisting of brackets and asked Valentina to count the number of distinct non-empty substrings of s that are correct sequences of brackets. In other words, her task is to count the number of non-empty correct sequences of brackets that occur in a string s as a substring (don't mix up with subsequences).
When Valentina finished the task, Alex noticed he doesn't know the answer. Help him don't loose face in front of Valentina and solve the problem!
Input
The first line of the input contains an integer n (1 β€ n β€ 500 000) β the length of the string s.
The second line contains a string s of length n consisting of only '(' and ')'.
Output
Print the number of distinct non-empty correct sequences that occur in s as substring.
Examples
Input
10
()()()()()
Output
5
Input
7
)(())()
Output
3
Note
In the first sample, there are 5 distinct substrings we should count: "()", "()()", "()()()", "()()()()" and "()()()()()".
In the second sample, there are 3 distinct substrings we should count: "()", "(())" and "(())()".
Submitted Solution:
```
# http://codeforces.com/problemset/problem/653/F
def BracketCounter(S):
counter = 0
length = int(S.split('\n')[0].strip())
bracket_string = S.split('\n')[1].strip()
#print('bracket string is: %s' %bracket_string)
if len(bracket_string) == 0:
#print('zero length string')
return 0
ind = bracket_string[0]
if ind == '(':
#print("first character is a open")
ind2 = bracket_string.find(')')
if ind2 == -1:
#print("no close brackets found")
return 0
else:
#print("close bracket at %s" %ind2)
L_bracket_string = list(bracket_string)
L_bracket_string.pop(ind2)
L_bracket_string.pop(0)
S_new = str(length-2) + '\n' + ''.join(L_bracket_string)
#print("This is the new string %s" %S_new)
ret_counter = BracketCounter(S_new)
counter += ret_counter + 1
# elif bracket_string[:] == ')':
# print("close bracket is at end")
else:
#print("first character is a close, disregard")
S_new = str(length-1) + '\n' + bracket_string[1:]
ret_counter = BracketCounter(S_new)
counter += ret_counter
return counter
if __name__ == '__main__':
S = str(input()) + '\n' + str(input())
counted = BracketCounter(S)
print(counted)
else:
print("I am being imported")
```
No
| 443
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alex was programming while Valentina (his toddler daughter) got there and started asking many questions about the round brackets (or parenthesis) in the code. He explained her a bit and when she got it he gave her a task in order to finish his code on time.
For the purpose of this problem we consider only strings consisting of opening and closing round brackets, that is characters '(' and ')'.
The sequence of brackets is called correct if:
1. it's empty;
2. it's a correct sequence of brackets, enclosed in a pair of opening and closing brackets;
3. it's a concatenation of two correct sequences of brackets.
For example, the sequences "()()" and "((()))(())" are correct, while ")(()", "(((((" and "())" are not.
Alex took a piece of paper, wrote a string s consisting of brackets and asked Valentina to count the number of distinct non-empty substrings of s that are correct sequences of brackets. In other words, her task is to count the number of non-empty correct sequences of brackets that occur in a string s as a substring (don't mix up with subsequences).
When Valentina finished the task, Alex noticed he doesn't know the answer. Help him don't loose face in front of Valentina and solve the problem!
Input
The first line of the input contains an integer n (1 β€ n β€ 500 000) β the length of the string s.
The second line contains a string s of length n consisting of only '(' and ')'.
Output
Print the number of distinct non-empty correct sequences that occur in s as substring.
Examples
Input
10
()()()()()
Output
5
Input
7
)(())()
Output
3
Note
In the first sample, there are 5 distinct substrings we should count: "()", "()()", "()()()", "()()()()" and "()()()()()".
In the second sample, there are 3 distinct substrings we should count: "()", "(())" and "(())()".
Submitted Solution:
```
# http://codeforces.com/problemset/problem/653/F
import sys
def SubSequence(S_sub):
count = 0
#subsequence
open_count = 0
open_pos = []
close_pos = []
close_count = 0
for pos, char in enumerate(S_sub):
if char == '(':
open_count += 1
open_pos.append(pos)
elif char == ')':
close_count += 1
close_pos.append(pos)
if close_count > open_count:
#too many closed, can't be a sub sequence
string_rem = S_sub[pos+1:]
count += SubSequence(string_rem)
break
if open_count == close_count:
#found subsequence
count += BracketCounter(S_sub[0:pos+1])
string_rem = S_sub[pos+1:]
count += SubSequence(string_rem)
break
if open_count > close_count:
#loop ended and no close bracket
#don't need to do anything
count = 0
return count
def BracketCounter(S):
counter = 0
bracket_string = str(S)
print('bracket string is: %s' %bracket_string)
counter = len(S)/2
return counter
# if len(bracket_string) == 0:
# #print('zero length string')
# return 0
# ind = bracket_string[0]
# open_pos = []
# close_pos = []
# counter_bracket = -
# for pos, char in enumerate(bracket_string):
# if char == '(':
# open_pos.append(pos)
# if char == ')':
# close_pos.append(pos)
# for ix in len(open_pos):
# if ix+1 in open_pos:
# #there is another open directly after
# if ix+1 in close_pos:
# counter
# print(open_pos)
# print(close_pos)
# if ind == '(':
# #print("first character is a open")
# ind2 = bracket_string.find(')')
# if ind2 == -1:
# #print("no close brackets found")
# return 0
# else:
# #print("close bracket at %s" %ind2)
# L_bracket_string = list(bracket_string)
# L_bracket_string.pop(ind2)
# L_bracket_string.pop(0)
# S_new = str(length-2) + '\n' + ''.join(L_bracket_string)
# #print("This is the new string %s" %S_new)
# ret_counter = BracketCounter(S_new)
# counter += ret_counter + 1
# # elif bracket_string[:] == ')':
# # print("close bracket is at end")
# else:
# #print("first character is a close, disregard")
# S_new = str(length-1) + '\n' + bracket_string[1:]
# ret_counter = BracketCounter(S_new)
# counter += ret_counter
# return counter
if __name__ == '__main__':
NOPE = str(input())
S = str(input())
#S = '(())(()())(()()'
counted = SubSequence(S)
print(counted)
else:
print("I am being imported")
```
No
| 444
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alex was programming while Valentina (his toddler daughter) got there and started asking many questions about the round brackets (or parenthesis) in the code. He explained her a bit and when she got it he gave her a task in order to finish his code on time.
For the purpose of this problem we consider only strings consisting of opening and closing round brackets, that is characters '(' and ')'.
The sequence of brackets is called correct if:
1. it's empty;
2. it's a correct sequence of brackets, enclosed in a pair of opening and closing brackets;
3. it's a concatenation of two correct sequences of brackets.
For example, the sequences "()()" and "((()))(())" are correct, while ")(()", "(((((" and "())" are not.
Alex took a piece of paper, wrote a string s consisting of brackets and asked Valentina to count the number of distinct non-empty substrings of s that are correct sequences of brackets. In other words, her task is to count the number of non-empty correct sequences of brackets that occur in a string s as a substring (don't mix up with subsequences).
When Valentina finished the task, Alex noticed he doesn't know the answer. Help him don't loose face in front of Valentina and solve the problem!
Input
The first line of the input contains an integer n (1 β€ n β€ 500 000) β the length of the string s.
The second line contains a string s of length n consisting of only '(' and ')'.
Output
Print the number of distinct non-empty correct sequences that occur in s as substring.
Examples
Input
10
()()()()()
Output
5
Input
7
)(())()
Output
3
Note
In the first sample, there are 5 distinct substrings we should count: "()", "()()", "()()()", "()()()()" and "()()()()()".
In the second sample, there are 3 distinct substrings we should count: "()", "(())" and "(())()".
Submitted Solution:
```
# http://codeforces.com/problemset/problem/653/F
def BracketCounter(S):
counter = 0
length = int(S.split('\n')[0].strip())
bracket_string = S.split('\n')[1].strip()
# print('bracket string is: %s' %bracket_string)
if len(bracket_string) == 0:
print('zero length string')
return 0
ind = bracket_string[0]
if ind == '(':
#print("first character is a open")
ind2 = bracket_string.find(')')
if ind2 == -1:
#print("no close brackets found")
return 0
else:
#print("close bracket at %s" %ind2)
L_bracket_string = list(bracket_string)
L_bracket_string.pop(ind2)
L_bracket_string.pop(0)
S_new = str(length-2) + '\n' + ''.join(L_bracket_string)
#print("This is the new string %s" %S_new)
ret_counter = BracketCounter(S_new)
counter += ret_counter + 1
# elif bracket_string[:] == ')':
# print("close bracket is at end")
else:
#print("first character is a close, disregard")
S_new = str(length-1) + '\n' + bracket_string[1:]
ret_counter = BracketCounter(S_new)
counter += ret_counter
return counter
if __name__ == '__main__':
print("I am being called directly")
# S = '10 \n ()()()()()'
# counted = BracketCounter(S)
# print(counted)
S = '7 \n )(())()'
counted = BracketCounter(S)
print(counted)
else:
print("I am being imported")
```
No
| 445
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an undirected connected graph consisting of n vertices and m edges. There are no loops and no multiple edges in the graph.
You are also given two distinct vertices s and t, and two values ds and dt. Your task is to build any spanning tree of the given graph (note that the graph is not weighted), such that the degree of the vertex s doesn't exceed ds, and the degree of the vertex t doesn't exceed dt, or determine, that there is no such spanning tree.
The spanning tree of the graph G is a subgraph which is a tree and contains all vertices of the graph G. In other words, it is a connected graph which contains n - 1 edges and can be obtained by removing some of the edges from G.
The degree of a vertex is the number of edges incident to this vertex.
Input
The first line of the input contains two integers n and m (2 β€ n β€ 200 000, 1 β€ m β€ min(400 000, nΒ·(n - 1) / 2)) β the number of vertices and the number of edges in the graph.
The next m lines contain the descriptions of the graph's edges. Each of the lines contains two integers u and v (1 β€ u, v β€ n, u β v) β the ends of the corresponding edge. It is guaranteed that the graph contains no loops and no multiple edges and that it is connected.
The last line contains four integers s, t, ds, dt (1 β€ s, t β€ n, s β t, 1 β€ ds, dt β€ n - 1).
Output
If the answer doesn't exist print "No" (without quotes) in the only line of the output.
Otherwise, in the first line print "Yes" (without quotes). In the each of the next (n - 1) lines print two integers β the description of the edges of the spanning tree. Each of the edges of the spanning tree must be printed exactly once.
You can output edges in any order. You can output the ends of each edge in any order.
If there are several solutions, print any of them.
Examples
Input
3 3
1 2
2 3
3 1
1 2 1 1
Output
Yes
3 2
1 3
Input
7 8
7 4
1 3
5 4
5 7
3 2
2 4
6 1
1 2
6 4 1 4
Output
Yes
1 3
5 7
3 2
7 4
2 4
6 1
Submitted Solution:
```
total_vertices, total_edges = map(int, input().split())
graph = [set() for _ in range(total_vertices + 1)]
tree_edges = []
in_tree = [False for _ in range(total_vertices + 1)]
for _ in range(total_edges):
start, end = map(int, input().split())
graph[start].add(end)
graph[end].add(start)
s, t, s_max, t_max = map(int, input().split())
stack = [s]
in_tree[s] = True
while stack:
cur_vertice = stack.pop()
for con_vertice in graph[cur_vertice]:
if not in_tree[con_vertice]:
tree_edges.append(" ".join((str(cur_vertice), str(con_vertice))))
in_tree[con_vertice] = True
stack.append(con_vertice)
for tree_edge in tree_edges:
print(tree_edge)
```
No
| 446
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an undirected connected graph consisting of n vertices and m edges. There are no loops and no multiple edges in the graph.
You are also given two distinct vertices s and t, and two values ds and dt. Your task is to build any spanning tree of the given graph (note that the graph is not weighted), such that the degree of the vertex s doesn't exceed ds, and the degree of the vertex t doesn't exceed dt, or determine, that there is no such spanning tree.
The spanning tree of the graph G is a subgraph which is a tree and contains all vertices of the graph G. In other words, it is a connected graph which contains n - 1 edges and can be obtained by removing some of the edges from G.
The degree of a vertex is the number of edges incident to this vertex.
Input
The first line of the input contains two integers n and m (2 β€ n β€ 200 000, 1 β€ m β€ min(400 000, nΒ·(n - 1) / 2)) β the number of vertices and the number of edges in the graph.
The next m lines contain the descriptions of the graph's edges. Each of the lines contains two integers u and v (1 β€ u, v β€ n, u β v) β the ends of the corresponding edge. It is guaranteed that the graph contains no loops and no multiple edges and that it is connected.
The last line contains four integers s, t, ds, dt (1 β€ s, t β€ n, s β t, 1 β€ ds, dt β€ n - 1).
Output
If the answer doesn't exist print "No" (without quotes) in the only line of the output.
Otherwise, in the first line print "Yes" (without quotes). In the each of the next (n - 1) lines print two integers β the description of the edges of the spanning tree. Each of the edges of the spanning tree must be printed exactly once.
You can output edges in any order. You can output the ends of each edge in any order.
If there are several solutions, print any of them.
Examples
Input
3 3
1 2
2 3
3 1
1 2 1 1
Output
Yes
3 2
1 3
Input
7 8
7 4
1 3
5 4
5 7
3 2
2 4
6 1
1 2
6 4 1 4
Output
Yes
1 3
5 7
3 2
7 4
2 4
6 1
Submitted Solution:
```
n,m=map(int,input().split())
adj=[[] for i in range(n+1)]
for i in range(m):
x,y=map(int,input().split())
adj[x-1].append(y-1)
adj[y-1].append(x-1)
level = [-1] * len(adj)
def bfs(s):
global level
level[s] = 0
queue = [s]
while queue:
v = queue.pop(0)
for w in adj[v]:
if level[w] is -1:
queue.append(w)
level[w] = level[v] + 1
for i in range(len(adj)):
if level[i] is -1:
bfs(i)
print(*level[:-1])
```
No
| 447
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an undirected connected graph consisting of n vertices and m edges. There are no loops and no multiple edges in the graph.
You are also given two distinct vertices s and t, and two values ds and dt. Your task is to build any spanning tree of the given graph (note that the graph is not weighted), such that the degree of the vertex s doesn't exceed ds, and the degree of the vertex t doesn't exceed dt, or determine, that there is no such spanning tree.
The spanning tree of the graph G is a subgraph which is a tree and contains all vertices of the graph G. In other words, it is a connected graph which contains n - 1 edges and can be obtained by removing some of the edges from G.
The degree of a vertex is the number of edges incident to this vertex.
Input
The first line of the input contains two integers n and m (2 β€ n β€ 200 000, 1 β€ m β€ min(400 000, nΒ·(n - 1) / 2)) β the number of vertices and the number of edges in the graph.
The next m lines contain the descriptions of the graph's edges. Each of the lines contains two integers u and v (1 β€ u, v β€ n, u β v) β the ends of the corresponding edge. It is guaranteed that the graph contains no loops and no multiple edges and that it is connected.
The last line contains four integers s, t, ds, dt (1 β€ s, t β€ n, s β t, 1 β€ ds, dt β€ n - 1).
Output
If the answer doesn't exist print "No" (without quotes) in the only line of the output.
Otherwise, in the first line print "Yes" (without quotes). In the each of the next (n - 1) lines print two integers β the description of the edges of the spanning tree. Each of the edges of the spanning tree must be printed exactly once.
You can output edges in any order. You can output the ends of each edge in any order.
If there are several solutions, print any of them.
Examples
Input
3 3
1 2
2 3
3 1
1 2 1 1
Output
Yes
3 2
1 3
Input
7 8
7 4
1 3
5 4
5 7
3 2
2 4
6 1
1 2
6 4 1 4
Output
Yes
1 3
5 7
3 2
7 4
2 4
6 1
Submitted Solution:
```
print(4)
```
No
| 448
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a rooted tree with n nodes. The Night King removes exactly one node from the tree and all the edges associated with it. Doing this splits the tree and forms a forest. The node which is removed is not a part of the forest.
The root of a tree in the forest is the node in that tree which does not have a parent. We define the strength of the forest as the size of largest tree in forest.
Jon Snow wants to minimize the strength of the forest. To do this he can perform the following operation at most once.
He removes the edge between a node and its parent and inserts a new edge between this node and any other node in forest such that the total number of trees in forest remain same.
For each node v you need to find the minimum value of strength of the forest formed when node v is removed.
Input
The first line of the input contains an integer n (1 β€ n β€ 105) β the number of vertices in the tree. Each of the next n lines contains a pair of vertex indices ui and vi (1 β€ ui, vi β€ n) where ui is the parent of vi. If ui = 0 then vi is the root.
Output
Print n line each containing a single integer. The i-th of them should be equal to minimum value of strength of forest formed when i-th node is removed and Jon Snow performs the operation described above at most once.
Examples
Input
10
0 1
1 2
1 3
1 4
2 5
2 6
3 7
4 8
4 9
5 10
Output
3
4
5
5
5
9
9
9
9
9
Input
2
2 1
0 2
Output
1
1
Note
The tree for first test case is depicted below. <image> When you remove the first node, the tree splits to form the following forest. The strength of this forest is 4. <image> Jon Snow now changes the parent of vertex 10 from 5 to 3. The strength of forest now becomes 3. <image>
Submitted Solution:
```
a=input()
b=input()
for i in range(0,len(a)):
if(a[i]==b[i]):
print(0,end='')
else:
print(1,end='')
```
No
| 449
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Vova plays a computer game known as Mages and Monsters. Vova's character is a mage. Though as he has just started, his character knows no spells.
Vova's character can learn new spells during the game. Every spell is characterized by two values xi and yi β damage per second and mana cost per second, respectively. Vova doesn't have to use a spell for an integer amount of seconds. More formally, if he uses a spell with damage x and mana cost y for z seconds, then he will deal xΒ·z damage and spend yΒ·z mana (no rounding). If there is no mana left (mana amount is set in the start of the game and it remains the same at the beginning of every fight), then character won't be able to use any spells. It is prohibited to use multiple spells simultaneously.
Also Vova can fight monsters. Every monster is characterized by two values tj and hj β monster kills Vova's character in tj seconds and has hj health points. Mana refills after every fight (or Vova's character revives with full mana reserve), so previous fights have no influence on further ones.
Vova's character kills a monster, if he deals hj damage to it in no more than tj seconds using his spells (it is allowed to use more than one spell in a fight) and spending no more mana than he had at the beginning of the fight. If monster's health becomes zero exactly in tj seconds (it means that the monster and Vova's character kill each other at the same time), then Vova wins the fight.
You have to write a program which can answer two types of queries:
* 1 x y β Vova's character learns new spell which deals x damage per second and costs y mana per second.
* 2 t h β Vova fights the monster which kills his character in t seconds and has h health points.
Note that queries are given in a different form. Also remember that Vova's character knows no spells at the beginning of the game.
For every query of second type you have to determine if Vova is able to win the fight with corresponding monster.
Input
The first line contains two integer numbers q and m (2 β€ q β€ 105, 1 β€ m β€ 1012) β the number of queries and the amount of mana at the beginning of every fight.
i-th of each next q lines contains three numbers ki, ai and bi (1 β€ ki β€ 2, 1 β€ ai, bi β€ 106).
Using them you can restore queries this way: let j be the index of the last query of second type with positive answer (j = 0 if there were none of these).
* If ki = 1, then character learns spell with x = (ai + j) mod 106 + 1, y = (bi + j) mod 106 + 1.
* If ki = 2, then you have to determine if Vova is able to win the fight against monster with t = (ai + j) mod 106 + 1, h = (bi + j) mod 106 + 1.
Output
For every query of second type print YES if Vova is able to win the fight with corresponding monster and NO otherwise.
Example
Input
3 100
1 4 9
2 19 49
2 19 49
Output
YES
NO
Note
In first example Vova's character at first learns the spell with 5 damage and 10 mana cost per second. Next query is a fight with monster which can kill character in 20 seconds and has 50 health points. Vova kills it in 10 seconds (spending 100 mana). Next monster has 52 health, so Vova can't deal that much damage with only 100 mana.
Tags: data structures, geometry
Correct Solution:
```
#!/usr/bin/env python3
# solution after hint
# (instead of best hit/mana spell store convex hull of spells)
# O(n^2) instead of O(n log n)
[q, m] = map(int, input().strip().split())
qis = [tuple(map(int, input().strip().split())) for _ in range(q)]
mod = 10**6
j = 0
spell_chull = [(0, 0)] # lower hull _/
def is_right(xy0, xy1, xy):
(x0, y0) = xy0
(x1, y1) = xy1
(x, y) = xy
return (x0 - x) * (y1 - y) >= (x1 - x) * (y0 - y)
def in_chull(x, y):
i = 0
if x > spell_chull[-1][0]:
return False
while spell_chull[i][0] < x:
i += 1
if spell_chull[i][0] == x:
return spell_chull[i][1] <= y
else:
return is_right(spell_chull[i - 1], spell_chull[i], (x, y))
def add_spell(x, y):
global spell_chull
if in_chull(x, y):
return
i_left = 0
while i_left < len(spell_chull) - 1 and not is_right(spell_chull[i_left + 1], spell_chull[i_left], (x, y)):
i_left += 1
i_right = i_left + 1
while i_right < len(spell_chull) - 1 and is_right(spell_chull[i_right + 1], spell_chull[i_right], (x, y)):
i_right += 1
if i_right == len(spell_chull) - 1 and x >= spell_chull[-1][0]:
i_right += 1
spell_chull = spell_chull[:i_left + 1] + [(x, y)] + spell_chull[i_right:]
for i, qi in enumerate(qis):
(k, a, b) = qi
x = (a + j) % mod + 1
y = (b + j) % mod + 1
if k == 1:
add_spell(x, y)
else: #2
if in_chull(y / x, m / x):
print ('YES')
j = i + 1
else:
print ('NO')
```
| 450
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vova plays a computer game known as Mages and Monsters. Vova's character is a mage. Though as he has just started, his character knows no spells.
Vova's character can learn new spells during the game. Every spell is characterized by two values xi and yi β damage per second and mana cost per second, respectively. Vova doesn't have to use a spell for an integer amount of seconds. More formally, if he uses a spell with damage x and mana cost y for z seconds, then he will deal xΒ·z damage and spend yΒ·z mana (no rounding). If there is no mana left (mana amount is set in the start of the game and it remains the same at the beginning of every fight), then character won't be able to use any spells. It is prohibited to use multiple spells simultaneously.
Also Vova can fight monsters. Every monster is characterized by two values tj and hj β monster kills Vova's character in tj seconds and has hj health points. Mana refills after every fight (or Vova's character revives with full mana reserve), so previous fights have no influence on further ones.
Vova's character kills a monster, if he deals hj damage to it in no more than tj seconds using his spells (it is allowed to use more than one spell in a fight) and spending no more mana than he had at the beginning of the fight. If monster's health becomes zero exactly in tj seconds (it means that the monster and Vova's character kill each other at the same time), then Vova wins the fight.
You have to write a program which can answer two types of queries:
* 1 x y β Vova's character learns new spell which deals x damage per second and costs y mana per second.
* 2 t h β Vova fights the monster which kills his character in t seconds and has h health points.
Note that queries are given in a different form. Also remember that Vova's character knows no spells at the beginning of the game.
For every query of second type you have to determine if Vova is able to win the fight with corresponding monster.
Input
The first line contains two integer numbers q and m (2 β€ q β€ 105, 1 β€ m β€ 1012) β the number of queries and the amount of mana at the beginning of every fight.
i-th of each next q lines contains three numbers ki, ai and bi (1 β€ ki β€ 2, 1 β€ ai, bi β€ 106).
Using them you can restore queries this way: let j be the index of the last query of second type with positive answer (j = 0 if there were none of these).
* If ki = 1, then character learns spell with x = (ai + j) mod 106 + 1, y = (bi + j) mod 106 + 1.
* If ki = 2, then you have to determine if Vova is able to win the fight against monster with t = (ai + j) mod 106 + 1, h = (bi + j) mod 106 + 1.
Output
For every query of second type print YES if Vova is able to win the fight with corresponding monster and NO otherwise.
Example
Input
3 100
1 4 9
2 19 49
2 19 49
Output
YES
NO
Note
In first example Vova's character at first learns the spell with 5 damage and 10 mana cost per second. Next query is a fight with monster which can kill character in 20 seconds and has 50 health points. Vova kills it in 10 seconds (spending 100 mana). Next monster has 52 health, so Vova can't deal that much damage with only 100 mana.
Submitted Solution:
```
#!/usr/bin/env python3
[q, m] = map(int, input().strip().split())
qis = [tuple(map(int, input().strip().split())) for _ in range(q)]
mod = 10**6
j = 0
(xb, yb) = (0, 1)
for i, qi in enumerate(qis):
(k, a, b) = qi
x = (a + j) % mod + 1
y = (b + j) % mod + 1
if k == 1:
if x * yb > y * xb:
(xb, yb) = (x, y)
else: #2
if min(m, x * yb) * xb >= y * yb:
print ('YES')
j = i + 1
else:
print ('NO')
```
No
| 451
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vova plays a computer game known as Mages and Monsters. Vova's character is a mage. Though as he has just started, his character knows no spells.
Vova's character can learn new spells during the game. Every spell is characterized by two values xi and yi β damage per second and mana cost per second, respectively. Vova doesn't have to use a spell for an integer amount of seconds. More formally, if he uses a spell with damage x and mana cost y for z seconds, then he will deal xΒ·z damage and spend yΒ·z mana (no rounding). If there is no mana left (mana amount is set in the start of the game and it remains the same at the beginning of every fight), then character won't be able to use any spells. It is prohibited to use multiple spells simultaneously.
Also Vova can fight monsters. Every monster is characterized by two values tj and hj β monster kills Vova's character in tj seconds and has hj health points. Mana refills after every fight (or Vova's character revives with full mana reserve), so previous fights have no influence on further ones.
Vova's character kills a monster, if he deals hj damage to it in no more than tj seconds using his spells (it is allowed to use more than one spell in a fight) and spending no more mana than he had at the beginning of the fight. If monster's health becomes zero exactly in tj seconds (it means that the monster and Vova's character kill each other at the same time), then Vova wins the fight.
You have to write a program which can answer two types of queries:
* 1 x y β Vova's character learns new spell which deals x damage per second and costs y mana per second.
* 2 t h β Vova fights the monster which kills his character in t seconds and has h health points.
Note that queries are given in a different form. Also remember that Vova's character knows no spells at the beginning of the game.
For every query of second type you have to determine if Vova is able to win the fight with corresponding monster.
Input
The first line contains two integer numbers q and m (2 β€ q β€ 105, 1 β€ m β€ 1012) β the number of queries and the amount of mana at the beginning of every fight.
i-th of each next q lines contains three numbers ki, ai and bi (1 β€ ki β€ 2, 1 β€ ai, bi β€ 106).
Using them you can restore queries this way: let j be the index of the last query of second type with positive answer (j = 0 if there were none of these).
* If ki = 1, then character learns spell with x = (ai + j) mod 106 + 1, y = (bi + j) mod 106 + 1.
* If ki = 2, then you have to determine if Vova is able to win the fight against monster with t = (ai + j) mod 106 + 1, h = (bi + j) mod 106 + 1.
Output
For every query of second type print YES if Vova is able to win the fight with corresponding monster and NO otherwise.
Example
Input
3 100
1 4 9
2 19 49
2 19 49
Output
YES
NO
Note
In first example Vova's character at first learns the spell with 5 damage and 10 mana cost per second. Next query is a fight with monster which can kill character in 20 seconds and has 50 health points. Vova kills it in 10 seconds (spending 100 mana). Next monster has 52 health, so Vova can't deal that much damage with only 100 mana.
Submitted Solution:
```
#site : https://codeforces.com/contest/792/problem/F
#Spells characterized by 2 values : x[i] and y[i]
#Doesn't have to use spell for int(x) amounts of seconds
#x = damage , y = mana cost , z = seconds
#deals x * z damage spends y * z mana
#If no mana is left , canUseSpell = False
#Can fight monsters : t[j] and h[j] . t = time to kill vova's char , h = monster's hp
#After fight , mana is refilled
#if dealt h[j] damage no more than t[j] seconds using his spells , monster j dies and vova's mana refills (and if monster's health becomes exactly 0 in t[j] , the same thing happens)
#Program :
#Vova learns a new spell dealing x dps and y mps (mana per second(s) )
#Fights a monster which kills him in t seconds and has h hp
#(Vova doesn't know any spell at the beginning)
#What to do ?
#You have to determine if vova's able to win the fight or no
#Input :
#First line :
#q -> the number of queries , m -> amount of mana at the beginning of fight
#2 =< q <= 10 ** 5 , 1 <= m <= 10 ** 12
#then for i=1 in range(1, q) do this :
#input 3 int values : 1 <= k[i] <= 2 , 1 <= a[i] and b[i] <= 10 ** 6
#k is basically the action you want to do . either 1 or 2 . 1 means character learns a spell with x (dps) = (a[i] + j (the last monster you fought with) ) % (10 ** 6) + 1 <- for limiting it to be less than 10 ** 6
#and 2 means if character is able to win against the monster or no (output = "YES" or "NO") with time to kill of t = (a[i] + j) % (10 ** 6) + 1 and hp of h = (b[i] + j) % (10 ** 6) + 1
#inputs must be in input file in the same directory of this file
#Start of code :
x = []
y = []
killedMonster = False
j = 0
t, h = 0,0
q, m = 0, 0
def get_input():
global q, m
k, a, b = [],[],[]
values = input()
q, m = int(values.split(" ")[0]), int(values.split(" ")[1])
for i in range(0,q):
inp = input()
k.append(int(inp.split(" ")[0]))
a.append(int(inp.split(" ")[1]))
b.append(int(inp.split(" ")[2]) % 10 ** 6)
value = [k,a,b]
return value
k, a, b = get_input()
for i in range(q):
if k[i] == 1:
x.append((a[i] + j) % 10 ** 6 + 1)
y.append((b[i] + j) % 10 ** 6 + 1)
elif k[i] == 2:
t = (a[i] + j) % 10 ** 6 + 1
h = (b[i] + j) % 10 ** 6 + 1
for chosen in range(0,len(x)):
if x[chosen] * t >= h and y[chosen] * t <= m * 2:
print("YES")
killedMonster = True
break
if not killedMonster:
print("NO")
else:
killedMonster = False
j += 1
```
No
| 452
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vova plays a computer game known as Mages and Monsters. Vova's character is a mage. Though as he has just started, his character knows no spells.
Vova's character can learn new spells during the game. Every spell is characterized by two values xi and yi β damage per second and mana cost per second, respectively. Vova doesn't have to use a spell for an integer amount of seconds. More formally, if he uses a spell with damage x and mana cost y for z seconds, then he will deal xΒ·z damage and spend yΒ·z mana (no rounding). If there is no mana left (mana amount is set in the start of the game and it remains the same at the beginning of every fight), then character won't be able to use any spells. It is prohibited to use multiple spells simultaneously.
Also Vova can fight monsters. Every monster is characterized by two values tj and hj β monster kills Vova's character in tj seconds and has hj health points. Mana refills after every fight (or Vova's character revives with full mana reserve), so previous fights have no influence on further ones.
Vova's character kills a monster, if he deals hj damage to it in no more than tj seconds using his spells (it is allowed to use more than one spell in a fight) and spending no more mana than he had at the beginning of the fight. If monster's health becomes zero exactly in tj seconds (it means that the monster and Vova's character kill each other at the same time), then Vova wins the fight.
You have to write a program which can answer two types of queries:
* 1 x y β Vova's character learns new spell which deals x damage per second and costs y mana per second.
* 2 t h β Vova fights the monster which kills his character in t seconds and has h health points.
Note that queries are given in a different form. Also remember that Vova's character knows no spells at the beginning of the game.
For every query of second type you have to determine if Vova is able to win the fight with corresponding monster.
Input
The first line contains two integer numbers q and m (2 β€ q β€ 105, 1 β€ m β€ 1012) β the number of queries and the amount of mana at the beginning of every fight.
i-th of each next q lines contains three numbers ki, ai and bi (1 β€ ki β€ 2, 1 β€ ai, bi β€ 106).
Using them you can restore queries this way: let j be the index of the last query of second type with positive answer (j = 0 if there were none of these).
* If ki = 1, then character learns spell with x = (ai + j) mod 106 + 1, y = (bi + j) mod 106 + 1.
* If ki = 2, then you have to determine if Vova is able to win the fight against monster with t = (ai + j) mod 106 + 1, h = (bi + j) mod 106 + 1.
Output
For every query of second type print YES if Vova is able to win the fight with corresponding monster and NO otherwise.
Example
Input
3 100
1 4 9
2 19 49
2 19 49
Output
YES
NO
Note
In first example Vova's character at first learns the spell with 5 damage and 10 mana cost per second. Next query is a fight with monster which can kill character in 20 seconds and has 50 health points. Vova kills it in 10 seconds (spending 100 mana). Next monster has 52 health, so Vova can't deal that much damage with only 100 mana.
Submitted Solution:
```
#site : https://codeforces.com/contest/792/problem/F
#Spells characterized by 2 values : x[i] and y[i]
#Doesn't have to use spell for int(x) amounts of seconds
#x = damage , y = mana cost , z = seconds
#deals x * z damage spends y * z mana
#If no mana is left , canUseSpell = False
#Can fight monsters : t[j] and h[j] . t = time to kill vova's char , h = monster's hp
#After fight , mana is refilled
#if dealt h[j] damage no more than t[j] seconds using his spells , monster j dies and vova's mana refills (and if monster's health becomes exactly 0 in t[j] , the same thing happens)
#Program :
#Vova learns a new spell dealing x dps and y mps (mana per second(s) )
#Fights a monster which kills him in t seconds and has h hp
#(Vova doesn't know any spell at the beginning)
#What to do ?
#You have to determine if vova's able to win the fight or no
#Input :
#First line :
#q -> the number of queries , m -> amount of mana at the beginning of fight
#2 =< q <= 10 ** 5 , 1 <= m <= 10 ** 12
#then for i=1 in range(1, q) do this :
#input 3 int values : 1 <= k[i] <= 2 , 1 <= a[i] and b[i] <= 10 ** 6
#k is basically the action you want to do . either 1 or 2 . 1 means character learns a spell with x (dps) = (a[i] + j (the last monster you fought with) ) % (10 ** 6) + 1 <- for limiting it to be less than 10 ** 6
#and 2 means if character is able to win against the monster or no (output = "YES" or "NO") with time to kill of t = (a[i] + j) % (10 ** 6) + 1 and hp of h = (b[i] + j) % (10 ** 6) + 1
#inputs must be in input file in the same directory of this file
#Start of code :
x = 0
y = 0
j = 0
t, h = 0,0
q, m = 0, 0
def get_input():
global q, m
k, a, b = [],[],[]
values = input()
q, m = int(values.split(" ")[0]), int(values.split(" ")[1])
for i in range(0,q):
inp = input()
k.append(int(inp.split(" ")[0]))
a.append(int(inp.split(" ")[1]))
b.append(int(inp.split(" ")[2]) % 10 ** 6)
value = [k,a,b]
return value
k, a, b = get_input()
for i in range(q):
if k[i] == 1:
x = (a[i] + j) % 10 ** 6 + 1
y = (b[i] + j) % 10 ** 6 + 1
elif k[i] == 2:
t = (a[i] + j) % 10 ** 6 + 1
h = (b[i] + j) % 10 ** 6 + 1
j += 1
if x * t >= h and y * t <= m * 2:
print("YES")
else:
print("NO")
```
No
| 453
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vova plays a computer game known as Mages and Monsters. Vova's character is a mage. Though as he has just started, his character knows no spells.
Vova's character can learn new spells during the game. Every spell is characterized by two values xi and yi β damage per second and mana cost per second, respectively. Vova doesn't have to use a spell for an integer amount of seconds. More formally, if he uses a spell with damage x and mana cost y for z seconds, then he will deal xΒ·z damage and spend yΒ·z mana (no rounding). If there is no mana left (mana amount is set in the start of the game and it remains the same at the beginning of every fight), then character won't be able to use any spells. It is prohibited to use multiple spells simultaneously.
Also Vova can fight monsters. Every monster is characterized by two values tj and hj β monster kills Vova's character in tj seconds and has hj health points. Mana refills after every fight (or Vova's character revives with full mana reserve), so previous fights have no influence on further ones.
Vova's character kills a monster, if he deals hj damage to it in no more than tj seconds using his spells (it is allowed to use more than one spell in a fight) and spending no more mana than he had at the beginning of the fight. If monster's health becomes zero exactly in tj seconds (it means that the monster and Vova's character kill each other at the same time), then Vova wins the fight.
You have to write a program which can answer two types of queries:
* 1 x y β Vova's character learns new spell which deals x damage per second and costs y mana per second.
* 2 t h β Vova fights the monster which kills his character in t seconds and has h health points.
Note that queries are given in a different form. Also remember that Vova's character knows no spells at the beginning of the game.
For every query of second type you have to determine if Vova is able to win the fight with corresponding monster.
Input
The first line contains two integer numbers q and m (2 β€ q β€ 105, 1 β€ m β€ 1012) β the number of queries and the amount of mana at the beginning of every fight.
i-th of each next q lines contains three numbers ki, ai and bi (1 β€ ki β€ 2, 1 β€ ai, bi β€ 106).
Using them you can restore queries this way: let j be the index of the last query of second type with positive answer (j = 0 if there were none of these).
* If ki = 1, then character learns spell with x = (ai + j) mod 106 + 1, y = (bi + j) mod 106 + 1.
* If ki = 2, then you have to determine if Vova is able to win the fight against monster with t = (ai + j) mod 106 + 1, h = (bi + j) mod 106 + 1.
Output
For every query of second type print YES if Vova is able to win the fight with corresponding monster and NO otherwise.
Example
Input
3 100
1 4 9
2 19 49
2 19 49
Output
YES
NO
Note
In first example Vova's character at first learns the spell with 5 damage and 10 mana cost per second. Next query is a fight with monster which can kill character in 20 seconds and has 50 health points. Vova kills it in 10 seconds (spending 100 mana). Next monster has 52 health, so Vova can't deal that much damage with only 100 mana.
Submitted Solution:
```
#site : https://codeforces.com/contest/792/problem/F
#Spells characterized by 2 values : x[i] and y[i]
#Doesn't have to use spell for int(x) amounts of seconds
#x = damage , y = mana cost , z = seconds
#deals x * z damage spends y * z mana
#If no mana is left , canUseSpell = False
#Can fight monsters : t[j] and h[j] . t = time to kill vova's char , h = monster's hp
#After fight , mana is refilled
#if dealt h[j] damage no more than t[j] seconds using his spells , monster j dies and vova's mana refills (and if monster's health becomes exactly 0 in t[j] , the same thing happens)
#Program :
#Vova learns a new spell dealing x dps and y mps (mana per second(s) )
#Fights a monster which kills him in t seconds and has h hp
#(Vova doesn't know any spell at the beginning)
#What to do ?
#You have to determine if vova's able to win the fight or no
#Input :
#First line :
#q -> the number of queries , m -> amount of mana at the beginning of fight
#2 =< q <= 10 ** 5 , 1 <= m <= 10 ** 12
#then for i=1 in range(1, q) do this :
#input 3 int values : 1 <= k[i] <= 2 , 1 <= a[i] and b[i] <= 10 ** 6
#k is basically the action you want to do . either 1 or 2 . 1 means character learns a spell with x (dps) = (a[i] + j (the last monster you fought with) ) % (10 ** 6) + 1 <- for limiting it to be less than 10 ** 6
#and 2 means if character is able to win against the monster or no (output = "YES" or "NO") with time to kill of t = (a[i] + j) % (10 ** 6) + 1 and hp of h = (b[i] + j) % (10 ** 6) + 1
#inputs must be in input file in the same directory of this file
#Start of code :
x = []
y = []
killedMonster = False
j = 0
t, h = 0,0
q, m = 0, 0
def get_input():
global q, m
k, a, b = [],[],[]
values = input()
q, m = int(values.split(" ")[0]), int(values.split(" ")[1])
for i in range(0,q):
inp = input()
k.append(int(inp.split(" ")[0]))
a.append(int(inp.split(" ")[1]))
b.append(int(inp.split(" ")[2]) % 10 ** 6)
value = [k,a,b]
return value
k, a, b = get_input()
for i in range(q):
if k[i] == 1:
x.append((a[i] + j) % 10 ** 6 + 1)
y.append((b[i] + j) % 10 ** 6 + 1)
elif k[i] == 2:
j += 1
t = (a[i] + j) % 10 ** 6 + 1
h = (b[i] + j) % 10 ** 6 + 1
for chosen in range(0,len(x)):
if x[chosen] * t >= h and y[chosen] * t <= m * 2:
print("YES")
killedMonster = True
break
if not killedMonster:
print("NO")
else:
killedMonster = False
```
No
| 454
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Tags: dfs and similar, graphs
Correct Solution:
```
import sys
from math import *
def minp():
return sys.stdin.readline().strip()
def mint():
return int(minp())
def mints():
return map(int, minp().split())
n, x = mints()
e = [[] for i in range(n)]
for i in range(n-1):
a, b = mints()
e[a-1].append(b-1)
e[b-1].append(a-1)
x -= 1
q = [0]*n
d = [0]*n
p = [-1]*n
ql = 0
qr = 1
q[0] = x
d[x] = 1
while ql < qr:
u = q[ql]
ql += 1
for v in e[u]:
if d[v] == 0:
d[v] = d[u] + 1
p[v] = u
q[qr] = v
qr += 1
#v = 0
#u = 1
#while v != -1:
# if d[v] >= u:
# d[v] = 0
# v = p[v]
# u += 1
#print(d)
dd = [0]*n
ql = 0
qr = 1
q[0] = 0
dd[0] = 1
while ql < qr:
u = q[ql]
ql += 1
for v in e[u]:
if dd[v] == 0:
dd[v] = dd[u] + 1
q[qr] = v
qr += 1
r = 0
for i in range(n):
if d[i] < dd[i]:
r = max(r, dd[i])
print((r-1)*2)
```
| 455
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Tags: dfs and similar, graphs
Correct Solution:
```
import sys
from collections import deque
n, x = map(int, sys.stdin.buffer.readline().decode('utf-8').split())
x -= 1
adj = [[] for _ in range(n)]
for u, v in (map(int, line.decode('utf-8').split()) for line in sys.stdin.buffer):
adj[u-1].append(v-1)
adj[v-1].append(u-1)
bob = 1
color = [0]*n
color[0] = 1
color[x] = 2
dq = deque()
dq.extend(((x, 2, 1), (0, 1, 2)))
while dq:
v, c, t = dq.popleft()
if c == 2 and color[v] == 1:
continue
for dest in adj[v]:
if color[dest] == c or color[dest] == 1 and c == 2:
continue
if c == 1 and color[dest] == 2:
bob -= 1
if bob == 0:
print(t)
exit()
if c == 2:
bob += 1
color[dest] = c
dq.append((dest, c, t+2))
```
| 456
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Tags: dfs and similar, graphs
Correct Solution:
```
import sys
input = sys.stdin.buffer.readline
from collections import deque
def prog():
n,x = map(int,input().split())
adj = [[] for i in range(n + 1)]
for i in range(n-1):
u,v = map(int,input().split())
adj[u].append(v)
adj[v].append(u)
dist = [0]*(n+1)
parent = [0]*(n+1)
visited = [0]*(n+1)
dist2 = [0]*(n+1)
visited2 = [0]*(n+1)
s = deque([1])
while s:
curr = s[-1]
if not visited[curr]:
visited[curr] = 1
for neighbor in adj[curr]:
if not visited[neighbor]:
parent[neighbor] = curr
s.append(neighbor)
dist[neighbor] = dist[curr] + 1
else:
s.pop()
curr = x
moved_up = 0
while moved_up + 1 < dist[parent[curr]]:
curr = parent[curr]
moved_up += 1
s = deque([curr])
while s:
curr = s[-1]
if not visited2[curr]:
visited2[curr] = 1
for neighbor in adj[curr]:
if parent[curr] != neighbor:
s.append(neighbor)
dist2[neighbor] = dist2[curr] + 1
else:
s.pop()
best_loc = 0
best_dist = -1
for i in range(n + 1):
if visited2[i] and dist2[i] > best_dist:
best_dist = dist2[i]
best_loc = i
print(2*dist[best_loc])
prog()
```
| 457
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Tags: dfs and similar, graphs
Correct Solution:
```
def prog():
from sys import stdin
from collections import deque
n,x = map(int,stdin.readline().split())
x-=1
d = [[] for i in range(n)]
for i in range(n-1):
a,b = map(int,stdin.readline().split())
d[a-1].append(b-1)
d[b-1].append(a-1)
Alice = [1000000 for i in range(n)]
Bob = [1000000 for i in range(n)]
queue=deque()
queue.append([0,0])
while queue:
q1 = queue.popleft()
Alice[q1[0]]=min(Alice[q1[0]],q1[1])
for i,item in enumerate(d[q1[0]]):
if Alice[item]==1000000:
queue.append([item,q1[1]+1])
queue.append([x,0])
while queue:
q2 = queue.popleft()
Bob[q2[0]]=min(Bob[q2[0]],q2[1])
for i,item in enumerate(d[q2[0]]):
if Bob[item]==1000000:
queue.append([item,q2[1]+1])
res = 0
for i in range(n):
A=Alice[i]
if A>Bob[i]:
if A>res:
res=A
print(2*res)
prog()
```
| 458
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Tags: dfs and similar, graphs
Correct Solution:
```
from collections import deque
from sys import stdin
#parsea una linea
def parser():
return map(int, stdin.readline().split())
#Metodo usado para calcular las distancia de un vertice al resto de los vertices
def BFS(s):
distance=[-1 for i in range(n)]
distance[s]=0
q=deque()
q.append(s)
while len(q)>0:
v=q.popleft()
for u in adjacents_list[v]:
if distance[u] == -1:
distance[u]=distance[v]+1
q.append(u)
return distance
#Recibiendo los valores de n y x
n,x=parser()
#Armando el arbol
adjacents_list=[[] for i in range(n)]
for i in range(n-1):
#Leyendo una arista
v1,v2=parser()
adjacents_list[v1-1].append(v2-1)
adjacents_list[v2-1].append(v1-1)
#Hallando las distancias
distance_Alice=BFS(0)
distance_Bob=BFS(x-1)
#Obteniendo la distancia mayor desde el vertice 1 hasta un vertice alcanzable por Bob
max_distance=0
for i in range(n):
if max_distance<distance_Alice[i] and distance_Bob[i]<distance_Alice[i]:
max_distance=distance_Alice[i]
#Imprimiendo el resultado
print(max_distance*2)
```
| 459
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Tags: dfs and similar, graphs
Correct Solution:
```
from collections import deque
from sys import stdin
#parser
def parser():
return [int(i) for i in stdin.readline().split(" ")]
#Algoritmo BFS
def BFS(s):
if s==0:
distance=distance_Alice
else:
distance=distance_Bob
distance[s]=0
q=deque()
q.append(s)
while len(q)>0:
v=q.popleft()
for u in adjacents_list[v]:
if distance[u] == -1:
distance[u]=distance[v]+1
q.append(u)
#Recibiendo los valores de n y x
n,x=parser()
#Creando los arrays necesarios para la ejecucion de DFS
#visitados
distance_Alice=[-1 for i in range(n)]
distance_Bob=[-1 for i in range(n)]
#Armando el arbol
adjacents_list=[[] for i in range(n)]
for i in range(n-1):
edge=parser()
adjacents_list[edge[0]-1].append(edge[1]-1)
adjacents_list[edge[1]-1].append(edge[0]-1)
BFS(0)
BFS(x-1)
#Hallando el nodo mas alejado a Alice que puede alcanzar Bob antes que lo alcance Alice
max=0
for i in range(n):
if max<distance_Alice[i] and distance_Bob[i]<distance_Alice[i]:
max=distance_Alice[i]
print(max*2)
```
| 460
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Tags: dfs and similar, graphs
Correct Solution:
```
import sys,math,itertools
from collections import Counter,deque,defaultdict
from bisect import bisect_left,bisect_right
from heapq import heappop,heappush,heapify
mod = 10**9+7
INF = float('inf')
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))
def inpl_1(): return list(map(lambda x:int(x)-1, sys.stdin.readline().split()))
def inps(): return sys.stdin.readline()
def inpsl(x): tmp = sys.stdin.readline(); return list(tmp[:x])
def err(x): print(x); exit()
n,X = inpl(); X -= 1
g = [[] for _ in range(n)]
for _ in range(n-1):
a,b = inpl_1()
g[a].append(b)
g[b].append(a)
dist = [-1]*n; dist[0] = 0
q = deque([0])
pa = -1
while q:
u = q.popleft()
for v in g[u]:
if dist[v] != -1: continue
if v == X: pa = u
dist[v] = dist[u] + 1
q.append(v)
dist2 = [-1]*n; dist2[X] = 0
q = deque([X])
while q:
u = q.popleft()
for v in g[u]:
if dist2[v] != -1 or dist2[u]+1 >= dist[v]:
continue
dist2[v] = dist2[u] + 1
q.append(v)
# mx = max(dist2)
res = 0
for i in range(n):
if dist2[i] >= 0:
res = max(res, dist[i])
print(res*2)
```
| 461
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Tags: dfs and similar, graphs
Correct Solution:
```
from sys import stdin
#Clase nodo
class Node():
def __init__(self,value=None,prox=None):
self.value=value
self.prox=prox
#Clase cola
class Queue:
def __init__(self):
self.first=None
self.last=None
self.count=0
def Enqueue(self,value):
new_node=Node(value)
self.count+=1
if self.first is None:
self.last=self.first=new_node
else:
self.last.prox=new_node
self.last=new_node
def Dequeue(self):
value=self.first.value
self.count-=1
self.first=self.first.prox
return value
#Parser
def parser():
return [int(x) for x in input().split(" ")]
#Algoritmo BFS
def BFS(s):
if s==0:
distance=distance_Alice
else:
distance=distance_Bob
distance[s]=0
q=Queue()
q.Enqueue(s)
while q.count>0:
v=q.Dequeue()
for u in adjacents_list[v]:
if distance[u] == -1:
distance[u]=distance[v]+1
q.Enqueue(u)
#Recibiendo los valores de n y x
n,x=map(int, stdin.readline().split())
#Creando los arrays necesarios para la ejecucion de DFS
#visitados
distance_Alice=[-1 for i in range(n)]
distance_Bob=[-1 for i in range(n)]
#Armando el arbol
adjacents_list=[[] for i in range(n)]
for i in range(n-1):
v1,v2=map(int, stdin.readline().split())
adjacents_list[v1-1].append(v2-1)
adjacents_list[v2-1].append(v1-1)
BFS(0)
BFS(x-1)
#Hallando el nodo mas alejado a Alice que puede alcanzar Bob antes que lo alcance Alice
max=0
for i in range(n):
if max<distance_Alice[i] and distance_Bob[i]<distance_Alice[i]:
max=distance_Alice[i]
print(max*2)
```
| 462
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Submitted Solution:
```
from collections import deque
from sys import stdin
#parser
def parser():
return map(int, stdin.readline().split())
#Algoritmo BFS
def BFS(s):
distance=[-1 for i in range(n)]
distance[s]=0
q=deque()
q.append(s)
while len(q)>0:
v=q.popleft()
for u in adjacents_list[v]:
if distance[u] == -1:
distance[u]=distance[v]+1
q.append(u)
return distance
#Recibiendo los valores de n y x
n,x=parser()
#Armando el arbol
adjacents_list=[[] for i in range(n)]
for i in range(n-1):
v1,v2=parser()
adjacents_list[v1-1].append(v2-1)
adjacents_list[v2-1].append(v1-1)
distance_Alice=BFS(0)
distance_Bob=BFS(x-1)
#Hallando el nodo mas alejado a Alice que puede alcanzar Bob antes que lo alcance Alice
max=0
for i in range(n):
if max<distance_Alice[i] and distance_Bob[i]<distance_Alice[i]:
max=distance_Alice[i]
print(max*2)
```
Yes
| 463
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Submitted Solution:
```
from collections import deque
from sys import stdin
#Algoritmo BFS
def BFS(s):
if s==0:
distance=distance_Alice
else:
distance=distance_Bob
distance[s]=0
q=deque()
q.append(s)
while len(q)>0:
v=q.popleft()
for u in adjacents_list[v]:
if distance[u] == -1:
distance[u]=distance[v]+1
q.append(u)
#Recibiendo los valores de n y x
n,x=map(int, stdin.readline().split())
#Creando los arrays necesarios para la ejecucion de DFS
#visitados
distance_Alice=[-1 for i in range(n)]
distance_Bob=[-1 for i in range(n)]
#Armando el arbol
adjacents_list=[[] for i in range(n)]
for i in range(n-1):
v1,v2=map(int, stdin.readline().split())
adjacents_list[v1-1].append(v2-1)
adjacents_list[v2-1].append(v1-1)
BFS(0)
BFS(x-1)
#Hallando el nodo mas alejado a Alice que puede alcanzar Bob antes que lo alcance Alice
max=0
for i in range(n):
if max<distance_Alice[i] and distance_Bob[i]<distance_Alice[i]:
max=distance_Alice[i]
print(max*2)
```
Yes
| 464
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Submitted Solution:
```
from collections import deque
from sys import stdin
n, x = map(int, stdin.readline().split())
leafs = set(range(n))
graph = [[] for i in range(n)]
count = [False for i in range(n)]
for i in range(n - 1):
a, b = map(int, stdin.readline().split())
graph[a - 1].append(b - 1)
graph[b - 1].append(a - 1)
if not count[a - 1]:
count[a - 1] = True
else:
leafs.discard(a - 1)
if not count[b - 1]:
count[b - 1] = True
else:
leafs.discard(b - 1)
queue = deque()
way_a = [10 ** 6 for i in range(n)]
way_b = [10 ** 6 for i in range(n)]
used = [False for i in range(n)]
queue.append([0, 0])
while queue:
j = queue.popleft()
way_a[j[0]] = min(way_a[j[0]], j[1])
for i in graph[j[0]]:
if not used[i]:
used[i] = True
queue.append([i, j[1] + 1])
queue.append([x - 1, 0])
used = [False for i in range(n)]
while queue:
j = queue.popleft()
way_b[j[0]] = min(way_b[j[0]], j[1])
for i in graph[j[0]]:
if not used[i]:
used[i] = True
queue.append([i, j[1] + 1])
res = way_a[x - 1]
for i in leafs:
if way_a[i] > way_b[i]:
res = max(res, way_a[i])
print(res * 2)
```
Yes
| 465
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Submitted Solution:
```
from sys import stdin
from collections import deque
def bfs(G, s):
Q = deque()
Q.append(s)
infinite = 10 ** 6
d = [infinite]*n
d[s] = 0
while Q:
u = Q.popleft()
for v in graph[u]:
if d[v] == infinite:
d[v] = d[u] + 1
Q.append(v)
return d
n, x = map(int, stdin.readline().split())
x = x - 1
graph = [[] for i in range(n)]
for i in range(n - 1):
a, b = map(int, stdin.readline().split())
graph[a - 1].append(b - 1)
graph[b - 1].append(a - 1)
d_Alice = bfs(graph, 0)
d_Bob = bfs(graph, x)
resp = d_Alice[x]
for i,v in enumerate(graph):
if len(v) == 1 and d_Alice[i] > d_Bob[i]:
resp = max(resp, d_Alice[i])
print(2*resp)
```
Yes
| 466
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Submitted Solution:
```
n, x = map(int, input().split())
E = []
WHITE = 0
GREY = 1
BLACK = 2
color = [-1] + [WHITE for i in range(n)]
path = []
max_path = 0
for i in range(n - 1):
E.append(list(map(int, input().split())))
def get_nbs(v):
for e in E:
if e[0] == v:
yield e[1]
elif e[1] == v:
yield e[0]
def dfs(v):
global max_path
color[v] = GREY
path.append(v)
lp = len(path)
if lp >= max_path:
max_path = lp
for u in get_nbs(v):
if color[u] == WHITE:
dfs(u)
elif color[u] == GREY and u in path and u != path[-2]:
e = [u, v] if [u, v] in E else [v, u]
E.remove(e)
path.remove(v)
# print(path)
dfs(1)
print((max_path - 1) * 2)
```
No
| 467
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Submitted Solution:
```
import sys
from math import *
def minp():
return sys.stdin.readline().strip()
def mint():
return int(minp())
def mints():
return map(int, minp().split())
n, x = mints()
e = [[] for i in range(n)]
for i in range(n-1):
a, b = mints()
e[a-1].append(b-1)
e[b-1].append(a-1)
x -= 1
q = [0]*n
d = [0]*n
p = [-1]*n
ql = 0
qr = 1
q[0] = x
d[x] = 1
while ql < qr:
u = q[ql]
ql += 1
for v in e[u]:
if d[v] == 0:
d[v] = d[u] + 1
p[v] = u
q[qr] = v
qr += 1
v = 0
u = 1
while v != -1 and d[v] > u:
d[v] = 0
v = p[v]
u += 1
rv = d.index(max(d))
#print(d, rv)
d = [0]*n
ql = 0
qr = 1
q[0] = 0
d[0] = 1
while ql < qr:
u = q[ql]
ql += 1
for v in e[u]:
if d[v] == 0:
d[v] = d[u] + 1
q[qr] = v
qr += 1
print((d[rv]-1)*2)
```
No
| 468
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Submitted Solution:
```
def bottomm(x):
if len(dic[x])==0:
return 0
h=0
for i in dic[x]:
h= max(1+bottomm(i),h)
return h
def getheight(x,dic,ph):
if x in dic[ph]:
return 1
else:
h=0
for j in dic[ph]:
h=1+getheight(x,dic,j)
return h
n,x=map(int,input().split())
dic={}
par={}
for i in range(n):
dic[i+1]=[]
par[i+1]=[]
for _ in range(n-1):
a,b=map(int,input().split())
dic[a].append(b)
par[b]=a
pos_a=1
pos_b=x
ha=1
hb=getheight(x,dic,1)
ans=0
f=0
if hb==2:
if len(dic[pos_b])==0:
ans=4
f=1
elif f==0:
uptil=hb//2
maxh=bottomm(x)
k=0
while(uptil!=0):
node=par[pos_b]
pos_b=node
uptil-=1
k+=1
maxh=max(maxh,bottomm(node)+k)
node=x
while(k!=0):
node=par[x]
x=node
k-=1
ans=maxh+getheight(node,dic,1)+bottomm(node)+1
print(ans)
```
No
| 469
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice got tired of playing the tag game by the usual rules so she offered Bob a little modification to it. Now the game should be played on an undirected rooted tree of n vertices. Vertex 1 is the root of the tree.
Alice starts at vertex 1 and Bob starts at vertex x (x β 1). The moves are made in turns, Bob goes first. In one move one can either stay at the current vertex or travel to the neighbouring one.
The game ends when Alice goes to the same vertex where Bob is standing. Alice wants to minimize the total number of moves and Bob wants to maximize it.
You should write a program which will determine how many moves will the game last.
Input
The first line contains two integer numbers n and x (2 β€ n β€ 2Β·105, 2 β€ x β€ n).
Each of the next n - 1 lines contains two integer numbers a and b (1 β€ a, b β€ n) β edges of the tree. It is guaranteed that the edges form a valid tree.
Output
Print the total number of moves Alice and Bob will make.
Examples
Input
4 3
1 2
2 3
2 4
Output
4
Input
5 2
1 2
2 3
3 4
2 5
Output
6
Note
In the first example the tree looks like this:
<image>
The red vertex is Alice's starting position, the blue one is Bob's. Bob will make the game run the longest by standing at the vertex 3 during all the game. So here are the moves:
B: stay at vertex 3
A: go to vertex 2
B: stay at vertex 3
A: go to vertex 3
In the second example the tree looks like this:
<image>
The moves in the optimal strategy are:
B: go to vertex 3
A: go to vertex 2
B: go to vertex 4
A: go to vertex 3
B: stay at vertex 4
A: go to vertex 4
Submitted Solution:
```
'''n=int(input())
a=list(map(int,input().split()))
m=int(input())
per=[]
tt=sum(a)
f=0
for _ in range(m):
l,r=map(int,input().split())
#print(l,r,tt)
if l<=tt and tt<=r:
print(tt)
f=1
break
elif l>tt and f==0:
print(l)
f=1
break
if f==0:
print(-1)
'''
def bottomm(x):
if len(dic[x])==0:
return 0
h=0
for i in dic[x]:
h= max(1+bottomm(i),h)
return h
def getheight(x,dic,ph):
if x in dic[ph]:
return 1
else:
h=0
for j in dic[ph]:
h=1+getheight(x,dic,j)
return h
n,x=map(int,input().split())
dic={}
par={}
for i in range(n):
dic[i+1]=[]
par[i+1]=[]
for _ in range(n-1):
a,b=map(int,input().split())
dic[a].append(b)
par[b]=a
pos_a=1
pos_b=x
ha=1
hb=getheight(x,dic,1)
ans=0
f=0
if hb==2:
if len(dic[pos_b])==0:
ans=4
f=1
elif f==0:
uptil=hb//2
maxh=bottomm(x)
k=1
while(uptil!=0):
node=par[pos_b]
pos_b=node
uptil-=1
maxh=max(maxh,bottomm(node)+k)
k+=1
ans=2*(maxh+hb)
print(ans)
```
No
| 470
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Tags: brute force, greedy, implementation
Correct Solution:
```
n, k = map(int, input().split())
l = list(map(int, input().split()))
l = sorted(l, reverse=True)
s = 0
for _ in range(n):
if l[0] <= 0:
break
if l[0] <= 2:
l[0] -= min(l[0],2)
s += 1
l[0] -= min(l[0],4)
l = sorted(l, reverse=True)
for _ in range(n):
if l[0] <= 0:
break
l[0] -= min(l[0],2)
l = sorted(l, reverse=True)
for _ in range(n):
if l[0] <= 0:
break
l[0] -= min(l[0],2)
l = sorted(l, reverse=True)
for _ in range(s):
if l[0] <= 0:
break
l[0] -= min(l[0],1)
l = sorted(l, reverse=True)
if l[0] <= 0:
print("YES")
else:
print("NO")
```
| 471
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Tags: brute force, greedy, implementation
Correct Solution:
```
n,m=map(int,input().split())
l=list(map(int,input().split()))
p=n
for i in range(m) :
b=l[i]//4
l[i]=l[i]-4*min(p,l[i]//4)
p=p-min(p,b)
p1=n*2
for i in range(m) :
b=l[i]//2
l[i]=l[i]-2*min(p1,l[i]//2)
p1=p1-min(p1,b)
p2=p+p1
p3=p
for i in range(m) :
b=l[i]//2
l[i]=l[i]-2*min(p2,l[i]//2)
p2=p2-min(p2,b)
k=0
p3+=p2
for i in range(m) :
k=k+l[i]
if k>p3 :
print('NO')
else :
print('YES')
```
| 472
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Tags: brute force, greedy, implementation
Correct Solution:
```
import sys
n, k = [ int(x) for x in input().split() ]
arr = list( map( int, input().split()) )
cnt_2 = 2 * n
cnt_4 = n
cnt_1 = 0
i = 0
while(cnt_4 > 0 and i < k):
tmp = int(arr[i] / 4)
if(tmp > 0 and cnt_4 > 0):
arr[i] = arr[i] - 4 * min(tmp, cnt_4)
cnt_4 = cnt_4 - min(tmp, cnt_4)
i = i + 1
if(cnt_4 > 0):
cnt_2 = cnt_2 + cnt_4
cnt_1 = cnt_1 + cnt_4
cnt_4 = 0
i = 0
while(cnt_2 > 0 and i < k):
tmp = int(arr[i] / 2)
if(tmp > 0 and cnt_2 > 0):
arr[i] = arr[i] - 2 * min(tmp, cnt_2)
cnt_2 = cnt_2 - min(tmp, cnt_2)
i = i + 1
if(cnt_2 > 0):
cnt_1 = cnt_1 + cnt_2
cnt_2 = 0
i = 0
while(i < k):
tmp = arr[i]
if(tmp > cnt_1):
print("NO")
sys.exit(0)
elif(tmp > 0 and tmp <= cnt_1):
cnt_1 = cnt_1 - tmp
arr[i] = arr[i] - tmp
i = i + 1
print("YES")
```
| 473
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Tags: brute force, greedy, implementation
Correct Solution:
```
from math import ceil
n,k = map(int, input().split())
a = list(map(int, input().split()))
def solve(n,k,a):
one,two,four = 0, n*2, n
for size in a:
while size >= 4:
if four > 0:
four -= 1
else:
two -= 2
size -= 4
while size > 0:
if four > 0:
four -= 1
if size == 2:
one += 1
elif size == 1:
two += 1
break
elif two > 0:
two -= 1
size -= 2
elif one > 0:
one -= 1
size -= 1
else:
return "NO"
return "YES"
print(solve(n,k,sorted(a, reverse=True)))
```
| 474
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Tags: brute force, greedy, implementation
Correct Solution:
```
n,k = map(int,input().split(" "))
a = list(map(int,input().split(" ")))
count = 0
for i in range(0,len(a)):
if a[i]%2 == 0:
count = count + 1
if k-count <= n*8-sum(a):
if k-count < n and k==n*4:
print("NO")
else:
print('YES')
else:print('NO')
```
| 475
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Tags: brute force, greedy, implementation
Correct Solution:
```
def solve(a, n, k):
cnt =[0 for i in range(5)]
duplas, quads, sozinhos = 2*n, n, 0
for i in a:
for j in range(k):
while i >= 3:
if quads > 0:
i -= 4; quads -= 1
elif duplas > 0:
i -= 2; duplas -= 1
else: return "no"
if i > 0:
cnt[i] += 1
while cnt[2]:
if duplas > 0:
duplas -= 1; cnt[2] -= 1
elif quads > 0:
cnt[2] -= 1; quads -= 1; sozinhos += 1
else:
cnt[2] -= 1; cnt[1] += 2
if cnt[1] > sozinhos + duplas + 2*quads:
return "no"
return "yes"
n, k = [int(i) for i in input().split()]
a = [int(i) for i in input().split()]
print(solve(a, n, k))
# 1522848694321
```
| 476
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Tags: brute force, greedy, implementation
Correct Solution:
```
n, k = map(int, input().split())
a = list(map(int, input().split()))
c = [0, 0, 0, 0]
for t in a:
c[0] += t//4
if t%4: c[t%4] += 1
c[0] += c[3]
c[3] = 0
if c[0] > n:
c[2] += 2*(c[0]-n)
c[0] = n
t = min(n-c[0], c[1], c[2])
c[0] += t
c[1] -= t
c[2] -= t
t = min(n-c[0], (c[1]+1)//2)
c[0] += t
c[1] -= min(c[1], t*2)
t = min(n-c[0], c[2])
c[0] += t
c[2] -= min(c[2], t+t//2)
c[2] += c[1]
c[1] = 0
print("YES" if c[2] <= 2*n else "NO")
```
| 477
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Tags: brute force, greedy, implementation
Correct Solution:
```
# encoding:utf-8
def main():
n, k = list(map(int, input().split()))
nums = list(map(int, input().split()))
seat_two = n * 2
seat_four = n
seat_one = 0
n_four = sum([x // 4 for x in nums])
nums = [x % 4 for x in nums]
n_two = sum([x // 2 for x in nums])
n_one = sum([x % 2 for x in nums])
#print(n_one, n_two, n_four)
#print(seat_one, seat_two, seat_four)
if seat_four >= n_four:
# there is rest of 4 seat
seat_four -= n_four
n_four = 0
# break seat seat_one and seat_two
seat_two += seat_four
seat_one += seat_four
seat_four = 0
else:
# there is rest of 4 people
n_four -= seat_four
seat_four = 0
# break 4 people to 2, 2
n_two += n_four * 2
n_four = 0
#print(n_one, n_two, n_four)
#print(seat_one, seat_two, seat_four)
if seat_two >= n_two:
seat_two -= n_two
n_two = 0
if seat_two + seat_one >= n_one:
print("YES")
else:
print("NO")
else:
n_two -= seat_two
seat_two = 0
n_one += n_two * 2
if seat_one >= n_one:
print("YES")
else:
print("NO")
if __name__ == '__main__':
main()
1
```
| 478
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Submitted Solution:
```
def solve(n, k, a):
fourSeatLeft = n
twoSeatLeft = n * 2
for i in range(k):
while a[i] >= 4:
if fourSeatLeft > 0:
fourSeatLeft -= 1
a[i] -= min(a[i], 4)
else:
break
for i in range(k):
while a[i] >= 3:
if fourSeatLeft > 0:
fourSeatLeft -= 1
a[i] -= min(a[i], 4)
else:
break
for i in range(k):
while a[i] >= 2:
if twoSeatLeft > 0:
twoSeatLeft -= 1
a[i] -= min(a[i], 2)
else:
break
for i in range(k):
while a[i] >= 1:
if twoSeatLeft > 0:
twoSeatLeft -= 1
a[i] -= min(a[i], 2)
else:
break
twoSeatLeft += fourSeatLeft
oneSeatLeft = fourSeatLeft
fourSeatLeft = 0
for i in range(k):
while a[i] >= 2:
if twoSeatLeft > 0:
twoSeatLeft -= 1
a[i] -= min(a[i], 2)
else:
break
oneSeatLeft += twoSeatLeft
twoSeatLeft = 0
for i in range(k):
while a[i] >= 1:
if oneSeatLeft > 0:
oneSeatLeft -= 1
a[i] -= min(a[i], 1)
else:
break
if sum(a) > 0:
return 'NO'
return 'YES'
##if __name__ == '__main__':
##
## import sys
##
## stdin = sys.stdin
## sys.stdin = open('cf839b.txt')
##
## testcaseNo = eval(input())
##
## for c in range(testcaseNo):
## [n, k] = [eval(v) for v in input().split()]
## a = [eval(v) for v in input().split()]
##
## result = solve(n, k, a)
##
## print('Case#' + str(c + 1) + ':', end=' ')
## print(result)
##
## sys.stdin = stdin
[n, k] = [eval(v) for v in input().split()]
a = [eval(v) for v in input().split()]
print(solve(n, k, a))
```
Yes
| 479
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Submitted Solution:
```
#coding=utf-8
def test():
n, k = map(int, input().split())
a = list(map(int, input().split()))
total = n * 8
place = 0
sum = 0
i = 0
temp = 0
flag = 0
while i < k:
sum += a[i]
if a[i] % 2 is 1:
place += 1
else:
flag += 1
if a[i] % 4 != 0:
temp += 1
i += 1
if sum == total:
if place!=0 or (flag%4==0 and n*4==k):
print("NO")
else:
print("YES")
else:
if (sum + place) > total or (n*4==k and (flag//4)==place ):
print("NO")
else:
print("YES")
test()
```
Yes
| 480
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Submitted Solution:
```
import sys
import os
import math
import re
n,k = map(int,input().split())
sol = list(map(int,input().split()))
totalSeats = 8*n
middle = n
leftRight = 2*n
single = 0
for i in range(k):
fours = min((sol[i]+1)//4,middle) #take the min of 4s needed + one empty and the middle
middle -= fours
sol[i] = max(0,sol[i]-4*fours) #soldiers remaining
leftRight += middle
single += middle
for i in range(k): #now deal with the twos
twos = min(sol[i]//2, leftRight)
leftRight -= twos
sol[i] = max(0, sol[i]-2*twos) #soldiers remaining
single += leftRight
for i in range(k): #all the singles that need a seat
single -= sol[i]
if single < 0:
print('No')
else:
print('Yes')
```
Yes
| 481
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Submitted Solution:
```
n,k=map(int,input().split())
wuya=[int(x) for x in input().split()]
n_4=sum([x//4 for x in wuya])
wuya=[x%4 for x in wuya]
n_2=sum([x//2 for x in wuya])
n_1=sum([x%2 for x in wuya])
p4=n
p4,n_4=p4-min(n_4,p4),n_4-min(n_4,p4)
p2=2*n+p4
n_2+=2*n_4
p2,n_2=p2-min(n_2,p2),n_2-min(n_2,p2)
p1=p4+p2
n_1+=n_2*2
if p1>=n_1:
print('YES')
else:
print('NO')
```
Yes
| 482
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Submitted Solution:
```
debug = 0
read = lambda: map(int, input().split())
k, n = read()
a = list(read())
cnt4 = k
cnt2 = 2 * k
for i in range(n):
cnt = min(cnt4, a[i] // 4)
a[i] -= cnt * 4
cnt4 -= cnt
if debug: print(*a)
for i in range(n):
cnt = min(cnt2, a[i] // 2)
a[i] -= cnt * 2
cnt2 -= cnt
if debug: print(' '.join(map(str, a)), ' ', cnt2, cnt4)
c = [0] * 20
for i in a:
c[min(i, 19)] += 1
d = min(cnt4, c[1], c[2])
c[1] -= d
c[2] -= d
cnt4 -= d
d = min(cnt2, c[2])
c[2] -= d
cnt2 -= d
d = min(cnt2, c[1])
c[1] -= d
cnt2 -= d
d = min(cnt4, c[2])
c[2] -= d
cnt4 -= d
if debug:
print('cnt4 = ', cnt4)
print('c[1] = ', c[1])
d = min(cnt4, (c[1] + 1) // 2)
c[1] -= d * 2
cnt4 -= d
print('YES' if sum(c[1:]) == 0 else 'NO')
```
No
| 483
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Submitted Solution:
```
n, k = map(int, input().split())
s = list(map(int, input().split()))
q = n
double = 2*n
for i in range(k):
if double>=s[i]//2+s[i]%2 :
s[i]=0
double-=s[i]//2+s[i]%2
else:
s[i]-=double*2
double=0
break
for i in range(k):
p = min(q, s[i]//4)
q -= p
s[i] -= (p*4)
if q != 0:
for i in range(k):
if s[i] == 0:
continue
if s[i] == 1 and q != 0:
q -= 0.5
s[i]=0
elif s[i] == 2:
if q % 1 == 0.5:
q -= 1.5
s[i]=0
elif q > 0:
q -= 1
s[i]=0
elif s[i] >= 3 and q >= 1:
q -= 1
s[i]=0
if double!=0:
for i in range(k):
if s[i]!=0:
if (double>=s[i]//2+s[i]%2):
double-=s[i]//2+s[i]%2
s[i]=0
else:
print('NO')
exit()
for i in s:
if i!=0:
print('NO')
exit()
print('YES')
```
No
| 484
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Submitted Solution:
```
def main():
n,_=[int(i) for i in input().split(" ")]
a=[int(i) for i in input().split(" ")]
sides=n*2
mid=n
single=0
for g in a:
while g>0:
if g>=4 and mid>0:
mid-=1
g-=4
elif g>=2 and sides>0:
sides-=1
g-=2
elif g>=2: #no sides g<4
mid-=1
single+=1
g-=2
elif g==1:
if single>0:
single-=1
g-=1
elif sides>0:
sides-=1
g-=1
elif mid>0:
mid-=1
g-=1
else:
print("NO")
return
else:
print("NO")
return
print("YES")
main()
```
No
| 485
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.
<image> A row in the airplane
Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.
Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.
Input
The first line contains two integers n and k (1 β€ n β€ 10000, 1 β€ k β€ 100) β the number of rows and the number of groups of soldiers, respectively.
The second line contains k integers a1, a2, a3, ..., ak (1 β€ ai β€ 10000), where ai denotes the number of soldiers in the i-th group.
It is guaranteed that a1 + a2 + ... + ak β€ 8Β·n.
Output
If we can place the soldiers in the airplane print "YES" (without quotes). Otherwise print "NO" (without quotes).
You can choose the case (lower or upper) for each letter arbitrary.
Examples
Input
2 2
5 8
Output
YES
Input
1 2
7 1
Output
NO
Input
1 2
4 4
Output
YES
Input
1 4
2 2 1 2
Output
YES
Note
In the first sample, Daenerys can place the soldiers like in the figure below:
<image>
In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.
In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.
In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6).
Submitted Solution:
```
def main():
n, k = map(int, input().split())
cnt, a4 = [0] * 4, 0
for a in map(int, input().split()):
a4 += a // 4
cnt[a % 4] += 1
_, a1, a2, a3 = cnt
if (a3 + a4) * 2 < a2:
a4 += a3
a2 -= a4 * 2
n -= ((a2 + 2) // 3) if a2 > a1 * 3 else ((a2 + a1 + 3) // 4)
print(("YES", "NO")[n < a4])
else:
print(("YES", "NO")[n * 4 < (a4 + a3) * 2 + a2 + a1])
if __name__ == '__main__':
main()
```
No
| 486
|
Provide tags and a correct Python 3 solution for this coding contest problem.
A new set of desks just arrived, and it's about time! Things were getting quite cramped in the office. You've been put in charge of creating a new seating chart for the engineers. The desks are numbered, and you sent out a survey to the engineering team asking each engineer the number of the desk they currently sit at, and the number of the desk they would like to sit at (which may be the same as their current desk). Each engineer must either remain where they sit, or move to the desired seat they indicated in the survey. No two engineers currently sit at the same desk, nor may any two engineers sit at the same desk in the new seating arrangement.
How many seating arrangements can you create that meet the specified requirements? The answer may be very large, so compute it modulo 1000000007 = 109 + 7.
Input
Input will begin with a line containing N (1 β€ N β€ 100000), the number of engineers.
N lines follow, each containing exactly two integers. The i-th line contains the number of the current desk of the i-th engineer and the number of the desk the i-th engineer wants to move to. Desks are numbered from 1 to 2Β·N. It is guaranteed that no two engineers sit at the same desk.
Output
Print the number of possible assignments, modulo 1000000007 = 109 + 7.
Examples
Input
4
1 5
5 2
3 7
7 3
Output
6
Input
5
1 10
2 10
3 10
4 10
5 5
Output
5
Note
These are the possible assignments for the first example:
* 1 5 3 7
* 1 2 3 7
* 5 2 3 7
* 1 5 7 3
* 1 2 7 3
* 5 2 7 3
Tags: combinatorics, dfs and similar, dsu, graphs, trees
Correct Solution:
```
n = int(input())
m = 2 * n + 1
u = [[] for i in range(m)]
v = [0] * m
s = [0] * m
d = 10 ** 9 + 7
y = 1
for j in range(n):
a, b = map(int, input().split())
v[a] = b
if a != b:
s[b] += 1
u[b].append(a)
for b in range(m):
if not v[b]:
x = 0
p = [b]
while p:
x += 1
a = p.pop()
s[a] = -1
p += u[a]
y = (x * y) % d
for a in range(m):
if s[a] == 0:
b = v[a]
while s[b] == 1:
s[b] = -1
b = v[b]
s[b] -= 1
for a in range(m):
if s[a] == 1:
y = (2 * y) % d
while s[a]:
s[a] = 0
a = v[a]
print(y)
```
| 487
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A new set of desks just arrived, and it's about time! Things were getting quite cramped in the office. You've been put in charge of creating a new seating chart for the engineers. The desks are numbered, and you sent out a survey to the engineering team asking each engineer the number of the desk they currently sit at, and the number of the desk they would like to sit at (which may be the same as their current desk). Each engineer must either remain where they sit, or move to the desired seat they indicated in the survey. No two engineers currently sit at the same desk, nor may any two engineers sit at the same desk in the new seating arrangement.
How many seating arrangements can you create that meet the specified requirements? The answer may be very large, so compute it modulo 1000000007 = 109 + 7.
Input
Input will begin with a line containing N (1 β€ N β€ 100000), the number of engineers.
N lines follow, each containing exactly two integers. The i-th line contains the number of the current desk of the i-th engineer and the number of the desk the i-th engineer wants to move to. Desks are numbered from 1 to 2Β·N. It is guaranteed that no two engineers sit at the same desk.
Output
Print the number of possible assignments, modulo 1000000007 = 109 + 7.
Examples
Input
4
1 5
5 2
3 7
7 3
Output
6
Input
5
1 10
2 10
3 10
4 10
5 5
Output
5
Note
These are the possible assignments for the first example:
* 1 5 3 7
* 1 2 3 7
* 5 2 3 7
* 1 5 7 3
* 1 2 7 3
* 5 2 7 3
Submitted Solution:
```
import sys
input = sys.stdin.readline
M = 10**9 + 7
n = int(input())
G = [list() for _ in range(2*n+1)]
for _ in range(n):
u, v = map(int, input().split())
G[u].append(v)
G[v].append(u)
visited = [False]*(2*n+1)
sys.setrecursionlimit(10**6)
E, V, loop = None, None, False
def dfs(s):
global E, V, loop
V.add(s)
visited[s] = True
if len(G[s]) > 2:
loop = True
for v in G[s]:
E += 1
if not visited[v]:
dfs(v)
ans = 1
for v in range(2*n+1):
if not visited[v]:
E, V = 1, set()
loop = False
dfs(v)
cnt = 1
if E < 2*len(V):
cnt = len(V)
elif not loop:
cnt = 2
ans = (ans*cnt) % M
print(ans)
```
No
| 488
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A new set of desks just arrived, and it's about time! Things were getting quite cramped in the office. You've been put in charge of creating a new seating chart for the engineers. The desks are numbered, and you sent out a survey to the engineering team asking each engineer the number of the desk they currently sit at, and the number of the desk they would like to sit at (which may be the same as their current desk). Each engineer must either remain where they sit, or move to the desired seat they indicated in the survey. No two engineers currently sit at the same desk, nor may any two engineers sit at the same desk in the new seating arrangement.
How many seating arrangements can you create that meet the specified requirements? The answer may be very large, so compute it modulo 1000000007 = 109 + 7.
Input
Input will begin with a line containing N (1 β€ N β€ 100000), the number of engineers.
N lines follow, each containing exactly two integers. The i-th line contains the number of the current desk of the i-th engineer and the number of the desk the i-th engineer wants to move to. Desks are numbered from 1 to 2Β·N. It is guaranteed that no two engineers sit at the same desk.
Output
Print the number of possible assignments, modulo 1000000007 = 109 + 7.
Examples
Input
4
1 5
5 2
3 7
7 3
Output
6
Input
5
1 10
2 10
3 10
4 10
5 5
Output
5
Note
These are the possible assignments for the first example:
* 1 5 3 7
* 1 2 3 7
* 5 2 3 7
* 1 5 7 3
* 1 2 7 3
* 5 2 7 3
Submitted Solution:
```
n = int(input())
m = 2 * n + 2
u = [[] for i in range(m)]
v = [0] * m
s = [0] * m
d = 10 ** 9 + 7
y = 1
for j in range(n):
a, b = map(int, input().split())
u[b].append(a)
v[a] = b
s[b] += 1
for b in range(m):
if not v[b]:
x = 0
p = [b]
while p:
x += 1
a = p.pop()
s[a] = -1
p += u[a]
y = (x * y) % d
for a in range(m):
if s[a] == 0:
b = v[a]
while s[b] == 1:
b = v[b]
s[b] -= 1
for a in range(m):
if s[a] == 1 and a != v[a]:
y = (2 * y) % d
while s[a]: a, s[a] = v[a], 0
print(y)
```
No
| 489
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A new set of desks just arrived, and it's about time! Things were getting quite cramped in the office. You've been put in charge of creating a new seating chart for the engineers. The desks are numbered, and you sent out a survey to the engineering team asking each engineer the number of the desk they currently sit at, and the number of the desk they would like to sit at (which may be the same as their current desk). Each engineer must either remain where they sit, or move to the desired seat they indicated in the survey. No two engineers currently sit at the same desk, nor may any two engineers sit at the same desk in the new seating arrangement.
How many seating arrangements can you create that meet the specified requirements? The answer may be very large, so compute it modulo 1000000007 = 109 + 7.
Input
Input will begin with a line containing N (1 β€ N β€ 100000), the number of engineers.
N lines follow, each containing exactly two integers. The i-th line contains the number of the current desk of the i-th engineer and the number of the desk the i-th engineer wants to move to. Desks are numbered from 1 to 2Β·N. It is guaranteed that no two engineers sit at the same desk.
Output
Print the number of possible assignments, modulo 1000000007 = 109 + 7.
Examples
Input
4
1 5
5 2
3 7
7 3
Output
6
Input
5
1 10
2 10
3 10
4 10
5 5
Output
5
Note
These are the possible assignments for the first example:
* 1 5 3 7
* 1 2 3 7
* 5 2 3 7
* 1 5 7 3
* 1 2 7 3
* 5 2 7 3
Submitted Solution:
```
#!/bin/python3
# template
import sys
from collections import defaultdict
def read_ints(inp = sys.stdin):
return list(map(int,next(inp).strip().split()))
MOD = 10**9 + 7
def adjacency_lists_directed(e):
"""
form adjacency lists from sequences of (s,e) edges
:warning doesn't handle multi-edges
:param e: edge of non-directed graph
:return: dict of adjacency vertices for each vertex
"""
e_al = defaultdict(set)
for s,e in e:
e_al[s].add(e)
return e_al
def sol1(edges):
#revert
edges = [(v, u) for u, v in edges]
vs = set(u for u, _ in edges)
adj = adjacency_lists_directed(edges)
def count(u):
# return # of arrangement and visited vertices
# 1 if loop
# 2 if cycle
# nb nodes otherwise
visited = set()
stack = [u]
loop = False
cycle = False
while stack:
cur = stack.pop()
ch = adj[cur]
if cur in ch:
loop = True
if cur in visited:
cycle = True
continue
visited.add(cur)
stack.extend(ch)
return (1 if loop else (2 if cycle else len(visited))), visited
res = 1
while vs:
# each connected component
u = next(iter(vs))
c, vis = count(u)
res = (res * c) % MOD
vs -= vis
return res
def main(): # prevent variables at main scope
for i in range(1):
n, = read_ints()
E = []
for _ in range(n):
u,v = read_ints()
E.append((u,v))
d = sol1(E)
print(d)
if __name__=='__main__':
main()
```
No
| 490
|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A new set of desks just arrived, and it's about time! Things were getting quite cramped in the office. You've been put in charge of creating a new seating chart for the engineers. The desks are numbered, and you sent out a survey to the engineering team asking each engineer the number of the desk they currently sit at, and the number of the desk they would like to sit at (which may be the same as their current desk). Each engineer must either remain where they sit, or move to the desired seat they indicated in the survey. No two engineers currently sit at the same desk, nor may any two engineers sit at the same desk in the new seating arrangement.
How many seating arrangements can you create that meet the specified requirements? The answer may be very large, so compute it modulo 1000000007 = 109 + 7.
Input
Input will begin with a line containing N (1 β€ N β€ 100000), the number of engineers.
N lines follow, each containing exactly two integers. The i-th line contains the number of the current desk of the i-th engineer and the number of the desk the i-th engineer wants to move to. Desks are numbered from 1 to 2Β·N. It is guaranteed that no two engineers sit at the same desk.
Output
Print the number of possible assignments, modulo 1000000007 = 109 + 7.
Examples
Input
4
1 5
5 2
3 7
7 3
Output
6
Input
5
1 10
2 10
3 10
4 10
5 5
Output
5
Note
These are the possible assignments for the first example:
* 1 5 3 7
* 1 2 3 7
* 5 2 3 7
* 1 5 7 3
* 1 2 7 3
* 5 2 7 3
Submitted Solution:
```
n = int(input())
m = 2 * n + 2
u = [[] for i in range(m)]
v = [0] * m
s = [0] * m
d = 10 ** 9 + 7
y = 1
for j in range(n):
a, b = map(int, input().split())
u[b].append(a)
v[a] = b
s[b] += 1
for b in range(m):
if not v[b]:
x = 0
p = [b]
while p:
x += 1
a = p.pop()
s[a] = -1
p += u[a]
y = (x * y) % d
for a in range(m):
if s[a] == 0:
b = v[a]
while s[b] == 1:
s[b] -= 1
b = v[b]
s[b] -= 1
for a in range(m):
if s[a] == 1 and a != v[a]:
y = (2 * y) % d
while s[a]:
s[a] = 0
a = v[a]
print(y)
```
No
| 491
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Ivan has n different boxes. The first of them contains some balls of n different colors.
Ivan wants to play a strange game. He wants to distribute the balls into boxes in such a way that for every i (1 β€ i β€ n) i-th box will contain all balls with color i.
In order to do this, Ivan will make some turns. Each turn he does the following:
1. Ivan chooses any non-empty box and takes all balls from this box;
2. Then Ivan chooses any k empty boxes (the box from the first step becomes empty, and Ivan is allowed to choose it), separates the balls he took on the previous step into k non-empty groups and puts each group into one of the boxes. He should put each group into a separate box. He can choose either k = 2 or k = 3.
The penalty of the turn is the number of balls Ivan takes from the box during the first step of the turn. And penalty of the game is the total penalty of turns made by Ivan until he distributes all balls to corresponding boxes.
Help Ivan to determine the minimum possible penalty of the game!
Input
The first line contains one integer number n (1 β€ n β€ 200000) β the number of boxes and colors.
The second line contains n integer numbers a1, a2, ..., an (1 β€ ai β€ 109), where ai is the number of balls with color i.
Output
Print one number β the minimum possible penalty of the game.
Examples
Input
3
1 2 3
Output
6
Input
4
2 3 4 5
Output
19
Note
In the first example you take all the balls from the first box, choose k = 3 and sort all colors to corresponding boxes. Penalty is 6.
In the second example you make two turns:
1. Take all the balls from the first box, choose k = 3, put balls of color 3 to the third box, of color 4 β to the fourth box and the rest put back into the first box. Penalty is 14;
2. Take all the balls from the first box, choose k = 2, put balls of color 1 to the first box, of color 2 β to the second box. Penalty is 5.
Total penalty is 19.
Tags: data structures, greedy
Correct Solution:
```
import heapq
n = int(input())
resp=0
test = [int(i) for i in input().split()]
test.sort()
if(n%2==0):
test = [0]+test
n+=1
while n!=1:
c = heapq.heappop(test) + heapq.heappop(test) + heapq.heappop(test)
resp+=c
heapq.heappush(test,c)
n-=2
print(resp)
```
| 492
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Ivan has n different boxes. The first of them contains some balls of n different colors.
Ivan wants to play a strange game. He wants to distribute the balls into boxes in such a way that for every i (1 β€ i β€ n) i-th box will contain all balls with color i.
In order to do this, Ivan will make some turns. Each turn he does the following:
1. Ivan chooses any non-empty box and takes all balls from this box;
2. Then Ivan chooses any k empty boxes (the box from the first step becomes empty, and Ivan is allowed to choose it), separates the balls he took on the previous step into k non-empty groups and puts each group into one of the boxes. He should put each group into a separate box. He can choose either k = 2 or k = 3.
The penalty of the turn is the number of balls Ivan takes from the box during the first step of the turn. And penalty of the game is the total penalty of turns made by Ivan until he distributes all balls to corresponding boxes.
Help Ivan to determine the minimum possible penalty of the game!
Input
The first line contains one integer number n (1 β€ n β€ 200000) β the number of boxes and colors.
The second line contains n integer numbers a1, a2, ..., an (1 β€ ai β€ 109), where ai is the number of balls with color i.
Output
Print one number β the minimum possible penalty of the game.
Examples
Input
3
1 2 3
Output
6
Input
4
2 3 4 5
Output
19
Note
In the first example you take all the balls from the first box, choose k = 3 and sort all colors to corresponding boxes. Penalty is 6.
In the second example you make two turns:
1. Take all the balls from the first box, choose k = 3, put balls of color 3 to the third box, of color 4 β to the fourth box and the rest put back into the first box. Penalty is 14;
2. Take all the balls from the first box, choose k = 2, put balls of color 1 to the first box, of color 2 β to the second box. Penalty is 5.
Total penalty is 19.
Tags: data structures, greedy
Correct Solution:
```
import heapq
n = int(input())
colors_lens = list(map(int, input().split()))
if len(colors_lens) % 2 == 0:
colors_lens.append(0)
heapq.heapify(colors_lens)
ans = 0
l = len(colors_lens)
while l > 1:
su = 0
su += heapq.heappop(colors_lens)
su += heapq.heappop(colors_lens)
su += heapq.heappop(colors_lens)
ans += su
heapq.heappush(colors_lens, su)
l -= 2
print(ans)
```
| 493
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Ivan has n different boxes. The first of them contains some balls of n different colors.
Ivan wants to play a strange game. He wants to distribute the balls into boxes in such a way that for every i (1 β€ i β€ n) i-th box will contain all balls with color i.
In order to do this, Ivan will make some turns. Each turn he does the following:
1. Ivan chooses any non-empty box and takes all balls from this box;
2. Then Ivan chooses any k empty boxes (the box from the first step becomes empty, and Ivan is allowed to choose it), separates the balls he took on the previous step into k non-empty groups and puts each group into one of the boxes. He should put each group into a separate box. He can choose either k = 2 or k = 3.
The penalty of the turn is the number of balls Ivan takes from the box during the first step of the turn. And penalty of the game is the total penalty of turns made by Ivan until he distributes all balls to corresponding boxes.
Help Ivan to determine the minimum possible penalty of the game!
Input
The first line contains one integer number n (1 β€ n β€ 200000) β the number of boxes and colors.
The second line contains n integer numbers a1, a2, ..., an (1 β€ ai β€ 109), where ai is the number of balls with color i.
Output
Print one number β the minimum possible penalty of the game.
Examples
Input
3
1 2 3
Output
6
Input
4
2 3 4 5
Output
19
Note
In the first example you take all the balls from the first box, choose k = 3 and sort all colors to corresponding boxes. Penalty is 6.
In the second example you make two turns:
1. Take all the balls from the first box, choose k = 3, put balls of color 3 to the third box, of color 4 β to the fourth box and the rest put back into the first box. Penalty is 14;
2. Take all the balls from the first box, choose k = 2, put balls of color 1 to the first box, of color 2 β to the second box. Penalty is 5.
Total penalty is 19.
Tags: data structures, greedy
Correct Solution:
```
import heapq
N=int(input())
colors=list(map(int,input().split()))
if (N%2==0):
colors.append(0)
penalty=0
heapq.heapify(colors)
while (len(colors)>2):
a = heapq.heappop(colors)
b = heapq.heappop(colors)
c = heapq.heappop(colors)
penalty+=a+b+c
heapq.heappush(colors,a+b+c)
print(penalty)
```
| 494
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Ivan has n different boxes. The first of them contains some balls of n different colors.
Ivan wants to play a strange game. He wants to distribute the balls into boxes in such a way that for every i (1 β€ i β€ n) i-th box will contain all balls with color i.
In order to do this, Ivan will make some turns. Each turn he does the following:
1. Ivan chooses any non-empty box and takes all balls from this box;
2. Then Ivan chooses any k empty boxes (the box from the first step becomes empty, and Ivan is allowed to choose it), separates the balls he took on the previous step into k non-empty groups and puts each group into one of the boxes. He should put each group into a separate box. He can choose either k = 2 or k = 3.
The penalty of the turn is the number of balls Ivan takes from the box during the first step of the turn. And penalty of the game is the total penalty of turns made by Ivan until he distributes all balls to corresponding boxes.
Help Ivan to determine the minimum possible penalty of the game!
Input
The first line contains one integer number n (1 β€ n β€ 200000) β the number of boxes and colors.
The second line contains n integer numbers a1, a2, ..., an (1 β€ ai β€ 109), where ai is the number of balls with color i.
Output
Print one number β the minimum possible penalty of the game.
Examples
Input
3
1 2 3
Output
6
Input
4
2 3 4 5
Output
19
Note
In the first example you take all the balls from the first box, choose k = 3 and sort all colors to corresponding boxes. Penalty is 6.
In the second example you make two turns:
1. Take all the balls from the first box, choose k = 3, put balls of color 3 to the third box, of color 4 β to the fourth box and the rest put back into the first box. Penalty is 14;
2. Take all the balls from the first box, choose k = 2, put balls of color 1 to the first box, of color 2 β to the second box. Penalty is 5.
Total penalty is 19.
Tags: data structures, greedy
Correct Solution:
```
import heapq
n = int(input())
lst = list(map(int, input().strip().split()))
if n%2 == 0:
lst.append(0)
penalty = 0
heapq.heapify(lst)
while(len(lst) > 1):
a = heapq.heappop(lst)
b = heapq.heappop(lst)
c = heapq.heappop(lst)
penalty += a+b+c
heapq.heappush(lst, a+b+c)
print(penalty)
```
| 495
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Ivan has n different boxes. The first of them contains some balls of n different colors.
Ivan wants to play a strange game. He wants to distribute the balls into boxes in such a way that for every i (1 β€ i β€ n) i-th box will contain all balls with color i.
In order to do this, Ivan will make some turns. Each turn he does the following:
1. Ivan chooses any non-empty box and takes all balls from this box;
2. Then Ivan chooses any k empty boxes (the box from the first step becomes empty, and Ivan is allowed to choose it), separates the balls he took on the previous step into k non-empty groups and puts each group into one of the boxes. He should put each group into a separate box. He can choose either k = 2 or k = 3.
The penalty of the turn is the number of balls Ivan takes from the box during the first step of the turn. And penalty of the game is the total penalty of turns made by Ivan until he distributes all balls to corresponding boxes.
Help Ivan to determine the minimum possible penalty of the game!
Input
The first line contains one integer number n (1 β€ n β€ 200000) β the number of boxes and colors.
The second line contains n integer numbers a1, a2, ..., an (1 β€ ai β€ 109), where ai is the number of balls with color i.
Output
Print one number β the minimum possible penalty of the game.
Examples
Input
3
1 2 3
Output
6
Input
4
2 3 4 5
Output
19
Note
In the first example you take all the balls from the first box, choose k = 3 and sort all colors to corresponding boxes. Penalty is 6.
In the second example you make two turns:
1. Take all the balls from the first box, choose k = 3, put balls of color 3 to the third box, of color 4 β to the fourth box and the rest put back into the first box. Penalty is 14;
2. Take all the balls from the first box, choose k = 2, put balls of color 1 to the first box, of color 2 β to the second box. Penalty is 5.
Total penalty is 19.
Tags: data structures, greedy
Correct Solution:
```
import heapq
N = int(input())
colors = list(map(int,input().strip().split()))
# if N%2:
# colors.append(0)
# heapq.heapify(colors)
# while (len(colors) > 2):
# a = heapq.heappop(colors)
# b = heapq.heappop(colors)
# c = heapq.heappop(colors)
# panalty += a + b + c
# heapq.heappush(colors,a+b+c)
# print(penalty)
heapq.heapify(colors)
if(len(colors) % 2 == 0):
colors.append(0)
ans = 0
while(len(colors) > 2):
a = heapq.heappop(colors)
b = heapq.heappop(colors)
c = heapq.heappop(colors)
heapq.heappush(colors,a+b+c)
ans += a+b+c
print(ans)
```
| 496
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Ivan has n different boxes. The first of them contains some balls of n different colors.
Ivan wants to play a strange game. He wants to distribute the balls into boxes in such a way that for every i (1 β€ i β€ n) i-th box will contain all balls with color i.
In order to do this, Ivan will make some turns. Each turn he does the following:
1. Ivan chooses any non-empty box and takes all balls from this box;
2. Then Ivan chooses any k empty boxes (the box from the first step becomes empty, and Ivan is allowed to choose it), separates the balls he took on the previous step into k non-empty groups and puts each group into one of the boxes. He should put each group into a separate box. He can choose either k = 2 or k = 3.
The penalty of the turn is the number of balls Ivan takes from the box during the first step of the turn. And penalty of the game is the total penalty of turns made by Ivan until he distributes all balls to corresponding boxes.
Help Ivan to determine the minimum possible penalty of the game!
Input
The first line contains one integer number n (1 β€ n β€ 200000) β the number of boxes and colors.
The second line contains n integer numbers a1, a2, ..., an (1 β€ ai β€ 109), where ai is the number of balls with color i.
Output
Print one number β the minimum possible penalty of the game.
Examples
Input
3
1 2 3
Output
6
Input
4
2 3 4 5
Output
19
Note
In the first example you take all the balls from the first box, choose k = 3 and sort all colors to corresponding boxes. Penalty is 6.
In the second example you make two turns:
1. Take all the balls from the first box, choose k = 3, put balls of color 3 to the third box, of color 4 β to the fourth box and the rest put back into the first box. Penalty is 14;
2. Take all the balls from the first box, choose k = 2, put balls of color 1 to the first box, of color 2 β to the second box. Penalty is 5.
Total penalty is 19.
Tags: data structures, greedy
Correct Solution:
```
import heapq
N = int(input())
colors = list(map(int,input().strip().split()))
if N%2 == 0:
colors.append(0)
penalty = 0
heapq.heapify(colors)
# while (len(colors) > 2):
# a = heapq.heappop(colors)
# b = heapq.heappop(colors)
# c = heapq.heappop(colors)
# panalty += a + b + c
# heapq.heappush(colors,a+b+c)
while(len(colors) > 2):
a = heapq.heappop(colors)
b = heapq.heappop(colors)
c = heapq.heappop(colors)
heapq.heappush(colors,a+b+c)
penalty += a+b+c
print(penalty)
```
| 497
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Ivan has n different boxes. The first of them contains some balls of n different colors.
Ivan wants to play a strange game. He wants to distribute the balls into boxes in such a way that for every i (1 β€ i β€ n) i-th box will contain all balls with color i.
In order to do this, Ivan will make some turns. Each turn he does the following:
1. Ivan chooses any non-empty box and takes all balls from this box;
2. Then Ivan chooses any k empty boxes (the box from the first step becomes empty, and Ivan is allowed to choose it), separates the balls he took on the previous step into k non-empty groups and puts each group into one of the boxes. He should put each group into a separate box. He can choose either k = 2 or k = 3.
The penalty of the turn is the number of balls Ivan takes from the box during the first step of the turn. And penalty of the game is the total penalty of turns made by Ivan until he distributes all balls to corresponding boxes.
Help Ivan to determine the minimum possible penalty of the game!
Input
The first line contains one integer number n (1 β€ n β€ 200000) β the number of boxes and colors.
The second line contains n integer numbers a1, a2, ..., an (1 β€ ai β€ 109), where ai is the number of balls with color i.
Output
Print one number β the minimum possible penalty of the game.
Examples
Input
3
1 2 3
Output
6
Input
4
2 3 4 5
Output
19
Note
In the first example you take all the balls from the first box, choose k = 3 and sort all colors to corresponding boxes. Penalty is 6.
In the second example you make two turns:
1. Take all the balls from the first box, choose k = 3, put balls of color 3 to the third box, of color 4 β to the fourth box and the rest put back into the first box. Penalty is 14;
2. Take all the balls from the first box, choose k = 2, put balls of color 1 to the first box, of color 2 β to the second box. Penalty is 5.
Total penalty is 19.
Tags: data structures, greedy
Correct Solution:
```
import heapq
N = int(input())
colors = list(map(int,input().strip().split()))
if N%2 == 0:
colors.append(0)
penalty = 0
heapq.heapify(colors)
while (len(colors) > 2):
# a = heapq.heappop(colors)
# b = heapq.heappop(colors)
# c = heapq.heappop(colors)
# panalty += a + b + c
# heapq.heappush(colors,a+b+c)
# while(len(colors) > 2):
a = heapq.heappop(colors)
b = heapq.heappop(colors)
c = heapq.heappop(colors)
heapq.heappush(colors,a+b+c)
penalty += a+b+c
print(penalty)
```
| 498
|
Provide tags and a correct Python 3 solution for this coding contest problem.
Ivan has n different boxes. The first of them contains some balls of n different colors.
Ivan wants to play a strange game. He wants to distribute the balls into boxes in such a way that for every i (1 β€ i β€ n) i-th box will contain all balls with color i.
In order to do this, Ivan will make some turns. Each turn he does the following:
1. Ivan chooses any non-empty box and takes all balls from this box;
2. Then Ivan chooses any k empty boxes (the box from the first step becomes empty, and Ivan is allowed to choose it), separates the balls he took on the previous step into k non-empty groups and puts each group into one of the boxes. He should put each group into a separate box. He can choose either k = 2 or k = 3.
The penalty of the turn is the number of balls Ivan takes from the box during the first step of the turn. And penalty of the game is the total penalty of turns made by Ivan until he distributes all balls to corresponding boxes.
Help Ivan to determine the minimum possible penalty of the game!
Input
The first line contains one integer number n (1 β€ n β€ 200000) β the number of boxes and colors.
The second line contains n integer numbers a1, a2, ..., an (1 β€ ai β€ 109), where ai is the number of balls with color i.
Output
Print one number β the minimum possible penalty of the game.
Examples
Input
3
1 2 3
Output
6
Input
4
2 3 4 5
Output
19
Note
In the first example you take all the balls from the first box, choose k = 3 and sort all colors to corresponding boxes. Penalty is 6.
In the second example you make two turns:
1. Take all the balls from the first box, choose k = 3, put balls of color 3 to the third box, of color 4 β to the fourth box and the rest put back into the first box. Penalty is 14;
2. Take all the balls from the first box, choose k = 2, put balls of color 1 to the first box, of color 2 β to the second box. Penalty is 5.
Total penalty is 19.
Tags: data structures, greedy
Correct Solution:
```
import heapq
input()
heap = [int(i) for i in input().split()]
heapq.heapify(heap)
cost = 0
while len(heap) > 1:
amountToMerge = 3
if len(heap) % 2 == 0:
amountToMerge = 2
mergedPileSize = 0
for _ in range(amountToMerge):
mergedPileSize += heapq.heappop(heap)
cost += mergedPileSize
heapq.heappush(heap, mergedPileSize)
print(cost)
```
| 499
|
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