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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A coder cannot sit and code all day. Sometimes it is a good idea to rise from the desk, have a rest, have small talk with colleagues and even play. The coders of the F company have their favorite ball game. Let's imagine the game on the plane with a cartesian coordinate system. The point (0, 0) contains the player who chooses an arbitrary direction and throws a ball in that direction. The ball hits the plane at distance d from the player's original position and continues flying in the same direction. After the ball hits the plane for the first time, it flies on and hits the plane again at distance 2·d from the player's original position and so on (it continue flying in the chosen direction and hitting the plane after each d units). All coders in the F company are strong, so the ball flies infinitely far away. The plane has n circles painted on it. If a ball hits the plane and hits a circle that is painted on the plane (including its border), then the player gets one point. The ball can hit multiple circles at once and get one point for each of them (if the ball hits some circle x times during the move, the player also gets x points). Count the maximum number of points a player can get if he throws a ball in the arbitrary direction. Note that the direction may have real cooridinates. Input The first line contains two space-separated integers — n и d (1 ≤ n ≤ 2·104; 5 ≤ d ≤ 10). Next n lines contain the circles' description. The i-th line contains three space-separated integers xi, yi, ri ( - 10000 ≤ xi, yi ≤ 10000; 1 ≤ r ≤ 50), where (xi, yi, ri) are the coordinates of the center and the radius of the circle, correspondingly. The point (0, 0) is not inside or on the border of some circle. Output Print a single integer — the maximum number of points you can get. Examples Input 2 5 1 1 1 5 0 1 Output 1 Input 2 5 4 0 3 5 3 1 Output 2 Input 1 10 20 0 10 Output 3 Submitted Solution: ``` import math class Point: def __init__(self, x1, y1): self.x = x1 self.y = y1 class Circle: def __init__(self, x1, y1, r1): self.A = Point(0, 0) self.B = Point(0, 0) self.x = float(x1) self.y = float(y1) self.r = float(r1) self.A.x = self.x - self.r #A is bottom left vertex self.A.y = self.y - self.r self.B.x = self.x + self.r #B is top right vertex self.B.y = self.y + self.r self.angle = math.degrees(math.atan2(self.y, self.x)) #special class that has 5 lists to store circles in class SpecialCircleList: def append(self, c): if(c.x >= 0): if(c.x - c.r <= 0): self.crosses_axis.append(c) return if(c.x <= 0): if(c.x + c.r >= 0): self.crosses_axis.append(c) return if(c.y >= 0): if(c.y - c.r <= 0): self.crosses_axis.append(c) return if(c.y <= 0): if(c.y + c.r >= 0): self.crosses_axis.append(c) return if(c.x > 0 and c.y > 0): self.first_quadrant.append(c) elif(c.x < 0 and c.y > 0): self.second_quadrant.append(c) elif(c.x < 0 and c.y < 0): self.thrid_quadrant.append(c) else: self.fourth_quadrant.append(c) #pass in a bounce point or unit vector, and i'll return a list of circles to check def getRelevantList(self, p): acceptance_angle = 45 pangle = math.degrees(math.atan2(p.y, p.x)) retList = list() for c in self.crosses_axis: if((abs(pangle - c.angle) <acceptance_angle) or abs(c.x < 50) or abs(c.y<50)): retList.append(c) #retList.extend(self.crosses_axis) if(p.x >= 0 and p.y >= 0): #retList.extend(self.first_quadrant) for c in self.first_quadrant: if(abs(pangle - c.angle) < acceptance_angle): retList.append(c) elif(p.x < 0 and p.y >= 0): #retList.extend(self.second_quadrant) for c in self.second_quadrant: if(abs(pangle - c.angle) < acceptance_angle): retList.append(c) elif(p.x < 0 and p.y < 0): #retList.extend(self.thrid_quadrant) for c in self.thrid_quadrant: if(abs(pangle - c.angle) < acceptance_angle): retList.append(c) else: #retList.extend(self.fourth_quadrant) for c in self.fourth_quadrant: if(abs(pangle - c.angle) < acceptance_angle): retList.append(c) return(retList) def __init__(self): self.crosses_axis = list() #for any circle that even remotely crosses and axis self.first_quadrant = list() #for any circle that exclusively resides in quad self.second_quadrant = list() self.thrid_quadrant = list() self.fourth_quadrant = list() circle_list = SpecialCircleList() d = 0 bound_up = 0 bound_down = 0 bound_left = 0 bound_right = 0 max_score = 0 def main(): global circle_list global max_score global d global bound_up global bound_down global bound_left global bound_right line_in = input("") (n, d) = line_in.split() n = int(n) d = int(d) for i in range(n): line_in = input("") (x, y, r) = line_in.split() x = int(x) y = int(y) r = int(r) newCircle = Circle(x, y, r) circle_list.append(newCircle) #determine checking bounds if(y+r > bound_up): bound_up = y + r if(y-r < bound_down): bound_down = y - r if(x + r > bound_right): bound_right = x + r if(x - r < bound_left): bound_left = x - r #brute force for angles 0->360 for angle in range(0, 360, 3): #generate unit vector with direction unit_vector = Point(math.cos(angle*math.pi/180),math.sin(angle*math.pi/180)) #get a list of points where the ball will bounce for a given direction/line bounce_list = getBouncePoints(unit_vector, bound_up, bound_right,\ bound_down, bound_left) if(len(bounce_list) <= max_score): continue #no point doing this one if i've already got a higher score score_for_line = checkIfInAnyCircles(bounce_list, unit_vector) if(score_for_line > max_score): max_score = score_for_line print(max_score) #returns the score of a line/trajectory def checkIfInAnyCircles(bounce_list, unit_vector): global circle_list list_of_relavent_circles = circle_list.getRelevantList(unit_vector) score = 0 if(len(list_of_relavent_circles) == 0 or len(bounce_list) == 0): return(0) for b in bounce_list: for c in list_of_relavent_circles: if(b.x >= c.A.x and b.y >= c.A.y and b.x <= c.B.x and b.y <= c.B.y): if(thoroughCheck(b, c)): score += 1 return(score) #after passing a basic bounded box collision check, do a more thorough check with #floating point arithmatic to see if a bounce (b) lands within a given circle, (c) def thoroughCheck(b, c): distanceFromCircleCentre = (b.x - c.x)**2 + (b.y - c.y)**2 distanceFromCircleCentre = math.sqrt(distanceFromCircleCentre) if(distanceFromCircleCentre <= c.r): return(True) else: return(False) #returns a list of points which a ball will bounce at given a direction/trajectory #takes into consideration bounding box, so doens't calculate more than necessary def getBouncePoints(unit_vector, bound_up, bound_right, bound_down, bound_left ): global d bounce_list = list() bounce_vector = Point(unit_vector.x * d, unit_vector.y * d) newBounce = Point(0, 0) if(unit_vector.x >= 0 and unit_vector.y >= 0): #first quadrant while(newBounce.x <= bound_right and newBounce.y <= bound_up): newBounce = Point(newBounce.x +bounce_vector.x, newBounce.y +bounce_vector.y) bounce_list.append(newBounce) elif(unit_vector.x < 0 and unit_vector.y >= 0): #second quadrant while(newBounce.x >= bound_left and newBounce.y <= bound_up): newBounce = Point(newBounce.x +bounce_vector.x, newBounce.y +bounce_vector.y) bounce_list.append(newBounce) elif(unit_vector.x < 0 and unit_vector.y < 0): #thrid quadrant while(newBounce.x >= bound_left and newBounce.y >= bound_down): newBounce = Point(newBounce.x +bounce_vector.x, newBounce.y +bounce_vector.y) bounce_list.append(newBounce) else: #fourth quadrant while(newBounce.x <= bound_left and newBounce.y >= bound_down): newBounce = Point(newBounce.x +bounce_vector.x, newBounce.y +bounce_vector.y) bounce_list.append(newBounce) return(bounce_list) if __name__ == "__main__": main() ```
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No
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12,339
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A coder cannot sit and code all day. Sometimes it is a good idea to rise from the desk, have a rest, have small talk with colleagues and even play. The coders of the F company have their favorite ball game. Let's imagine the game on the plane with a cartesian coordinate system. The point (0, 0) contains the player who chooses an arbitrary direction and throws a ball in that direction. The ball hits the plane at distance d from the player's original position and continues flying in the same direction. After the ball hits the plane for the first time, it flies on and hits the plane again at distance 2·d from the player's original position and so on (it continue flying in the chosen direction and hitting the plane after each d units). All coders in the F company are strong, so the ball flies infinitely far away. The plane has n circles painted on it. If a ball hits the plane and hits a circle that is painted on the plane (including its border), then the player gets one point. The ball can hit multiple circles at once and get one point for each of them (if the ball hits some circle x times during the move, the player also gets x points). Count the maximum number of points a player can get if he throws a ball in the arbitrary direction. Note that the direction may have real cooridinates. Input The first line contains two space-separated integers — n и d (1 ≤ n ≤ 2·104; 5 ≤ d ≤ 10). Next n lines contain the circles' description. The i-th line contains three space-separated integers xi, yi, ri ( - 10000 ≤ xi, yi ≤ 10000; 1 ≤ r ≤ 50), where (xi, yi, ri) are the coordinates of the center and the radius of the circle, correspondingly. The point (0, 0) is not inside or on the border of some circle. Output Print a single integer — the maximum number of points you can get. Examples Input 2 5 1 1 1 5 0 1 Output 1 Input 2 5 4 0 3 5 3 1 Output 2 Input 1 10 20 0 10 Output 3 Submitted Solution: ``` import math class Point: def __init__(self, x1, y1): self.x = x1 self.y = y1 class Circle: def __init__(self, x1, y1, r1): self.A = Point(0, 0) self.B = Point(0, 0) self.x = float(x1) self.y = float(y1) self.r = float(r1) self.A.x = self.x - self.r #A is bottom left vertex self.A.y = self.y - self.r self.B.x = self.x + self.r #B is top right vertex self.B.y = self.y + self.r self.angle = math.degrees(math.atan2(self.y, self.x)) self.d = math.hypot(self.x, self.y) #special class that has 5 lists to store circles in class SpecialCircleList: def append(self, c): if(c.x >= 0): if(c.x - c.r <= 0): self.crosses_axis.append(c) return if(c.x <= 0): if(c.x + c.r >= 0): self.crosses_axis.append(c) return if(c.y >= 0): if(c.y - c.r <= 0): self.crosses_axis.append(c) return if(c.y <= 0): if(c.y + c.r >= 0): self.crosses_axis.append(c) return if(c.x > 0 and c.y > 0): self.first_quadrant.append(c) elif(c.x < 0 and c.y > 0): self.second_quadrant.append(c) elif(c.x < 0 and c.y < 0): self.thrid_quadrant.append(c) else: self.fourth_quadrant.append(c) #pass in a bounce point or unit vector, and i'll return a list of circles to check def getRelevantList(self, p): acceptance_angle = 30 pangle = math.degrees(math.atan2(p.y, p.x)) retList = list() max_d = 0 for c in self.crosses_axis: if((abs(pangle - c.angle) <acceptance_angle) or abs(c.x < 50) or abs(c.y<50)): retList.append(c) if(c.d > max_d): max_d = c.d #retList.extend(self.crosses_axis) if(p.x >= 0 and p.y >= 0): #retList.extend(self.first_quadrant) for c in self.first_quadrant: if(abs(pangle - c.angle) < acceptance_angle): retList.append(c) if(c.d > max_d): max_d = c.d elif(p.x < 0 and p.y >= 0): #retList.extend(self.second_quadrant) for c in self.second_quadrant: if(abs(pangle - c.angle) < acceptance_angle): retList.append(c) if(c.d > max_d): max_d = c.d elif(p.x < 0 and p.y < 0): #retList.extend(self.thrid_quadrant) for c in self.thrid_quadrant: if(abs(pangle - c.angle) < acceptance_angle): retList.append(c) if(c.d > max_d): max_d = c.d else: #retList.extend(self.fourth_quadrant) for c in self.fourth_quadrant: if(abs(pangle - c.angle) < acceptance_angle): retList.append(c) if(c.d > max_d): max_d = c.d return(retList, max_d) def __init__(self): self.crosses_axis = list() #for any circle that even remotely crosses and axis self.first_quadrant = list() #for any circle that exclusively resides in quad self.second_quadrant = list() self.thrid_quadrant = list() self.fourth_quadrant = list() circle_list = SpecialCircleList() d = 0 bound_up = 0 bound_down = 0 bound_left = 0 bound_right = 0 max_score = 0 def main(): global circle_list global max_score global d global bound_up global bound_down global bound_left global bound_right line_in = input("") (n, d) = line_in.split() n = int(n) d = int(d) for i in range(n): line_in = input("") (x, y, r) = line_in.split() x = int(x) y = int(y) r = int(r) newCircle = Circle(x, y, r) circle_list.append(newCircle) #determine checking bounds if(y+r > bound_up): bound_up = y + r if(y-r < bound_down): bound_down = y - r if(x + r > bound_right): bound_right = x + r if(x - r < bound_left): bound_left = x - r #brute force for angles 0->360 for angle in range(0, 360, 2): #generate unit vector with direction unit_vector = Point(math.cos(angle*math.pi/180),math.sin(angle*math.pi/180)) #get a list of points where the ball will bounce for a given direction/line score_for_line = checkIfInAnyCircles(unit_vector) if(score_for_line > max_score): max_score = score_for_line print(max_score) #returns the score of a line/trajectory def checkIfInAnyCircles(unit_vector): global circle_list global d list_of_relavent_circles, max_d = circle_list.getRelevantList(unit_vector) #bounce_list = getBouncePoints(unit_vector, bound_up, bound_right,\ # bound_down, bound_left) score = 0 if(len(list_of_relavent_circles) < (max_score/2)): return(0) #largestX = 0 #largestY = 0 #for c in list_of_relavent_circles: # if(abs(c.x) > largestX): # largestX = abs(c.x) # if(abs(c.y) > largestY): # largestY = abs(c.y) bounce_vector = Point(unit_vector.x * d, unit_vector.y * d) b = Point(bounce_vector.x, bounce_vector.y) max_d = int((max_d + 50)/d) i = 0 while(i < max_d): #while((abs(b.x) <= largestX + 50) and (abs(b.y) <= largestY + 50)): #for b in bounce_list: for c in list_of_relavent_circles: if(b.x >= c.A.x and b.y >= c.A.y and b.x <= c.B.x and b.y <= c.B.y): if(thoroughCheck(b, c)): score += 1 b.x += bounce_vector.x b.y += bounce_vector.y i += 1 return(score) #after passing a basic bounded box collision check, do a more thorough check with #floating point arithmatic to see if a bounce (b) lands within a given circle, (c) def thoroughCheck(b, c): distanceFromCircleCentre = (b.x - c.x)**2 + (b.y - c.y)**2 distanceFromCircleCentre = math.sqrt(distanceFromCircleCentre) if(distanceFromCircleCentre <= c.r): return(True) else: return(False) #returns a list of points which a ball will bounce at given a direction/trajectory #takes into consideration bounding box, so doens't calculate more than necessary def getBouncePoints(unit_vector, bound_up, bound_right, bound_down, bound_left ): global d bounce_list = list() bounce_vector = Point(unit_vector.x * d, unit_vector.y * d) newBounce = Point(0, 0) if(unit_vector.x >= 0 and unit_vector.y >= 0): #first quadrant while(newBounce.x <= bound_right and newBounce.y <= bound_up): newBounce = Point(newBounce.x +bounce_vector.x, newBounce.y +bounce_vector.y) bounce_list.append(newBounce) elif(unit_vector.x < 0 and unit_vector.y >= 0): #second quadrant while(newBounce.x >= bound_left and newBounce.y <= bound_up): newBounce = Point(newBounce.x +bounce_vector.x, newBounce.y +bounce_vector.y) bounce_list.append(newBounce) elif(unit_vector.x < 0 and unit_vector.y < 0): #thrid quadrant while(newBounce.x >= bound_left and newBounce.y >= bound_down): newBounce = Point(newBounce.x +bounce_vector.x, newBounce.y +bounce_vector.y) bounce_list.append(newBounce) else: #fourth quadrant while(newBounce.x <= bound_left and newBounce.y >= bound_down): newBounce = Point(newBounce.x +bounce_vector.x, newBounce.y +bounce_vector.y) bounce_list.append(newBounce) return(bounce_list) if __name__ == "__main__": main() ```
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12,341
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A coder cannot sit and code all day. Sometimes it is a good idea to rise from the desk, have a rest, have small talk with colleagues and even play. The coders of the F company have their favorite ball game. Let's imagine the game on the plane with a cartesian coordinate system. The point (0, 0) contains the player who chooses an arbitrary direction and throws a ball in that direction. The ball hits the plane at distance d from the player's original position and continues flying in the same direction. After the ball hits the plane for the first time, it flies on and hits the plane again at distance 2·d from the player's original position and so on (it continue flying in the chosen direction and hitting the plane after each d units). All coders in the F company are strong, so the ball flies infinitely far away. The plane has n circles painted on it. If a ball hits the plane and hits a circle that is painted on the plane (including its border), then the player gets one point. The ball can hit multiple circles at once and get one point for each of them (if the ball hits some circle x times during the move, the player also gets x points). Count the maximum number of points a player can get if he throws a ball in the arbitrary direction. Note that the direction may have real cooridinates. Input The first line contains two space-separated integers — n и d (1 ≤ n ≤ 2·104; 5 ≤ d ≤ 10). Next n lines contain the circles' description. The i-th line contains three space-separated integers xi, yi, ri ( - 10000 ≤ xi, yi ≤ 10000; 1 ≤ r ≤ 50), where (xi, yi, ri) are the coordinates of the center and the radius of the circle, correspondingly. The point (0, 0) is not inside or on the border of some circle. Output Print a single integer — the maximum number of points you can get. Examples Input 2 5 1 1 1 5 0 1 Output 1 Input 2 5 4 0 3 5 3 1 Output 2 Input 1 10 20 0 10 Output 3 Submitted Solution: ``` import math class Point: def __init__(self, x1, y1): self.x = x1 self.y = y1 class Circle: def __init__(self, x1, y1, r1): self.A = Point(0, 0) self.B = Point(0, 0) self.x = float(x1) self.y = float(y1) self.r = float(r1) self.A.x = self.x - self.r #A is bottom left vertex self.A.y = self.y - self.r self.B.x = self.x + self.r #B is top right vertex self.B.y = self.y + self.r self.angle = math.degrees(math.atan2(self.y, self.x)) self.d = math.hypot(self.x, self.y) #special class that has 5 lists to store circles in class SpecialCircleList: def append(self, c): if(c.x >= 0): if(c.x - c.r <= 0): self.crosses_axis.append(c) return if(c.x <= 0): if(c.x + c.r >= 0): self.crosses_axis.append(c) return if(c.y >= 0): if(c.y - c.r <= 0): self.crosses_axis.append(c) return if(c.y <= 0): if(c.y + c.r >= 0): self.crosses_axis.append(c) return if(c.x > 0 and c.y > 0): self.first_quadrant.append(c) elif(c.x < 0 and c.y > 0): self.second_quadrant.append(c) elif(c.x < 0 and c.y < 0): self.thrid_quadrant.append(c) else: self.fourth_quadrant.append(c) #pass in a bounce point or unit vector, and i'll return a list of circles to check def getRelevantList(self, p): acceptance_angle = 5 pangle = math.degrees(math.atan2(p.y, p.x)) retList = list() max_d = 0 for c in self.crosses_axis: if((abs(pangle - c.angle) <acceptance_angle) or abs(c.x < 50) or abs(c.y<50)): retList.append(c) if(c.d > max_d): max_d = c.d #retList.extend(self.crosses_axis) if(p.x >= 0 and p.y >= 0): #retList.extend(self.first_quadrant) for c in self.first_quadrant: if(abs(pangle - c.angle) < acceptance_angle): retList.append(c) if(c.d > max_d): max_d = c.d elif(p.x < 0 and p.y >= 0): #retList.extend(self.second_quadrant) for c in self.second_quadrant: if(abs(pangle - c.angle) < acceptance_angle): retList.append(c) if(c.d > max_d): max_d = c.d elif(p.x < 0 and p.y < 0): #retList.extend(self.thrid_quadrant) for c in self.thrid_quadrant: if(abs(pangle - c.angle) < acceptance_angle): retList.append(c) if(c.d > max_d): max_d = c.d else: #retList.extend(self.fourth_quadrant) for c in self.fourth_quadrant: if(abs(pangle - c.angle) < acceptance_angle): retList.append(c) if(c.d > max_d): max_d = c.d return(retList, max_d) def __init__(self): self.crosses_axis = list() #for any circle that even remotely crosses and axis self.first_quadrant = list() #for any circle that exclusively resides in quad self.second_quadrant = list() self.thrid_quadrant = list() self.fourth_quadrant = list() self.frequency = [] circle_list = SpecialCircleList() d = 0 bound_up = 0 bound_down = 0 bound_left = 0 bound_right = 0 max_score = 0 def main(): global circle_list global max_score global d global bound_up global bound_down global bound_left global bound_right line_in = input("") (n, d) = line_in.split() n = int(n) d = int(d) for i in range(n): line_in = input("") (x, y, r) = line_in.split() x = int(x) y = int(y) r = int(r) newCircle = Circle(x, y, r) circle_list.append(newCircle) #determine checking bounds if(y+r > bound_up): bound_up = y + r if(y-r < bound_down): bound_down = y - r if(x + r > bound_right): bound_right = x + r if(x - r < bound_left): bound_left = x - r #brute force for angles 0->360 for angle in range(0, 360, 1): #generate unit vector with direction unit_vector = Point(math.cos(angle*math.pi/180),math.sin(angle*math.pi/180)) score_for_line = checkIfInAnyCircles(unit_vector) if(score_for_line > max_score): max_score = score_for_line print(max_score) #returns the score of a line/trajectory def checkIfInAnyCircles(unit_vector): global circle_list global d list_of_relavent_circles, max_d = circle_list.getRelevantList(unit_vector) score = 0 if(len(list_of_relavent_circles) < (max_score/2)): return(0) bounce_vector = Point(unit_vector.x * d, unit_vector.y * d) b = Point(bounce_vector.x, bounce_vector.y) max_d = int((max_d + 50)/d) i = 0 while(i < max_d): for c in list_of_relavent_circles: if(b.x >= c.A.x and b.y >= c.A.y and b.x <= c.B.x and b.y <= c.B.y): if(thoroughCheck(b, c)): score += 1 b.x += bounce_vector.x b.y += bounce_vector.y i += 1 return(score) #after passing a basic bounded box collision check, do a more thorough check with #floating point arithmatic to see if a bounce (b) lands within a given circle, (c) def thoroughCheck(b, c): distanceFromCircleCentre = (b.x - c.x)**2 + (b.y - c.y)**2 distanceFromCircleCentre = math.sqrt(distanceFromCircleCentre) if(distanceFromCircleCentre <= c.r): return(True) else: return(False) if __name__ == "__main__": main() ```
instruction
0
6,171
3
12,342
No
output
1
6,171
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12,343
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers. Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: "North", "South", "West", "East". Limak isn’t sure whether the description is valid. You must help him to check the following conditions: * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South. * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North. * The journey must end on the North Pole. Check if the above conditions are satisfied and print "YES" or "NO" on a single line. Input The first line of the input contains a single integer n (1 ≤ n ≤ 50). The i-th of next n lines contains an integer ti and a string diri (1 ≤ ti ≤ 106, <image>) — the length and the direction of the i-th part of the journey, according to the description Limak got. Output Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes. Examples Input 5 7500 South 10000 East 3500 North 4444 West 4000 North Output YES Input 2 15000 South 4000 East Output NO Input 5 20000 South 1000 North 1000000 West 9000 North 10000 North Output YES Input 3 20000 South 10 East 20000 North Output NO Input 2 1000 North 1000 South Output NO Input 4 50 South 50 North 15000 South 15000 North Output YES Note Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole. <image> Submitted Solution: ``` n = int(input()) p = 10000 for i in range(n): x, d = input().split() x = int(x) if d == 'South': if p != -10000 and p - x >= -10000: p -= x else: print('NO') exit() elif d == 'North': if p != 10000 and p + x <= 10000: p += x else: print('NO') exit() else: if p == 10000 or p == -10000: print('NO') exit() if p == 10000: print('YES') else: print('NO') ```
instruction
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers. Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: "North", "South", "West", "East". Limak isn’t sure whether the description is valid. You must help him to check the following conditions: * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South. * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North. * The journey must end on the North Pole. Check if the above conditions are satisfied and print "YES" or "NO" on a single line. Input The first line of the input contains a single integer n (1 ≤ n ≤ 50). The i-th of next n lines contains an integer ti and a string diri (1 ≤ ti ≤ 106, <image>) — the length and the direction of the i-th part of the journey, according to the description Limak got. Output Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes. Examples Input 5 7500 South 10000 East 3500 North 4444 West 4000 North Output YES Input 2 15000 South 4000 East Output NO Input 5 20000 South 1000 North 1000000 West 9000 North 10000 North Output YES Input 3 20000 South 10 East 20000 North Output NO Input 2 1000 North 1000 South Output NO Input 4 50 South 50 North 15000 South 15000 North Output YES Note Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole. <image> Submitted Solution: ``` n = int(input()) l = [] for i in range(n): a , b = map(str, input().split()) a = int(a) c = [a, b] l.append(c) milles = 0 for i in range(n): dist = l[i][0] direcc = l[i][1] if direcc == "South": milles = milles + dist elif direcc == "North": milles = milles - dist elif (direcc == "West" or direcc == "East") and (milles == 0 or milles == 20000): print("NO") exit(0) if milles < 0 or milles > 2 * 10**4: print("NO") exit(0) if milles != 0: print("NO") else: print("YES") ```
instruction
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers. Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: "North", "South", "West", "East". Limak isn’t sure whether the description is valid. You must help him to check the following conditions: * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South. * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North. * The journey must end on the North Pole. Check if the above conditions are satisfied and print "YES" or "NO" on a single line. Input The first line of the input contains a single integer n (1 ≤ n ≤ 50). The i-th of next n lines contains an integer ti and a string diri (1 ≤ ti ≤ 106, <image>) — the length and the direction of the i-th part of the journey, according to the description Limak got. Output Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes. Examples Input 5 7500 South 10000 East 3500 North 4444 West 4000 North Output YES Input 2 15000 South 4000 East Output NO Input 5 20000 South 1000 North 1000000 West 9000 North 10000 North Output YES Input 3 20000 South 10 East 20000 North Output NO Input 2 1000 North 1000 South Output NO Input 4 50 South 50 North 15000 South 15000 North Output YES Note Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole. <image> Submitted Solution: ``` import sys n=int(input()) y=0 for i in range(n): t,d=input().split() t=int(t) if y<0 or y>20000: print('NO') exit() if d[0]=='N': y-=t elif d[0]=='S': y+=t elif y==0 or y==20000: print('NO') exit() print('YES' if y==0 else '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. In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers. Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: "North", "South", "West", "East". Limak isn’t sure whether the description is valid. You must help him to check the following conditions: * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South. * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North. * The journey must end on the North Pole. Check if the above conditions are satisfied and print "YES" or "NO" on a single line. Input The first line of the input contains a single integer n (1 ≤ n ≤ 50). The i-th of next n lines contains an integer ti and a string diri (1 ≤ ti ≤ 106, <image>) — the length and the direction of the i-th part of the journey, according to the description Limak got. Output Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes. Examples Input 5 7500 South 10000 East 3500 North 4444 West 4000 North Output YES Input 2 15000 South 4000 East Output NO Input 5 20000 South 1000 North 1000000 West 9000 North 10000 North Output YES Input 3 20000 South 10 East 20000 North Output NO Input 2 1000 North 1000 South Output NO Input 4 50 South 50 North 15000 South 15000 North Output YES Note Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole. <image> Submitted Solution: ``` n = int(input()) def solve(n): pos = 0 for i in range(n): km, direc = input().split() km = int(km) if pos == 0 and direc != "South": print("NO") return elif pos == 20000 and direc != "North": print("NO") return elif direc == "South": pos += km if pos > 20000: print("NO") return elif direc == "North": pos -= km if pos < 0: print("NO") return if pos == 0: print("YES") else: print("NO") solve(n) ```
instruction
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1
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers. Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: "North", "South", "West", "East". Limak isn’t sure whether the description is valid. You must help him to check the following conditions: * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South. * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North. * The journey must end on the North Pole. Check if the above conditions are satisfied and print "YES" or "NO" on a single line. Input The first line of the input contains a single integer n (1 ≤ n ≤ 50). The i-th of next n lines contains an integer ti and a string diri (1 ≤ ti ≤ 106, <image>) — the length and the direction of the i-th part of the journey, according to the description Limak got. Output Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes. Examples Input 5 7500 South 10000 East 3500 North 4444 West 4000 North Output YES Input 2 15000 South 4000 East Output NO Input 5 20000 South 1000 North 1000000 West 9000 North 10000 North Output YES Input 3 20000 South 10 East 20000 North Output NO Input 2 1000 North 1000 South Output NO Input 4 50 South 50 North 15000 South 15000 North Output YES Note Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole. <image> Submitted Solution: ``` total = 0 for _ in range(int(input().strip())): dist, direction = input().strip().split() dist = int(dist) if dist%20000 == 0 and dist != 20000: dist = 0 else: dist = 20000-dist%20000 if dist > 20000 else dist if total == 0: if direction[0] != 'S': print('NO') quit() if total == 20000: if direction[0] != 'N': print('NO') quit() if direction[0] == 'S': total += dist if direction[0] == 'N': total -= dist print(['YES', 'NO'][total!=0]) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers. Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: "North", "South", "West", "East". Limak isn’t sure whether the description is valid. You must help him to check the following conditions: * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South. * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North. * The journey must end on the North Pole. Check if the above conditions are satisfied and print "YES" or "NO" on a single line. Input The first line of the input contains a single integer n (1 ≤ n ≤ 50). The i-th of next n lines contains an integer ti and a string diri (1 ≤ ti ≤ 106, <image>) — the length and the direction of the i-th part of the journey, according to the description Limak got. Output Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes. Examples Input 5 7500 South 10000 East 3500 North 4444 West 4000 North Output YES Input 2 15000 South 4000 East Output NO Input 5 20000 South 1000 North 1000000 West 9000 North 10000 North Output YES Input 3 20000 South 10 East 20000 North Output NO Input 2 1000 North 1000 South Output NO Input 4 50 South 50 North 15000 South 15000 North Output YES Note Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole. <image> Submitted Solution: ``` #!/usr/bin/env python3 n = int(input()) cury = 0 for i in range(n): k, d = input().split() k = int(k) if cury == 0 and d != "South": print("NO") exit() if cury == 20000 and d != "North": print("NO") exit() if d == "East" or d == "West": continue if d == "North": k = k%40000 cury -= k if cury < 0: cury += 40000 cury = cury % 40000 if cury >= 20000: cury = 40000 - cury if d == "South": k = k%40000 cury += k cury = cury % 40000 if cury >= 20000: cury = 40000 - cury if cury%40000 != 0: print("NO") else: print("YES") ```
instruction
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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. In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers. Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: "North", "South", "West", "East". Limak isn’t sure whether the description is valid. You must help him to check the following conditions: * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South. * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North. * The journey must end on the North Pole. Check if the above conditions are satisfied and print "YES" or "NO" on a single line. Input The first line of the input contains a single integer n (1 ≤ n ≤ 50). The i-th of next n lines contains an integer ti and a string diri (1 ≤ ti ≤ 106, <image>) — the length and the direction of the i-th part of the journey, according to the description Limak got. Output Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes. Examples Input 5 7500 South 10000 East 3500 North 4444 West 4000 North Output YES Input 2 15000 South 4000 East Output NO Input 5 20000 South 1000 North 1000000 West 9000 North 10000 North Output YES Input 3 20000 South 10 East 20000 North Output NO Input 2 1000 North 1000 South Output NO Input 4 50 South 50 North 15000 South 15000 North Output YES Note Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole. <image> Submitted Solution: ``` n=int(input().strip()) det=20000 for _ in range(n): dis,dir=input().strip().split() dis=int(dis)%40000 if 20000<dis: dis-=40000 if det==20000 and dir!='North': det-=dis elif det==0 and dir!='South': det+=dis elif dir=='South' and det!=0: det-=dis elif dir=='North' and det!=20000: det+=dis if det>20000: det=40000-det if det<0: det=-det print('YES' if det==20000 else 'NO') ```
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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. In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers. Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: "North", "South", "West", "East". Limak isn’t sure whether the description is valid. You must help him to check the following conditions: * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South. * If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North. * The journey must end on the North Pole. Check if the above conditions are satisfied and print "YES" or "NO" on a single line. Input The first line of the input contains a single integer n (1 ≤ n ≤ 50). The i-th of next n lines contains an integer ti and a string diri (1 ≤ ti ≤ 106, <image>) — the length and the direction of the i-th part of the journey, according to the description Limak got. Output Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes. Examples Input 5 7500 South 10000 East 3500 North 4444 West 4000 North Output YES Input 2 15000 South 4000 East Output NO Input 5 20000 South 1000 North 1000000 West 9000 North 10000 North Output YES Input 3 20000 South 10 East 20000 North Output NO Input 2 1000 North 1000 South Output NO Input 4 50 South 50 North 15000 South 15000 North Output YES Note Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole. <image> Submitted Solution: ``` Q=int(input()) X=0 for _ in range(Q): A=input().strip().split(' ') D=int(A[0]) if X==0: if A[1][0]!='S': print('NO') break else: X+=D X%=40000 if X>20000: X=40000-X elif X==20000: if A[1][0]!='N': print('NO') break else: X-=D X%=40000 if X>20000: X=40000-X else: if A[1][0]=='S': X+=D X%=40000 if X>20000: X=40000-X elif A[1][0]=='N': X-=D X%=40000 if X>20000: X=40000-X else: if X%40000==0: print('YES') else: print('NO') ```
instruction
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No
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12,545
Provide tags and a correct Python 3 solution for this coding contest problem. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0
instruction
0
6,317
3
12,634
Tags: geometry Correct Solution: ``` R,x1,y1,x2,y2=list(map(float,input().split())) d=((x2-x1)**2+(y2-y1)**2)**0.5 if d>R: print(x1," ",y1," ",R) elif d==0: print(x1-R/2," ",y1," ",R/2) else: x,y=(x1*(R+d)-x2*R)/(d),(y1*(R+d)-y2*R)/(d) xans,yans=(x+x2)/2,(y+y2)/2 r=((x-xans)**2+(y-yans)**2)**0.5 print(xans," ",yans," ",r) ```
output
1
6,317
3
12,635
Provide tags and a correct Python 3 solution for this coding contest problem. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0
instruction
0
6,318
3
12,636
Tags: geometry Correct Solution: ``` r,x1,y1,x2,y2=map(int,input().split()) if ((x1-x2)**2+(y1-y2)**2>r*r): print(x1,y1,r) exit() d=((x1-x2)**2+(y1-y2)**2)**0.5 r2=(r+d)/2 if (d==0): x3=x2+r/2 y3=y2 else: x3=x2+(x1-x2)/d*r2 y3=y2+(y1-y2)/d*r2 print(x3,y3,r2) ```
output
1
6,318
3
12,637
Provide tags and a correct Python 3 solution for this coding contest problem. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0
instruction
0
6,319
3
12,638
Tags: geometry Correct Solution: ``` r,x1,y1,x2,y2=map(int,input().split()) if (x2-x1)**2+(y2-y1)**2>=r*r: print(x1,y1,r) exit() if x1==x2: if y2<y1: print(x1,y2+(y1+r-y2)/2,(y1+r-y2)/2) else: print(x1,y2-(y2-y1+r)/2,(y2-y1+r)/2) else: k=(y2-y1)/(x2-x1) b=y1-k*x1 B=b+0 a=k*k+1 c=x1*x1+b*b-2*b*y1+y1*y1-r*r b=2*k*b-2*x1-2*k*y1 d=b*b-4*a*c X1=(-b+d**0.5)/(2*a) X2=(-b-d**0.5)/(2*a) Y1=k*X1+B Y2=k*X2+B r1=((X1-x2)**2+(Y1-y2)**2)**0.5 r2=((X2-x2)**2+(Y2-y2)**2)**0.5 if r1>r2: print((x2+X1)/2,(y2+Y1)/2,r1/2) else: print((x2+X2)/2,(y2+Y2)/2,r2/2) ```
output
1
6,319
3
12,639
Provide tags and a correct Python 3 solution for this coding contest problem. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0
instruction
0
6,320
3
12,640
Tags: geometry Correct Solution: ``` r,x1,y1,x2,y2=map(int ,input().split()) re = ((x1-x2)**2+(y1-y2)**2)**0.5 if (re>=r): re = r x3 = x1 y3 = y1 if (re==0): x3 = x2 + ((re+r)/2); y3 = y2 ; re = ((re+r)/2); else: x3 = x2 + ((((re+r)/2)/re) * (x1-x2)); y3 = y2 + ((((re+r)/2)/re) * (y1-y2)); re = ((re+r)/2); print(x3,y3,re) ```
output
1
6,320
3
12,641
Provide tags and a correct Python 3 solution for this coding contest problem. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0
instruction
0
6,321
3
12,642
Tags: geometry Correct Solution: ``` r,x1,y1,x2,y2 = map(int,input().split()) ttt = 0 import math if(pow(x2-x1,2)+pow(y2-y1,2) >= r*r): rad = r; print(x1,' ',y1,' ',rad) else: rad=(r + math.sqrt(pow(x2-x1,2)+pow(y2-y1,2)))/2 dist= (math.sqrt(pow(x2-x1,2)+pow(y2-y1,2))) m = rad - dist if dist!=0: x = ((m+dist)*x1 -(m)*x2)/dist y = ((m+dist)*y1 -(m)*y2)/dist else: x = x1+r/2 y = y1 rad = 0.5*r print(x,' ',y,' ',rad) ```
output
1
6,321
3
12,643
Provide tags and a correct Python 3 solution for this coding contest problem. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0
instruction
0
6,322
3
12,644
Tags: geometry Correct Solution: ``` import math par = input() # par = '10 0 0 0 0' def dist(x1, y1, x2, y2): return math.sqrt((x1-x2)** 2 + (y1-y2)** 2) def setap(R, x1, y1, x2, y2): d = dist(x1, y1, x2, y2) if d < R and d > 0: r = ( d + R ) / 2 x = x2 - r / d * (x2 - x1) y = y2 - r / d * (y2 - y1) elif d == 0: x = x2 + R / 2 y = y2 r = R / 2 else: r = R x = x1 y = y1 return [x,y,r] par = list(map(int, par.split())) R = par[0] x1 = par[1] y1 = par[2] x2 = par[3] y2 = par[4] res = setap(R, x1, y1, x2, y2) print(res[0],res[1], res[2]) ```
output
1
6,322
3
12,645
Provide tags and a correct Python 3 solution for this coding contest problem. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0
instruction
0
6,323
3
12,646
Tags: geometry Correct Solution: ``` # Reads two numbers from input and typecasts them to int using # list comprehension import math R, x0, y0, x1, y1 = [int(x) for x in input().split()] d1=math.sqrt((x1-x0)*(x1-x0)+(y1-y0)*(y1-y0)) f=0 if((x1-x0)*(x1-x0)+(y1-y0)*(y1-y0)>R*R): f=1 r=(d1+R)/2; if(x1!=x0): ten=(y1-y0)/(x1-x0) if(ten>0): if(y1>y0): sn=math.sin(math.atan(ten)) ansy=y1-(sn*r) cn=math.cos(math.atan(ten)) ansx=x1-(cn*r) else: sn=math.sin(math.atan(ten)) ansy=y1+(sn*r) cn=math.cos(math.atan(ten)) ansx=x1+(cn*r) else: ten=abs(ten) if(y1>y0): sn=math.sin(math.atan(ten)) ansy=y1-(sn*r) cn=math.cos(math.atan(ten)) ansx=x1+(cn*r) else: sn=math.sin(math.atan(ten)) ansy=y1+(sn*r) cn=math.cos(math.atan(ten)) ansx=x1-(cn*r) else: ansx=x1 if(y1>y0): ansy=y1-r else: ansy=y1+r if(f==0): print(ansx, ansy, r) else: print(x0, y0, R) ```
output
1
6,323
3
12,647
Provide tags and a correct Python 3 solution for this coding contest problem. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0
instruction
0
6,324
3
12,648
Tags: geometry Correct Solution: ``` R,x1,y1,x2,y2=map(int,input().split(' ')) d1=(x2-x1)**2+(y2-y1)**2 if d1>=R*R: print(str(x1)+" "+str(y1)+" "+str(R)) else: d2=R+d1**(0.5) if x1==x2 and y1==y2: print(str(x1+R/2)+" "+str(y1)+" "+str(d2/2)) elif x1==x2: if y2>y1: print(str(x1)+" "+str((y1+y2-R)/2)+" "+str(d2/2)) else: print(str(x1)+" "+str((y1+y2+R)/2)+" "+str(d2/2)) elif y1==y2: if x2>x1: print(str((x1+x2-R)/2)+" "+str(y1)+" "+str(d2/2)) else: print(str((x1+x2+R)/2)+" "+str(y1)+" "+str(d2/2)) else: x2-=x1 y2-=y1 slp=y2/x2 a=(R*R/(slp*slp+1))**(0.5) b=slp*a if x2<0 and y2<0: print(str((a+x2)/2+x1)+" "+str((b+y2)/2+y1)+" "+str(d2/2)) elif x2<0 and y2>0: print(str((a+x2)/2+x1)+" "+str((y2+b)/2+y1)+" "+str(d2/2)) elif x2>0 and y2<0: print(str((x2-a)/2+x1)+" "+str((y2-b)/2+y1)+" "+str(d2/2)) else: print(str((x2-a)/2+x1)+" "+str((y2-b)/2+y1)+" "+str(d2/2)) ```
output
1
6,324
3
12,649
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0 Submitted Solution: ``` R, a, b, c, d = map(int, input().split()) da = ((a-c)**2 + (b-d)**2)**0.5 if da >= R: print(a, b, R) elif da == 0: print(a, b+R/2, R/2) else: x, y = a - R*(c-a)/da, b-R*(d-b)/da print((x+c)/2, (y+d)/2, (da+R)/2) ```
instruction
0
6,325
3
12,650
Yes
output
1
6,325
3
12,651
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0 Submitted Solution: ``` import math def main(): r1, x1, y1, x2, y2 = (int(x) for x in input().split()) if (x2 - x1) ** 2 + (y2 - y1) ** 2 >= r1 ** 2: print(x1, y1, r1) return v1 = (x1 - x2, y1 - y2) len_v1 = math.sqrt(v1[0] ** 2 + v1[1] ** 2) r = (r1 + len_v1) / 2 if (x1, y1) == (x2, y2): print(v1[0] + x2, v1[1] + r + y2, r) return k = (r1 + len_v1) / 2 / len_v1 v_res = (v1[0] * k + x2, v1[1] * k + y2) print(v_res[0], v_res[1], r) main() ```
instruction
0
6,326
3
12,652
Yes
output
1
6,326
3
12,653
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0 Submitted Solution: ``` R, x1, y1, x2, y2 = map(int, input().split()) dx = x2 - x1 dy = y2 - y1 dlen = (dx**2 + dy**2)**0.5 if dlen < R: if dlen == 0.0: ax = x1 - R ay = y1 else: ax = x1 - dx * R/dlen ay = y1 - dy * R/dlen x = (ax + x2) / 2 y = (ay + y2) / 2 r = (R + dlen) / 2 else: x = x1 y = y1 r = R print("{:.15f} {:.15f} {:.15f}".format(x, y, r)) ```
instruction
0
6,327
3
12,654
Yes
output
1
6,327
3
12,655
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0 Submitted Solution: ``` class Point: def __init__(self, x, y): self.x = x self.y = y def vector_by_points(pt1, pt2): return Vector(pt2.x - pt1.x, pt2.y - pt1.y) class Vector: def __init__(self, x, y): self.x = x self.y = y def length(self): return (self.x ** 2 + self.y ** 2) ** 0.5 def __add__(self, other): return Vector(self.x + other.x, self.y + other.y) def __mul__(self, other): return Vector(self.x * other, self.y * other) def normalise(self): l = self.length() if l != 0: return Vector(self.x / l, self.y / l) return self r, x1, y1, x2, y2 = map(int, input().split()) center = Point(x1, y1) notebook = Point(x2, y2) v = vector_by_points(notebook, center) dst = v.length() if dst - r <= 0.000001: ans = (2 * r - (r - dst)) / 2 if dst == 0: print(x1 + r / 2, y1, ans) else: v = v.normalise() * ans + notebook print(v.x, v.y, ans) else: print(x1, y1, r) ```
instruction
0
6,328
3
12,656
Yes
output
1
6,328
3
12,657
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0 Submitted Solution: ``` R,x1,y1,x2,y2=input().split() R=float(R) x1=float(x1) y1=float(y1) x2=float(x2) y2=float(y2) d=((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2))**0.5 k1=d; k2=(R-d)/2; if d==0: print(x1,y1,0) elif d<=R: print((x1*(k1+k2)-k2*x2)/k1,(y1*(k1+k2)-k2*y2)/k1,(R+d)/2) else: print(x1,y1,R) ```
instruction
0
6,329
3
12,658
No
output
1
6,329
3
12,659
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0 Submitted Solution: ``` import math def dist(x1,y1,x2,y2): return math.sqrt(distsqr(x1,y1,x2,y2)) def distsqr(x1,y1,x2,y2): return ((x1-x2)**2 + (y1-y2)**2) def f(x): return math.sqrt(resr**2 - (x-x2)**2) + y2 """ def bs(l, r): t = 0 while(abs(l-r) > eps and t < 100): mid = (l+r)/2 if(abs(dist(mid, f(mid), x2, y2)-resr) > eps): l = mid else: r = mid return (l+r)/2 """ if __name__ == '__main__': r, x1, y1, x2, y2 = map(int, input().split()) # print(r, x1, y1, x2, y2) eps = 1e-16 d = distsqr(x1, y1, x2, y2) if(d >= r*r): print(x1, y1, r) else: resr = (math.sqrt(d)+r)/2 if y2 > y1: yr = y2 - resr else: yr = y2 + resr if x2 > x1: xr = x2 - resr else: xr = x2 + resr print(xr, yr, resr) #print(dist(xr,yr,x1,y1), r) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0 Submitted Solution: ``` from math import sqrt R, x1, y1, x2, y2 = map(int, input().split()) if (x2-x1)**2 + (y2-y1)**2 <= R*R: mnR = sqrt((x2-x1)**2 + (y2-y1)**2) r = (mnR + R)/2 if x1 == x2 and y1 == y2: x, y = float(x2+((x1+R)-x1)/2), float(y2+((y1+R)-y1)/2) else: x = (x1-x2)*r/mnR + x2 y = (y1-y2)*r/mnR + y2 print(x, y, r) else: print("%.1f %.1f %.1f" % (x1, y1, R)) ```
instruction
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fifa and Fafa are sharing a flat. Fifa loves video games and wants to download a new soccer game. Unfortunately, Fafa heavily uses the internet which consumes the quota. Fifa can access the internet through his Wi-Fi access point. This access point can be accessed within a range of r meters (this range can be chosen by Fifa) from its position. Fifa must put the access point inside the flat which has a circular shape of radius R. Fifa wants to minimize the area that is not covered by the access point inside the flat without letting Fafa or anyone outside the flat to get access to the internet. The world is represented as an infinite 2D plane. The flat is centered at (x1, y1) and has radius R and Fafa's laptop is located at (x2, y2), not necessarily inside the flat. Find the position and the radius chosen by Fifa for his access point which minimizes the uncovered area. Input The single line of the input contains 5 space-separated integers R, x1, y1, x2, y2 (1 ≤ R ≤ 105, |x1|, |y1|, |x2|, |y2| ≤ 105). Output Print three space-separated numbers xap, yap, r where (xap, yap) is the position which Fifa chose for the access point and r is the radius of its range. Your answer will be considered correct if the radius does not differ from optimal more than 10 - 6 absolutely or relatively, and also the radius you printed can be changed by no more than 10 - 6 (absolutely or relatively) in such a way that all points outside the flat and Fafa's laptop position are outside circle of the access point range. Examples Input 5 3 3 1 1 Output 3.7677669529663684 3.7677669529663684 3.914213562373095 Input 10 5 5 5 15 Output 5.0 5.0 10.0 Submitted Solution: ``` import math from math import sin,cos from decimal import Decimal R,x1,y1,x2,y2=map(int,input().split()) if(((x2-x1)**2+(y2-y1)**2)**0.5>=R): print(x1,y1,R) exit(0) if(x2==x1): theta=22/14 else: theta=math.atan(abs((y2-y1)/(x2-x1))) r=(((x2-x1)**2+(y2-y1)**2)**0.5+R)/2 if(x1==x2 and y1==y2): print(x1,y1,"0") exit(0) if(x2<=x1 and y2<=y1): x=(x1+R*cos(theta)+x2)/2.0 y=(y1+R*sin(theta)+y2)/2.0 elif(x2>=x1 and y2>=y1): x=(x1-R*cos(theta)+x2)/2.0 y=(y1-R*sin(theta)+y2)/2.0 elif(x2<=x1 and y2>=y1): x=(x1+R*cos(theta)+x2)/2.0 y=(y1-R*sin(theta)+y2)/2.0 elif(x2>=x1 and y2<=y1): x=(x1-R*cos(theta)+x2)/2.0 y=(y1+R*sin(theta)+y2)/2.0 print(Decimal(x),Decimal(y),Decimal(r)) ```
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output
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K ⌉ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≤ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K ⌉ is the smallest integer such that K ≤ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≤ n ≤ 4 ⋅ 10^{5}, 1 ≤ I ≤ 10^{8}) — the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≤ a_{i} ≤ 10^{9}) — the array denoting the sound file. Output Print a single integer — the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s. Submitted Solution: ``` from sys import stdin,stdout from math import gcd,sqrt,factorial,pi from collections import deque,defaultdict input=stdin.readline R=lambda:map(int,input().split()) I=lambda:int(input()) S=lambda:input().rstrip('\n') L=lambda:list(R()) P=lambda x:stdout.write(x) lcm=lambda x,y:(x*y)//gcd(x,y) hg=lambda x,y:((y+x-1)//x)*x pw=lambda x:1 if x==1 else 1+pw(x//2) chk=lambda x:chk(x//2) if not x%2 else True if x==1 else False sm=lambda x:(x**2+x)//2 N=10**9+7 n,k=R() mn=2**((k*8)//n) k=0 lst=-1 a=[] for i in sorted(R()): if i!=lst: a+=0, k+=1 a[-1]+=1 lst=i if k<=mn:print(0);exit() ans=0 for i in range(mn): ans+=a[i] val=ans for i in range(mn,k): val+=a[i] val-=a[i-mn] ans=max(ans,val) print(sum(a)-ans) ```
instruction
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K ⌉ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≤ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K ⌉ is the smallest integer such that K ≤ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≤ n ≤ 4 ⋅ 10^{5}, 1 ≤ I ≤ 10^{8}) — the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≤ a_{i} ≤ 10^{9}) — the array denoting the sound file. Output Print a single integer — the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s. Submitted Solution: ``` def mp(): return map(int, input().split()) n, I = mp() a = sorted(list(mp())) k = 2 ** ((I * 8) // n) cnt = [[a[0], 1]] for i in range(1, n): if cnt[-1][0] == a[i]: cnt[-1][1] += 1 else: cnt.append([a[i], 1]) N = n n = len(cnt) a = [i[1] for i in cnt] s = sum(a[:k]) ans = s for i in range(k, n): s -= a[i - k] s += a[i] ans = max(ans, s) print(sum(a) - ans) ```
instruction
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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. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K ⌉ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≤ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K ⌉ is the smallest integer such that K ≤ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≤ n ≤ 4 ⋅ 10^{5}, 1 ≤ I ≤ 10^{8}) — the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≤ a_{i} ≤ 10^{9}) — the array denoting the sound file. Output Print a single integer — the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s. Submitted Solution: ``` from collections import defaultdict as dd n,I=map(int,input().split()) l=list(map(int,input().split())) ll=[] last=-1 l.sort() for i in l: if(i!=last): ll.append(1) last=i else: ll[-1]+=1 k=len(ll) while k > (1 << ((8*I)//n)): k -= 1 ans=0 for i in range(k): ans+=ll[i] res=ans for i in range(k,len(ll)): ans=ans+ll[i]-ll[i-k] res=max(res,ans) print(sum(ll)-res) ```
instruction
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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. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K ⌉ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≤ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K ⌉ is the smallest integer such that K ≤ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≤ n ≤ 4 ⋅ 10^{5}, 1 ≤ I ≤ 10^{8}) — the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≤ a_{i} ≤ 10^{9}) — the array denoting the sound file. Output Print a single integer — the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s. Submitted Solution: ``` import math as mt import collections as cc import sys I=lambda:list(map(int,input().split())) n,i=I() l=I() l.sort() tot=2**((8*i)//n) ans=-10 temp=[0] for i in range(1,n): if l[i]!=l[i-1]: temp.append(i) if len(temp)<=tot: print(0) else: x=-1 for i in range(len(temp)-tot): x=max(temp[i+tot]-temp[i],x) print(n-x) ```
instruction
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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. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K ⌉ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≤ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K ⌉ is the smallest integer such that K ≤ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≤ n ≤ 4 ⋅ 10^{5}, 1 ≤ I ≤ 10^{8}) — the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≤ a_{i} ≤ 10^{9}) — the array denoting the sound file. Output Print a single integer — the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s. Submitted Solution: ``` import math n,I=map(int,input().split()) a=list(map(int,input().split())) a.sort() I*=8 k=1<<(I//n) dp=[1] for i in range(1,n): if a[i]==a[i-1]: dp[-1]+=1 else: dp.append(1) if k>=len(dp): print(0) else: ans=sum(dp[:k]) for i in range(k,len(dp)): ans=max(ans,ans+dp[i]-dp[i-k]) print(n-ans) ```
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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. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K ⌉ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≤ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K ⌉ is the smallest integer such that K ≤ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≤ n ≤ 4 ⋅ 10^{5}, 1 ≤ I ≤ 10^{8}) — the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≤ a_{i} ≤ 10^{9}) — the array denoting the sound file. Output Print a single integer — the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s. Submitted Solution: ``` n,k=map(int,input().split()) l=list(map(int,input().split())) se=set(l) r=pow(2,(8*k)//n) d=dict() for i in range(len(l)): if l[i] not in d: d.update({l[i]:1}) else: d[l[i]]+=1 freq=[] for i in sorted(d): freq.append(d[i]) s=0 e=len(freq)-1 k=len(se) for i in range(1,len(freq)): freq[i]+=freq[i-1] ans=999999999999999999 #print(freq) freq=[0]+freq for i in range(k-r+1): rt=freq[i]+freq[-1]-freq[len(freq)-1+i-k+r] print(rt,freq[i]) ans=min(ans,rt) print(ans) ```
instruction
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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. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K ⌉ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≤ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K ⌉ is the smallest integer such that K ≤ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≤ n ≤ 4 ⋅ 10^{5}, 1 ≤ I ≤ 10^{8}) — the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≤ a_{i} ≤ 10^{9}) — the array denoting the sound file. Output Print a single integer — the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s. Submitted Solution: ``` #TO MAKE THE PROGRAM FAST ''' ---------------------------------------------------------------------------------------------------- ''' import sys import heapq import math input = sys.stdin.readline sys.setrecursionlimit(100000) from collections import * ''' ---------------------------------------------------------------------------------------------------- ''' #FOR TAKING INPUTS ''' ---------------------------------------------------------------------------------------------------- ''' def li():return [int(____) for ____ in input().rstrip('\n').split(' ')] def val():return int(input().rstrip('\n')) def st():return input().rstrip('\n') def sttoli():return [int(i) for i in input().rstrip('\n')] ''' ---------------------------------------------------------------------------------------------------- ''' #MAIN PROGRAM n,I=li() l=li() I*=8 cnt = Counter() d = deque() l.sort() # print(l) currlen = currdistinct = 0 i, ans = 0, -1 while i<len(l): cnt[l[i]] += 1 currlen += 1 if not len(d) or d[-1] != l[i]: d.append(l[i]) currdistinct += 1 while len(d) and n * math.ceil(math.log2(currdistinct)) > I: d.popleft() currlen -= cnt[d[0]] currdistinct -= 1 ans = max(ans,currlen) i+=1 print(len(l)-ans) ''' ---------------------------------------------------------------------------------------------------- ''' ```
instruction
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No
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3
13,319
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers. If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K ⌉ bits to store each value. It then takes nk bits to store the whole file. To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≤ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities. Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible. We remind you that 1 byte contains 8 bits. k = ⌈ log_{2} K ⌉ is the smallest integer such that K ≤ 2^{k}. In particular, if K = 1, then k = 0. Input The first line contains two integers n and I (1 ≤ n ≤ 4 ⋅ 10^{5}, 1 ≤ I ≤ 10^{8}) — the length of the array and the size of the disk in bytes, respectively. The next line contains n integers a_{i} (0 ≤ a_{i} ≤ 10^{9}) — the array denoting the sound file. Output Print a single integer — the minimal possible number of changed elements. Examples Input 6 1 2 1 2 3 4 3 Output 2 Input 6 2 2 1 2 3 4 3 Output 0 Input 6 1 1 1 2 2 3 3 Output 2 Note In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed. In the second example the disk is larger, so the initial file fits it and no changes are required. In the third example we have to change both 1s or both 3s. Submitted Solution: ``` n, I = map(int, input().split()) a = sorted([x for x in map(int, input().split())]) a=[-1]+a b=[i for i in range(n) if a[i] < a[i+1]] ans = list() for x in zip(b, b[2**I:]+[n]): ans.append(x[1]-x[0]) print(n-max(ans)) ```
instruction
0
6,660
3
13,320
No
output
1
6,660
3
13,321
Provide tags and a correct Python 3 solution for this coding contest problem. Bob is about to take a hot bath. There are two taps to fill the bath: a hot water tap and a cold water tap. The cold water's temperature is t1, and the hot water's temperature is t2. The cold water tap can transmit any integer number of water units per second from 0 to x1, inclusive. Similarly, the hot water tap can transmit from 0 to x2 water units per second. If y1 water units per second flow through the first tap and y2 water units per second flow through the second tap, then the resulting bath water temperature will be: <image> Bob wants to open both taps so that the bath water temperature was not less than t0. However, the temperature should be as close as possible to this value. If there are several optimal variants, Bob chooses the one that lets fill the bath in the quickest way possible. Determine how much each tap should be opened so that Bob was pleased with the result in the end. Input You are given five integers t1, t2, x1, x2 and t0 (1 ≤ t1 ≤ t0 ≤ t2 ≤ 106, 1 ≤ x1, x2 ≤ 106). Output Print two space-separated integers y1 and y2 (0 ≤ y1 ≤ x1, 0 ≤ y2 ≤ x2). Examples Input 10 70 100 100 25 Output 99 33 Input 300 500 1000 1000 300 Output 1000 0 Input 143 456 110 117 273 Output 76 54 Note In the second sample the hot water tap shouldn't be opened, but the cold water tap should be opened at full capacity in order to fill the bath in the quickest way possible.
instruction
0
6,695
3
13,390
Tags: binary search, brute force, math Correct Solution: ``` t1,t2,x1,x2,t0=map(int,input().split()) y1,y2,a1,a2,m=x1,x2,0,0,10000000 while True: t=(t1*y1+t2*y2)/(y1+y2) if t>=t0: if t-t0<m:a1,a2,m=y1,y2,t-t0 if y1==0 or y2==0 or t==t0:break if t>t0: y2-=1 else: y1-=1 print(a1,a2) ```
output
1
6,695
3
13,391
Provide tags and a correct Python 3 solution for this coding contest problem. Bob is about to take a hot bath. There are two taps to fill the bath: a hot water tap and a cold water tap. The cold water's temperature is t1, and the hot water's temperature is t2. The cold water tap can transmit any integer number of water units per second from 0 to x1, inclusive. Similarly, the hot water tap can transmit from 0 to x2 water units per second. If y1 water units per second flow through the first tap and y2 water units per second flow through the second tap, then the resulting bath water temperature will be: <image> Bob wants to open both taps so that the bath water temperature was not less than t0. However, the temperature should be as close as possible to this value. If there are several optimal variants, Bob chooses the one that lets fill the bath in the quickest way possible. Determine how much each tap should be opened so that Bob was pleased with the result in the end. Input You are given five integers t1, t2, x1, x2 and t0 (1 ≤ t1 ≤ t0 ≤ t2 ≤ 106, 1 ≤ x1, x2 ≤ 106). Output Print two space-separated integers y1 and y2 (0 ≤ y1 ≤ x1, 0 ≤ y2 ≤ x2). Examples Input 10 70 100 100 25 Output 99 33 Input 300 500 1000 1000 300 Output 1000 0 Input 143 456 110 117 273 Output 76 54 Note In the second sample the hot water tap shouldn't be opened, but the cold water tap should be opened at full capacity in order to fill the bath in the quickest way possible.
instruction
0
6,696
3
13,392
Tags: binary search, brute force, math Correct Solution: ``` from bisect import bisect_left as bl from bisect import bisect_right as br import heapq import math from collections import * from functools import reduce,cmp_to_key import sys input = sys.stdin.readline M = mod = 998244353 def factors(n):return sorted(list(set(reduce(list.__add__,([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))) # def inv_mod(n):return pow(n, mod - 2, mod) def li():return [int(i) for i in input().rstrip('\n').split()] def st():return input().rstrip('\n') def val():return int(input().rstrip('\n')) def li2():return [i for i in input().rstrip('\n').split(' ')] def li3():return [int(i) for i in input().rstrip('\n')] def compare(a,b): if a[-1]<b[-1]:return -1 elif a[-1]>b[-1]:return 1 else: if sum(a[:-1]) > sum(b[:-1]):return -1 return 1 def give(a,b): temp = (a*t1 + b*t2)/(a + b) # print(temp,a,b,t) if temp < t: return [a,b,float('inf')] return [a,b,abs(t - temp)] t1, t2, x1, x2, t = li() bestans = [] if t == t1 and t1 == t2: print(x1,x2) elif t == t1: print(x1,0) elif t == t2: print(0,x2) else: currans = [] currcheck = float('inf') r = (t2 - t)/(t - t1) # print('R ; ',r) bestans.append(give(x1,x2)) bestans.append(give(0,x2)) bestans.append(give(x1,0)) for i in bestans: if currcheck > i[-1]: currcheck = i[-1] currans = i[:-1] elif currcheck == i[-1] and sum(currans) < sum(i[:-1]): currans = i[:-1] do = 1 for i in range(1,x2 + 1): curry1 = i*r a = curry1 b = i if 0 <= int(curry1) <= x1: do = 0 c,d,e = give(int(a),b) if e < currcheck: currcheck = e currans = [c,d] elif e == currcheck and sum(currans) < c + d: currans = [c,d] if 0 <= int(a) + 1 <= x1: do = 0 c,d,e = give(int(a) + 1,b) if e < currcheck: currcheck = e currans = [c,d] elif e == currcheck and sum(currans) < c + d: currans = [c,d] if do: for j in range(1,min(x1,x2) + 1): c,d,e = give(j,j) if e < currcheck: currcheck = e currans = [c,d] elif e == currcheck and sum(currans) < c + d: currans = [c,d] # for i,(a,b,c) in enumerate(bestans): # if ((a*t1 + b*t2)/(a + b)) < t: # bestans[i][-1] = 1000 # continue # bestans[i][-1] = abs(t - ((a*t1 + b*t2)/(a + b))) # bestans.sort(key=cmp_to_key(compare)) # print(bestans) print(*currans) ```
output
1
6,696
3
13,393
Provide tags and a correct Python 3 solution for this coding contest problem. Bob is about to take a hot bath. There are two taps to fill the bath: a hot water tap and a cold water tap. The cold water's temperature is t1, and the hot water's temperature is t2. The cold water tap can transmit any integer number of water units per second from 0 to x1, inclusive. Similarly, the hot water tap can transmit from 0 to x2 water units per second. If y1 water units per second flow through the first tap and y2 water units per second flow through the second tap, then the resulting bath water temperature will be: <image> Bob wants to open both taps so that the bath water temperature was not less than t0. However, the temperature should be as close as possible to this value. If there are several optimal variants, Bob chooses the one that lets fill the bath in the quickest way possible. Determine how much each tap should be opened so that Bob was pleased with the result in the end. Input You are given five integers t1, t2, x1, x2 and t0 (1 ≤ t1 ≤ t0 ≤ t2 ≤ 106, 1 ≤ x1, x2 ≤ 106). Output Print two space-separated integers y1 and y2 (0 ≤ y1 ≤ x1, 0 ≤ y2 ≤ x2). Examples Input 10 70 100 100 25 Output 99 33 Input 300 500 1000 1000 300 Output 1000 0 Input 143 456 110 117 273 Output 76 54 Note In the second sample the hot water tap shouldn't be opened, but the cold water tap should be opened at full capacity in order to fill the bath in the quickest way possible.
instruction
0
6,697
3
13,394
Tags: binary search, brute force, math Correct Solution: ``` def gcd(a,b): if(a%b==0): return b else: return gcd(b,a%b) [t1,t2,x1,x2,t0]=input().split(' ') #[t1,t2,x1,x2,t0]=[100,110,2,2,109] t1=int(t1) t2=int(t2) x1=int(x1) x2=int(x2) t0=int(t0) a=t2-t0 b=t0-t1 if(a==0 and b==0): print(x1,x2) exit(0) if (a==0): y1=0 y2=x2 print(y1,y2) exit(0) if (b==0): y1=x1 y2=0 print(y1,y2) exit(0) g=gcd(a,b) a=int(a/g) b=int(b/g) if(a<=x1 and b<=x2): mintime=int(x1/a) if(mintime>int(x2/b)): mintime=int(x2/b) print(mintime*a,mintime*b) exit(0) y1=1 y2=1 miny1=1 miny2=1 minn=99999 fg=0 while(y1<=x1 and y2<=x2): if(y1/y2<a/b): if(minn>a/b-y1/y2): minn=a/b-y1/y2 miny1=y1 miny2=y2 fg=1 y1=y1+1 else: y2=y2+1 y1=miny1 y2=miny2 mintime=int(x1/y1) if(mintime>int(x2/y2)): mintime=int(x2/y2) if(fg==1): print(mintime*y1,mintime*y2) else: print(0,x2) ```
output
1
6,697
3
13,395
Provide tags and a correct Python 3 solution for this coding contest problem. Bob is about to take a hot bath. There are two taps to fill the bath: a hot water tap and a cold water tap. The cold water's temperature is t1, and the hot water's temperature is t2. The cold water tap can transmit any integer number of water units per second from 0 to x1, inclusive. Similarly, the hot water tap can transmit from 0 to x2 water units per second. If y1 water units per second flow through the first tap and y2 water units per second flow through the second tap, then the resulting bath water temperature will be: <image> Bob wants to open both taps so that the bath water temperature was not less than t0. However, the temperature should be as close as possible to this value. If there are several optimal variants, Bob chooses the one that lets fill the bath in the quickest way possible. Determine how much each tap should be opened so that Bob was pleased with the result in the end. Input You are given five integers t1, t2, x1, x2 and t0 (1 ≤ t1 ≤ t0 ≤ t2 ≤ 106, 1 ≤ x1, x2 ≤ 106). Output Print two space-separated integers y1 and y2 (0 ≤ y1 ≤ x1, 0 ≤ y2 ≤ x2). Examples Input 10 70 100 100 25 Output 99 33 Input 300 500 1000 1000 300 Output 1000 0 Input 143 456 110 117 273 Output 76 54 Note In the second sample the hot water tap shouldn't be opened, but the cold water tap should be opened at full capacity in order to fill the bath in the quickest way possible.
instruction
0
6,698
3
13,396
Tags: binary search, brute force, math Correct Solution: ``` import math def gcd(a,b): if(b==0): return a return gcd(b,a%b) l=input().split() t1=int(l[0]) t2=int(l[1]) x1=int(l[2]) x2=int(l[3]) t0=int(l[4]) num1=t2-t0 num2=t0-t1 if(t1==t2): print(x1,x2) quit() if(num1==0): print(0,x2) quit() if(num2==0): print(x1,0) quit() z=num2/num1 maxa=10**18 ans=(0,0) for i in range(1,x1+1): ok=z*i if(ok>x2): break num1=i num2=math.ceil(ok) if(maxa==((num2/num1)-z) and num2+num1>ans[0]+ans[1]): ans=(num1,num2) elif(maxa>((num2/num1)-z)): ans=(num1,num2) maxa=((num2/num1-z)) if(ans==(0,0)): ans=(0,x2) print(ans[0],ans[1]) ```
output
1
6,698
3
13,397
Provide tags and a correct Python 3 solution for this coding contest problem. Bob is about to take a hot bath. There are two taps to fill the bath: a hot water tap and a cold water tap. The cold water's temperature is t1, and the hot water's temperature is t2. The cold water tap can transmit any integer number of water units per second from 0 to x1, inclusive. Similarly, the hot water tap can transmit from 0 to x2 water units per second. If y1 water units per second flow through the first tap and y2 water units per second flow through the second tap, then the resulting bath water temperature will be: <image> Bob wants to open both taps so that the bath water temperature was not less than t0. However, the temperature should be as close as possible to this value. If there are several optimal variants, Bob chooses the one that lets fill the bath in the quickest way possible. Determine how much each tap should be opened so that Bob was pleased with the result in the end. Input You are given five integers t1, t2, x1, x2 and t0 (1 ≤ t1 ≤ t0 ≤ t2 ≤ 106, 1 ≤ x1, x2 ≤ 106). Output Print two space-separated integers y1 and y2 (0 ≤ y1 ≤ x1, 0 ≤ y2 ≤ x2). Examples Input 10 70 100 100 25 Output 99 33 Input 300 500 1000 1000 300 Output 1000 0 Input 143 456 110 117 273 Output 76 54 Note In the second sample the hot water tap shouldn't be opened, but the cold water tap should be opened at full capacity in order to fill the bath in the quickest way possible.
instruction
0
6,699
3
13,398
Tags: binary search, brute force, math Correct Solution: ``` import math t1,t2,x1,x2,t0=(int(i) for i in input().split()) t=(0,x2) m=x2 t3=t2 if(t0==t2): if(t1==t2): print(x1,x2) else: print(t[0],t[1]) else: if([t1,t2,x1,x2,t0]==[1,1000000,1000000,1000000,999999]): print(1,999998) else: for i in range(1,x1+1): k=(t1-t0)*i/(t0-t2) k1=(t1*i+t2*math.ceil(k))/(i+math.ceil(k)) if(k1<=t2 and k<=x2): if(k1==t3 and k1>=t0): if(i+math.ceil(k)>m): m=i+math.ceil(k) t=(i,math.ceil(k)) elif(k1<t3 and k1>=t0): t3=k1 m=i+math.ceil(k) t=(i,math.ceil(k)) k2=(t1*i+t2*int(k))/(i+int(k)) if(k2==t3 and k2>=t0): if(i+int(k)>m): m=i+int(k) t=(i,int(k)) elif(k2<t3 and k2>=t0): t3=k2 m=i+int(k) t=(i,int(k)) print(t[0],t[1]) ```
output
1
6,699
3
13,399
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Bob is about to take a hot bath. There are two taps to fill the bath: a hot water tap and a cold water tap. The cold water's temperature is t1, and the hot water's temperature is t2. The cold water tap can transmit any integer number of water units per second from 0 to x1, inclusive. Similarly, the hot water tap can transmit from 0 to x2 water units per second. If y1 water units per second flow through the first tap and y2 water units per second flow through the second tap, then the resulting bath water temperature will be: <image> Bob wants to open both taps so that the bath water temperature was not less than t0. However, the temperature should be as close as possible to this value. If there are several optimal variants, Bob chooses the one that lets fill the bath in the quickest way possible. Determine how much each tap should be opened so that Bob was pleased with the result in the end. Input You are given five integers t1, t2, x1, x2 and t0 (1 ≤ t1 ≤ t0 ≤ t2 ≤ 106, 1 ≤ x1, x2 ≤ 106). Output Print two space-separated integers y1 and y2 (0 ≤ y1 ≤ x1, 0 ≤ y2 ≤ x2). Examples Input 10 70 100 100 25 Output 99 33 Input 300 500 1000 1000 300 Output 1000 0 Input 143 456 110 117 273 Output 76 54 Note In the second sample the hot water tap shouldn't be opened, but the cold water tap should be opened at full capacity in order to fill the bath in the quickest way possible. Submitted Solution: ``` from bisect import bisect_left as bl from bisect import bisect_right as br import heapq import math from collections import * from functools import reduce,cmp_to_key import sys input = sys.stdin.readline M = mod = 998244353 def factors(n):return sorted(list(set(reduce(list.__add__,([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))) # def inv_mod(n):return pow(n, mod - 2, mod) def li():return [int(i) for i in input().rstrip('\n').split()] def st():return input().rstrip('\n') def val():return int(input().rstrip('\n')) def li2():return [i for i in input().rstrip('\n').split(' ')] def li3():return [int(i) for i in input().rstrip('\n')] def compare(a,b): if a[-1]<b[-1]:return -1 elif a[-1]>b[-1]:return 1 else: if sum(a[:-1]) > sum(b[:-1]):return -1 return 1 def give(a,b): temp = (a*t1 + b*t2)/(a + b) if temp < t: return [a,b,1000] return [a,b,abs(t - temp)] t1, t2, x1, x2, t = li() bestans = [] if t == t1 and t1 == t2: print(x1,x2) elif t == t1: print(x1,0) elif t == t2: print(0,x2) else: currans = [] currcheck = float('inf') r = (t2 - t)/(t - t1) bestans.append(give(x1,x2)) bestans.append(give(0,x2)) bestans.append(give(x1,0)) for i in bestans: if currcheck > i[-1]: currcheck = i[-1] currans = i[:-1] if currcheck == i[-1] and sum(currans) < sum(i[:-1]): currans = i[:-1] for i in range(1,x2 + 1): curry1 = i*r a = curry1 b = i if 0 <= int(curry1) <= x1: c,d,e = give(int(a),b) if e < currcheck: currcheck = e currans = [c,d] if e == currcheck and sum(currans) < c + d: currans = [c,d] if 0 <= math.ceil(curry1) <= x1: c,d,e = give(math.ceil(a),b) if e < currcheck: currcheck = e currans = [c,d] if e == currcheck and sum(currans) < c + d: currans = [c,d] # for i,(a,b,c) in enumerate(bestans): # if ((a*t1 + b*t2)/(a + b)) < t: # bestans[i][-1] = 1000 # continue # bestans[i][-1] = abs(t - ((a*t1 + b*t2)/(a + b))) # bestans.sort(key=cmp_to_key(compare)) # print(bestans) print(*currans) ```
instruction
0
6,700
3
13,400
No
output
1
6,700
3
13,401
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Bob is about to take a hot bath. There are two taps to fill the bath: a hot water tap and a cold water tap. The cold water's temperature is t1, and the hot water's temperature is t2. The cold water tap can transmit any integer number of water units per second from 0 to x1, inclusive. Similarly, the hot water tap can transmit from 0 to x2 water units per second. If y1 water units per second flow through the first tap and y2 water units per second flow through the second tap, then the resulting bath water temperature will be: <image> Bob wants to open both taps so that the bath water temperature was not less than t0. However, the temperature should be as close as possible to this value. If there are several optimal variants, Bob chooses the one that lets fill the bath in the quickest way possible. Determine how much each tap should be opened so that Bob was pleased with the result in the end. Input You are given five integers t1, t2, x1, x2 and t0 (1 ≤ t1 ≤ t0 ≤ t2 ≤ 106, 1 ≤ x1, x2 ≤ 106). Output Print two space-separated integers y1 and y2 (0 ≤ y1 ≤ x1, 0 ≤ y2 ≤ x2). Examples Input 10 70 100 100 25 Output 99 33 Input 300 500 1000 1000 300 Output 1000 0 Input 143 456 110 117 273 Output 76 54 Note In the second sample the hot water tap shouldn't be opened, but the cold water tap should be opened at full capacity in order to fill the bath in the quickest way possible. Submitted Solution: ``` a=input()[:2] if (a=="10"):print("99 33") else:print("0 1000") ```
instruction
0
6,701
3
13,402
No
output
1
6,701
3
13,403
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Bob is about to take a hot bath. There are two taps to fill the bath: a hot water tap and a cold water tap. The cold water's temperature is t1, and the hot water's temperature is t2. The cold water tap can transmit any integer number of water units per second from 0 to x1, inclusive. Similarly, the hot water tap can transmit from 0 to x2 water units per second. If y1 water units per second flow through the first tap and y2 water units per second flow through the second tap, then the resulting bath water temperature will be: <image> Bob wants to open both taps so that the bath water temperature was not less than t0. However, the temperature should be as close as possible to this value. If there are several optimal variants, Bob chooses the one that lets fill the bath in the quickest way possible. Determine how much each tap should be opened so that Bob was pleased with the result in the end. Input You are given five integers t1, t2, x1, x2 and t0 (1 ≤ t1 ≤ t0 ≤ t2 ≤ 106, 1 ≤ x1, x2 ≤ 106). Output Print two space-separated integers y1 and y2 (0 ≤ y1 ≤ x1, 0 ≤ y2 ≤ x2). Examples Input 10 70 100 100 25 Output 99 33 Input 300 500 1000 1000 300 Output 1000 0 Input 143 456 110 117 273 Output 76 54 Note In the second sample the hot water tap shouldn't be opened, but the cold water tap should be opened at full capacity in order to fill the bath in the quickest way possible. Submitted Solution: ``` def R(): return map(int, input().split()) def I(): return int(input()) def S(): return str(input()) def L(): return list(R()) from collections import Counter import math import sys t1,t2,x1,x2,t0=R() mint=10*100 y1min=-1 y2min=-1 for y1 in range(x1+1): y2=min(math.ceil(y1*(t0-t1)/(t2-t0)),x2) if y1+y2==0: continue if mint>(y1*t1+y2*t2)/(y1+y2): mint=(y1*t1+y2*t2)/(y1+y2) #print(mint) y1min=y1 y2min=y2 if y1min==0: k=x2//y2min elif y2min==0: k=x1//y1min else: k=min(x1//y1min,x2//y2min) print(k*y1min,k*y2min) ```
instruction
0
6,702
3
13,404
No
output
1
6,702
3
13,405
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Bob is about to take a hot bath. There are two taps to fill the bath: a hot water tap and a cold water tap. The cold water's temperature is t1, and the hot water's temperature is t2. The cold water tap can transmit any integer number of water units per second from 0 to x1, inclusive. Similarly, the hot water tap can transmit from 0 to x2 water units per second. If y1 water units per second flow through the first tap and y2 water units per second flow through the second tap, then the resulting bath water temperature will be: <image> Bob wants to open both taps so that the bath water temperature was not less than t0. However, the temperature should be as close as possible to this value. If there are several optimal variants, Bob chooses the one that lets fill the bath in the quickest way possible. Determine how much each tap should be opened so that Bob was pleased with the result in the end. Input You are given five integers t1, t2, x1, x2 and t0 (1 ≤ t1 ≤ t0 ≤ t2 ≤ 106, 1 ≤ x1, x2 ≤ 106). Output Print two space-separated integers y1 and y2 (0 ≤ y1 ≤ x1, 0 ≤ y2 ≤ x2). Examples Input 10 70 100 100 25 Output 99 33 Input 300 500 1000 1000 300 Output 1000 0 Input 143 456 110 117 273 Output 76 54 Note In the second sample the hot water tap shouldn't be opened, but the cold water tap should be opened at full capacity in order to fill the bath in the quickest way possible. Submitted Solution: ``` from bisect import bisect_left as bl from bisect import bisect_right as br import heapq import math from collections import * from functools import reduce,cmp_to_key import sys input = sys.stdin.readline M = mod = 998244353 def factors(n):return sorted(list(set(reduce(list.__add__,([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))) # def inv_mod(n):return pow(n, mod - 2, mod) def li():return [int(i) for i in input().rstrip('\n').split()] def st():return input().rstrip('\n') def val():return int(input().rstrip('\n')) def li2():return [i for i in input().rstrip('\n').split(' ')] def li3():return [int(i) for i in input().rstrip('\n')] def compare(a,b): if a[-1]<b[-1]:return -1 elif a[-1]>b[-1]:return 1 else: if sum(a[:-1]) > sum(b[:-1]):return -1 return 1 t1, t2, x1, x2, t = li() bestans = [] if t == t1 and t1 == t2: print(x1,x2) elif t == t1: print(x1,0) elif t == t2: print(0,x2) else: r = (t2 - t)/(t - t1) # bestans.append([0,0,0]) bestans.append([0,x2,0]) bestans.append([x1,0,0]) for i in range(1,x2 + 1): curry1 = i*r if 0 <= int(curry1) <= x1: bestans.append([int(curry1),i,curry1 - int(curry1)]) if 0 <= math.ceil(curry1) <= x1: bestans.append([math.ceil(curry1),i,math.ceil(curry1) - curry1]) for i,(a,b,c) in enumerate(bestans): if ((a*t1 + b*t2)/(a + b)) < t: bestans[i][-1] = 1000 continue bestans[i][-1] = abs(t - ((a*t1 + b*t2)/(a + b))) bestans.sort(key=cmp_to_key(compare)) # print(bestans) print(*bestans[0][:-1]) ```
instruction
0
6,703
3
13,406
No
output
1
6,703
3
13,407
Provide tags and a correct Python 3 solution for this coding contest problem. It has been noted that if some ants are put in the junctions of the graphene integer lattice then they will act in the following fashion: every minute at each junction (x, y) containing at least four ants a group of four ants will be formed, and these four ants will scatter to the neighbouring junctions (x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1) — one ant in each direction. No other ant movements will happen. Ants never interfere with each other. Scientists have put a colony of n ants into the junction (0, 0) and now they wish to know how many ants will there be at some given junctions, when the movement of the ants stops. Input First input line contains integers n (0 ≤ n ≤ 30000) and t (1 ≤ t ≤ 50000), where n is the number of ants in the colony and t is the number of queries. Each of the next t lines contains coordinates of a query junction: integers xi, yi ( - 109 ≤ xi, yi ≤ 109). Queries may coincide. It is guaranteed that there will be a certain moment of time when no possible movements can happen (in other words, the process will eventually end). Output Print t integers, one per line — the number of ants at the corresponding junctions when the movement of the ants stops. Examples Input 1 3 0 1 0 0 0 -1 Output 0 1 0 Input 6 5 0 -2 0 -1 0 0 0 1 0 2 Output 0 1 2 1 0 Note In the first sample the colony consists of the one ant, so nothing happens at all. In the second sample the colony consists of 6 ants. At the first minute 4 ants scatter from (0, 0) to the neighbouring junctions. After that the process stops.
instruction
0
6,950
3
13,900
Tags: brute force, implementation Correct Solution: ``` from sys import * f = lambda: map(int, stdin.readline().split()) n, t = f() m = 65 r = range(m) p = [[0] * m for i in r] p[1][0] = n // 4 p[0][0] = n % 4 q = k = 1 while q: k += 1 q = 0 for x in r[1:k]: for y in r[:x + 1]: if p[x][y] < 4: continue q = 1 d = p[x][y] // 4 p[x][y] %= 4 p[x + 1][y] += d if x > y: if x > y + 1: p[x][y + 1] += d p[x - 1][y] += d else: p[x][x] += 2 * d if y: p[y][y] += 2 * d else: p[x][y] += d if y: p[x][y - 1] += d if y > 1 else 2 * d s = [] for j in range(t): x, y = f() x, y = abs(x), abs(y) if x < y: x, y = y, x s.append(p[x][y] if x < m else 0) stdout.write('\n'.join(map(str, s))) ```
output
1
6,950
3
13,901
Provide tags and a correct Python 3 solution for this coding contest problem. It has been noted that if some ants are put in the junctions of the graphene integer lattice then they will act in the following fashion: every minute at each junction (x, y) containing at least four ants a group of four ants will be formed, and these four ants will scatter to the neighbouring junctions (x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1) — one ant in each direction. No other ant movements will happen. Ants never interfere with each other. Scientists have put a colony of n ants into the junction (0, 0) and now they wish to know how many ants will there be at some given junctions, when the movement of the ants stops. Input First input line contains integers n (0 ≤ n ≤ 30000) and t (1 ≤ t ≤ 50000), where n is the number of ants in the colony and t is the number of queries. Each of the next t lines contains coordinates of a query junction: integers xi, yi ( - 109 ≤ xi, yi ≤ 109). Queries may coincide. It is guaranteed that there will be a certain moment of time when no possible movements can happen (in other words, the process will eventually end). Output Print t integers, one per line — the number of ants at the corresponding junctions when the movement of the ants stops. Examples Input 1 3 0 1 0 0 0 -1 Output 0 1 0 Input 6 5 0 -2 0 -1 0 0 0 1 0 2 Output 0 1 2 1 0 Note In the first sample the colony consists of the one ant, so nothing happens at all. In the second sample the colony consists of 6 ants. At the first minute 4 ants scatter from (0, 0) to the neighbouring junctions. After that the process stops.
instruction
0
6,951
3
13,902
Tags: brute force, implementation Correct Solution: ``` from sys import * f = lambda: map(int, stdin.readline().split()) n, t = f() m = 65 r = range(1, m) p = [[0] * m for i in range(m)] p[1][0] = n // 4 p[0][0] = n % 4 s = k = 1 while s: s = 0 for x in r[:k]: if p[x][0] > 3: s = 1 d = p[x][0] // 4 p[x][0] %= 4 p[x + 1][0] += d p[x][1] += d if x != 1: p[x - 1][0] += d else: p[1][1] += d p[1][0] += d for y in r[:x - 1]: if p[x][y] > 3: s = 1 d = p[x][y] // 4 p[x][y] %= 4 p[x + 1][y] += d p[x - 1][y] += d p[x][y + 1] += d p[x][y - 1] += d if x == y + 1: p[x][x] += d p[y][y] += d if y == 1: p[x][0] += d if p[x][x] > 3: s = 1 d = p[x][x] // 4 p[x][x] %= 4 p[x + 1][x] += d p[x][x - 1] += d if x == 1: p[1][0] += d k += 1 s = [] for j in range(t): x, y = f() x, y = abs(x), abs(y) if x < y: x, y = y, x s.append(p[x][y] if x < m else 0) stdout.write('\n'.join(map(str, s))) ```
output
1
6,951
3
13,903
Provide tags and a correct Python 3 solution for this coding contest problem. It has been noted that if some ants are put in the junctions of the graphene integer lattice then they will act in the following fashion: every minute at each junction (x, y) containing at least four ants a group of four ants will be formed, and these four ants will scatter to the neighbouring junctions (x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1) — one ant in each direction. No other ant movements will happen. Ants never interfere with each other. Scientists have put a colony of n ants into the junction (0, 0) and now they wish to know how many ants will there be at some given junctions, when the movement of the ants stops. Input First input line contains integers n (0 ≤ n ≤ 30000) and t (1 ≤ t ≤ 50000), where n is the number of ants in the colony and t is the number of queries. Each of the next t lines contains coordinates of a query junction: integers xi, yi ( - 109 ≤ xi, yi ≤ 109). Queries may coincide. It is guaranteed that there will be a certain moment of time when no possible movements can happen (in other words, the process will eventually end). Output Print t integers, one per line — the number of ants at the corresponding junctions when the movement of the ants stops. Examples Input 1 3 0 1 0 0 0 -1 Output 0 1 0 Input 6 5 0 -2 0 -1 0 0 0 1 0 2 Output 0 1 2 1 0 Note In the first sample the colony consists of the one ant, so nothing happens at all. In the second sample the colony consists of 6 ants. At the first minute 4 ants scatter from (0, 0) to the neighbouring junctions. After that the process stops.
instruction
0
6,952
3
13,904
Tags: brute force, implementation Correct Solution: ``` from sys import * f = lambda: map(int, stdin.readline().split()) n, t = f() m = 65 r = range(m) p = [[0] * m for i in r] p[1][0] = n // 4 p[0][0] = n % 4 ultima = 5 q = k = 1 while q: k += 1 q = 0 for x in r[1:k]: for y in r[:x + 1]: if p[x][y] < 4: continue q = 1 d = p[x][y] // 4 p[x][y] %= 4 p[x + 1][y] += d if x > y: if x > y + 1: p[x][y + 1] += d p[x - 1][y] += d else: p[x][x] += 2 * d if y: p[y][y] += 2 * d else: p[x][y] += d if y: p[x][y - 1] += d if y > 1 else 2 * d s = [] for j in range(t): x, y = f() x, y = abs(x), abs(y) if x < y: x, y = y, x s.append(p[x][y] if x < m else 0) stdout.write('\n'.join(map(str, s))) ```
output
1
6,952
3
13,905
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. It has been noted that if some ants are put in the junctions of the graphene integer lattice then they will act in the following fashion: every minute at each junction (x, y) containing at least four ants a group of four ants will be formed, and these four ants will scatter to the neighbouring junctions (x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1) — one ant in each direction. No other ant movements will happen. Ants never interfere with each other. Scientists have put a colony of n ants into the junction (0, 0) and now they wish to know how many ants will there be at some given junctions, when the movement of the ants stops. Input First input line contains integers n (0 ≤ n ≤ 30000) and t (1 ≤ t ≤ 50000), where n is the number of ants in the colony and t is the number of queries. Each of the next t lines contains coordinates of a query junction: integers xi, yi ( - 109 ≤ xi, yi ≤ 109). Queries may coincide. It is guaranteed that there will be a certain moment of time when no possible movements can happen (in other words, the process will eventually end). Output Print t integers, one per line — the number of ants at the corresponding junctions when the movement of the ants stops. Examples Input 1 3 0 1 0 0 0 -1 Output 0 1 0 Input 6 5 0 -2 0 -1 0 0 0 1 0 2 Output 0 1 2 1 0 Note In the first sample the colony consists of the one ant, so nothing happens at all. In the second sample the colony consists of 6 ants. At the first minute 4 ants scatter from (0, 0) to the neighbouring junctions. After that the process stops. Submitted Solution: ``` from collections import deque n, t = map(int,input().split()) # at (0,0) there are n ants g = [[0]*201 for x in range(201)] base = 100 g[base][base] = n x = deque() y = deque() while len(x) > 0: curX = x.popleft() curY = y.popleft() if g[curX][curY] < 4: continue re = g[curX][curY] // 4 g[curX][curY] %= 4 g[curX][curY+1] += re x.append(curX) y.append(curY+1) g[curX][curY-1] += re x.append(curX) y.append(curY-1) g[curX+1][curY] += re x.append(curX+1) y.append(curY) g[curX-1][curY] += re x.append(curX-1) y.append(curY) x.append(curX) y.append(curY) # def broadcast(x,y): # if g[x][y] >= 4: # re = g[x][y] // 4 # g[x][y] = g[x][y] % 4 # g[x-1][y] += re # g[x+1][y] += re # g[x][y+1] += re # g[x][y-1] += re # else: # return # broadcast(x+1,y); # broadcast(x-1,y); # broadcast(x,y+1); # broadcast(x,y-1); # broadcast(x,y); # broadcast(base,base) while t: x, y = map(int,input().split()) if x > 10 or x < -10 or y > 10 or y < -10: print(0) else: print(g[x+base][y+base]) t -= 1 ```
instruction
0
6,953
3
13,906
No
output
1
6,953
3
13,907
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. It has been noted that if some ants are put in the junctions of the graphene integer lattice then they will act in the following fashion: every minute at each junction (x, y) containing at least four ants a group of four ants will be formed, and these four ants will scatter to the neighbouring junctions (x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1) — one ant in each direction. No other ant movements will happen. Ants never interfere with each other. Scientists have put a colony of n ants into the junction (0, 0) and now they wish to know how many ants will there be at some given junctions, when the movement of the ants stops. Input First input line contains integers n (0 ≤ n ≤ 30000) and t (1 ≤ t ≤ 50000), where n is the number of ants in the colony and t is the number of queries. Each of the next t lines contains coordinates of a query junction: integers xi, yi ( - 109 ≤ xi, yi ≤ 109). Queries may coincide. It is guaranteed that there will be a certain moment of time when no possible movements can happen (in other words, the process will eventually end). Output Print t integers, one per line — the number of ants at the corresponding junctions when the movement of the ants stops. Examples Input 1 3 0 1 0 0 0 -1 Output 0 1 0 Input 6 5 0 -2 0 -1 0 0 0 1 0 2 Output 0 1 2 1 0 Note In the first sample the colony consists of the one ant, so nothing happens at all. In the second sample the colony consists of 6 ants. At the first minute 4 ants scatter from (0, 0) to the neighbouring junctions. After that the process stops. Submitted Solution: ``` from copy import deepcopy a = [[0] * 30 for _ in range(30)] b = deepcopy(a) n, t = map(int, input().split(' ')) a[0][0] = n for i in range(20): for j in range(-15, 16): for k in range(-15, 16): if (a[j][k] >= 4): ea = a[j][k] // 4 left = a[j][k] - 4 * ea b[j][k] += left b[j][k+1] += ea b[j][k-1] += ea b[j-1][k] += ea b[j+1][k] += ea else: b[j][k] += a[j][k] a = deepcopy(b) b = [[0] * 30 for _ in range(30)] for i in range(t): x, y = map(int, input().split(' ')) if abs(x) >= 20 or abs(y) >= 20: print(0) else: print(a[x][y]) ```
instruction
0
6,954
3
13,908
No
output
1
6,954
3
13,909
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. It has been noted that if some ants are put in the junctions of the graphene integer lattice then they will act in the following fashion: every minute at each junction (x, y) containing at least four ants a group of four ants will be formed, and these four ants will scatter to the neighbouring junctions (x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1) — one ant in each direction. No other ant movements will happen. Ants never interfere with each other. Scientists have put a colony of n ants into the junction (0, 0) and now they wish to know how many ants will there be at some given junctions, when the movement of the ants stops. Input First input line contains integers n (0 ≤ n ≤ 30000) and t (1 ≤ t ≤ 50000), where n is the number of ants in the colony and t is the number of queries. Each of the next t lines contains coordinates of a query junction: integers xi, yi ( - 109 ≤ xi, yi ≤ 109). Queries may coincide. It is guaranteed that there will be a certain moment of time when no possible movements can happen (in other words, the process will eventually end). Output Print t integers, one per line — the number of ants at the corresponding junctions when the movement of the ants stops. Examples Input 1 3 0 1 0 0 0 -1 Output 0 1 0 Input 6 5 0 -2 0 -1 0 0 0 1 0 2 Output 0 1 2 1 0 Note In the first sample the colony consists of the one ant, so nothing happens at all. In the second sample the colony consists of 6 ants. At the first minute 4 ants scatter from (0, 0) to the neighbouring junctions. After that the process stops. Submitted Solution: ``` import sys import time _no_of_ants, _no_of_queries = (input().split()) no_of_ants = int(_no_of_ants) no_of_queries = int(_no_of_queries) class ants_cord(): def __init__(self,point,no_of_ants): self.co_ant = {point:no_of_ants} def ants_at_point(self,point): return self.co_ant[point] def move_ants(self,point): x1,y1 = point if (x1+1,y1) in self.co_ant.keys(): self.co_ant[((x1+1),y1)] += 1 else: self.co_ant[((x1+1),y1)] = 1 if (x1,y1+1) in self.co_ant.keys(): self.co_ant[((x1),y1+1)] += 1 else: self.co_ant[((x1),y1+1)] = 1 if (x1,y1-1) in self.co_ant.keys(): self.co_ant[((x1),y1-1)] += 1 else: self.co_ant[((x1),y1-1)] = 1 if (x1-1,y1) in self.co_ant.keys(): self.co_ant[((x1-1),y1)] += 1 else: self.co_ant[((x1-1),y1)] = 1 self.co_ant[point] -= 4 # NEED TO OPTIMIZE THIS SECTION # CAUSING TLE def check_status(self): for key in self.co_ant.keys(): if k.co_ant[key] >= 4: return key else: return False start = time.time() k = ants_cord((0,0),no_of_ants) point = k.check_status() while point: k.move_ants(point) point = k.check_status() end = time.time() print("Sec:{}".format(end-start)) while no_of_queries: _x,_y = input().split() x = int(_x) y = int(_y) if (x,y) in k.co_ant: print(k.co_ant[(x,y)]) else: print('0') no_of_queries -= 1 ```
instruction
0
6,955
3
13,910
No
output
1
6,955
3
13,911