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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 ≀ n ≀ 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)) ```
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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 ≀ n ≀ 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) ```
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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 ≀ n ≀ 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 ≀ n ≀ 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 ≀ n ≀ 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
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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 ≀ n ≀ 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
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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 ≀ n ≀ 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 ≀ n ≀ 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 ≀ n ≀ 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 ≀ n ≀ 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
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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 ≀ n ≀ 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 ≀ n ≀ 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
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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 ≀ n, m ≀ 100 β€” dimensions of the board and 0 ≀ k ≀ 100 β€” the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 ≀ x ≀ n, 1 ≀ y ≀ 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") ```
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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 ≀ n, m ≀ 100 β€” dimensions of the board and 0 ≀ k ≀ 100 β€” the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 ≀ x ≀ n, 1 ≀ y ≀ 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 ≀ n, m ≀ 100 β€” dimensions of the board and 0 ≀ k ≀ 100 β€” the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 ≀ x ≀ n, 1 ≀ y ≀ 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") ```
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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 ≀ n, m ≀ 100 β€” dimensions of the board and 0 ≀ k ≀ 100 β€” the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 ≀ x ≀ n, 1 ≀ y ≀ 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 ≀ n, m ≀ 100 β€” dimensions of the board and 0 ≀ k ≀ 100 β€” the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 ≀ x ≀ n, 1 ≀ y ≀ 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') ```
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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 ≀ n, m ≀ 100 β€” dimensions of the board and 0 ≀ k ≀ 100 β€” the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 ≀ x ≀ n, 1 ≀ y ≀ 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 ≀ n, m ≀ 100 β€” dimensions of the board and 0 ≀ k ≀ 100 β€” the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 ≀ x ≀ n, 1 ≀ y ≀ 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 ≀ n, m ≀ 100 β€” dimensions of the board and 0 ≀ k ≀ 100 β€” the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 ≀ x ≀ n, 1 ≀ y ≀ 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 ```
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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 ≀ n, m ≀ 100 β€” dimensions of the board and 0 ≀ k ≀ 100 β€” the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 ≀ x ≀ n, 1 ≀ y ≀ 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 ≀ n, m ≀ 100 β€” dimensions of the board and 0 ≀ k ≀ 100 β€” the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 ≀ x ≀ n, 1 ≀ y ≀ 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 ≀ n, m ≀ 100 β€” dimensions of the board and 0 ≀ k ≀ 100 β€” the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 ≀ x ≀ n, 1 ≀ y ≀ 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 ≀ n, m ≀ 100 β€” dimensions of the board and 0 ≀ k ≀ 100 β€” the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 ≀ x ≀ n, 1 ≀ y ≀ 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 ≀ n, m ≀ 100 β€” dimensions of the board and 0 ≀ k ≀ 100 β€” the number of pies. Each of the next k lines contains 2 integers, separated by space: 1 ≀ x ≀ n, 1 ≀ y ≀ 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 ≀ 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 ≀ |s| ≀ 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 ≀ y, 2 ≀ d ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 100, 1 ≀ s ≀ 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 ≀ fi ≀ s, 1 ≀ ti ≀ 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 ≀ n ≀ 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 ≀ n ≀ 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 ≀ n ≀ 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 ≀ n ≀ 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 ≀ n ≀ 200 000, 1 ≀ m ≀ 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 ≀ u, v ≀ 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 ≀ s, t ≀ n, s β‰  t, 1 ≀ ds, dt ≀ 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 ≀ n ≀ 200 000, 1 ≀ m ≀ 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 ≀ u, v ≀ 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 ≀ s, t ≀ n, s β‰  t, 1 ≀ ds, dt ≀ 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 ≀ n ≀ 200 000, 1 ≀ m ≀ 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 ≀ u, v ≀ 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 ≀ s, t ≀ n, s β‰  t, 1 ≀ ds, dt ≀ 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 ≀ n ≀ 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 ≀ ui, vi ≀ 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 ≀ q ≀ 105, 1 ≀ m ≀ 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 ≀ ki ≀ 2, 1 ≀ ai, bi ≀ 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 ≀ q ≀ 105, 1 ≀ m ≀ 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 ≀ ki ≀ 2, 1 ≀ ai, bi ≀ 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 ≀ q ≀ 105, 1 ≀ m ≀ 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 ≀ ki ≀ 2, 1 ≀ ai, bi ≀ 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 ≀ q ≀ 105, 1 ≀ m ≀ 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 ≀ ki ≀ 2, 1 ≀ ai, bi ≀ 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 ≀ q ≀ 105, 1 ≀ m ≀ 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 ≀ ki ≀ 2, 1 ≀ ai, bi ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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) ```
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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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 2Β·105, 2 ≀ x ≀ n). Each of the next n - 1 lines contains two integer numbers a and b (1 ≀ a, b ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ n ≀ 10000, 1 ≀ k ≀ 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 ≀ ai ≀ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≀ 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 ≀ N ≀ 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 ≀ N ≀ 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 ≀ N ≀ 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 ≀ N ≀ 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 ≀ N ≀ 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 ≀ i ≀ 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 ≀ n ≀ 200000) β€” the number of boxes and colors. The second line contains n integer numbers a1, a2, ..., an (1 ≀ ai ≀ 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 ≀ i ≀ 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 ≀ n ≀ 200000) β€” the number of boxes and colors. The second line contains n integer numbers a1, a2, ..., an (1 ≀ ai ≀ 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 ≀ i ≀ 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 ≀ n ≀ 200000) β€” the number of boxes and colors. The second line contains n integer numbers a1, a2, ..., an (1 ≀ ai ≀ 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 ≀ i ≀ 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 ≀ n ≀ 200000) β€” the number of boxes and colors. The second line contains n integer numbers a1, a2, ..., an (1 ≀ ai ≀ 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 ≀ i ≀ 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 ≀ n ≀ 200000) β€” the number of boxes and colors. The second line contains n integer numbers a1, a2, ..., an (1 ≀ ai ≀ 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 ≀ i ≀ 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 ≀ n ≀ 200000) β€” the number of boxes and colors. The second line contains n integer numbers a1, a2, ..., an (1 ≀ ai ≀ 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 ≀ i ≀ 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 ≀ n ≀ 200000) β€” the number of boxes and colors. The second line contains n integer numbers a1, a2, ..., an (1 ≀ ai ≀ 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 ≀ i ≀ 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 ≀ n ≀ 200000) β€” the number of boxes and colors. The second line contains n integer numbers a1, a2, ..., an (1 ≀ ai ≀ 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