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Provide tags and a correct Python 3 solution for this coding contest problem. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins.
instruction
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Tags: bitmasks, constructive algorithms, dp, games, greedy, math Correct Solution: ``` import sys import math from collections import defaultdict import heapq def getnum(num): cnt=0 ans=0 while((1<<cnt)<=num): ans=cnt cnt+=1 if num==0: return 0 return ans+1 t=int(sys.stdin.readline()) for _ in range(t): n=int(sys.stdin.readline()) arr=list(map(int,sys.stdin.readline().split())) mp=[[] for x in range(31)] last=[] for i in range(n): x=getnum(arr[i]) mp[x].append(arr[i]) last.append(x) last.sort() rem=n z=True for i in range(30,0,-1): if len(mp[i])!=0: y=len(mp[i]) rem=n-y if y==1: z=False print('WIN') break if y%2!=0: if rem%2==0: first=(y+1)//2 second=y//2 if first%2!=0: print('WIN') else: print('LOSE') z=False break if rem%2!=0: print('WIN') z=False break else: for j in range(y): mp[i][j]%=(1<<(i-1)) x=getnum(mp[i][j]) mp[x].append(mp[i][j]) else: continue if z: print('DRAW') ```
output
1
6,764
19
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Provide tags and a correct Python 3 solution for this coding contest problem. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins.
instruction
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6,765
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Tags: bitmasks, constructive algorithms, dp, games, greedy, math Correct Solution: ``` from __future__ import division, print_function import os,sys from io import BytesIO, IOBase if sys.version_info[0] < 3: from __builtin__ import xrange as range from future_builtins import ascii, filter, hex, map, oct, zip from bisect import bisect_left as lower_bound, bisect_right as upper_bound def so(): return int(input()) def st(): return input() def mj(): return map(int,input().strip().split(" ")) def msj(): return map(str,input().strip().split(" ")) def le(): return list(map(int,input().split())) def lebe():return list(map(int, input())) def dmain(): sys.setrecursionlimit(1000000) threading.stack_size(1024000) thread = threading.Thread(target=main) thread.start() def joro(L): return(''.join(map(str, L))) def decimalToBinary(n): return bin(n).replace("0b","") def isprime(n): for i in range(2,int(n**0.5)+1): if n%i==0: return False return True def read(): sys.stdin = open('input.txt', 'r') sys.stdout = open('output.txt', 'w') def tr(n): return n*(n+1)//2 def iu(): m=so() L=le() i=30 while(i>=0): c=0 for j in range(m): c=c+((L[j]//(2**i))&1) if(c%4==1): print("WIN") return elif(m%2!=0 and c%2!=0): print("LOSE") return elif(1==c%2): print("WIN") return i=i-1 print("DRAW") return def main(): for i in range(so()): iu() # region fastio # template taken from https://github.com/cheran-senthil/PyRival/blob/master/templates/template.py BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") def print(*args, **kwargs): """Prints the values to a stream, or to sys.stdout by default.""" sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout) at_start = True for x in args: if not at_start: file.write(sep) file.write(str(x)) at_start = False file.write(kwargs.pop("end", "\n")) if kwargs.pop("flush", False): file.flush() if sys.version_info[0] < 3: sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout) else: sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # endregion if __name__ == "__main__": #read() main() #dmain() # Comment Read() ```
output
1
6,765
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13,531
Provide tags and a correct Python 3 solution for this coding contest problem. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins.
instruction
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Tags: bitmasks, constructive algorithms, dp, games, greedy, math Correct Solution: ``` ''' Auther: ghoshashis545 Ashis Ghosh College: jalpaiguri Govt Enggineering College ''' from os import path import sys from heapq import heappush,heappop,heapify from functools import cmp_to_key as ctk from collections import deque,defaultdict as dd from bisect import bisect,bisect_left,bisect_right,insort,insort_left,insort_right from itertools import permutations from datetime import datetime from math import ceil,sqrt,log,gcd def ii():return int(input()) def si():return input().rstrip() def mi():return map(int,input().split()) def li():return list(mi()) abc='abcdefghijklmnopqrstuvwxyz' mod=1000000007 # mod=998244353 inf = float("inf") vow=['a','e','i','o','u'] dx,dy=[-1,1,0,0],[0,0,1,-1] def bo(i): return ord(i)-ord('a') file=1 def solve(): for _ in range(ii()): n=ii() a=li() x=0 for i in a: x^=i if(x==0): print("DRAW") continue for i in range(30,-1,-1): if x>>i&1: one=0 zero=0 for j in a: if j>>i&1: one+=1 else: zero+=1 # if ith bit of even number element are not set # then her best friend forced Koa to chose (x*2 + 2)[x=one//4] no of elements # whose ith bit is set then Koa score ith bit will not set but her best # friend select (x*2 + 1) no of elements so her bestfriend score ith bit # will set. So,koa will lose. if(zero%2==0 and one%4==3): print('LOSE') else: print('WIN') break if __name__ =="__main__": if(file): if path.exists('input.txt'): sys.stdin=open('input.txt', 'r') sys.stdout=open('output.txt','w') else: input=sys.stdin.readline solve() ```
output
1
6,766
19
13,533
Provide tags and a correct Python 3 solution for this coding contest problem. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins.
instruction
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Tags: bitmasks, constructive algorithms, dp, games, greedy, math Correct Solution: ``` import sys input = sys.stdin.readline for _ in range(int(input())): n = int(input()) a = list(map(int, input().split())) ones = [0]*40 for i in range(40): for ai in a: ones[i] += (ai>>i)&1 for i in range(39, -1, -1): if ones[i]%2==0: continue else: if ones[i]%4==3 and (n-ones[i])%2==0: print('LOSE') else: print('WIN') break else: print('DRAW') ```
output
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13,535
Provide tags and a correct Python 3 solution for this coding contest problem. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins.
instruction
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Tags: bitmasks, constructive algorithms, dp, games, greedy, math Correct Solution: ``` for _ in range(int(input())): n=int(input()) a=[int(o) for o in input().split()] ones=[0]*35 zeros= [0]*35 for i in a: ba=bin(i)[2:][::-1] j=-1 for k in ba: if k=='1': ones[j]+=1 else: zeros[j]+=1 j-=1 res="DRAW" # print(ones) for i in range(35): if ones[i]%2!=0: if ones[i]%4==3 and (n-ones[i])%2==0: res="LOSE" else: res="WIN" break print(res) ```
output
1
6,768
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13,537
Provide tags and a correct Python 3 solution for this coding contest problem. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins.
instruction
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Tags: bitmasks, constructive algorithms, dp, games, greedy, math Correct Solution: ``` def solve(): n = int(input()) lst = list(map(int,input().split())) k = 1 while k < 10**9: k *= 2 num = 0 while k and num % 2 == 0: num = 0 for i in lst: if i % (k * 2) // k == 1: num += 1 k //= 2 if k == 0 and num % 2 == 0: print("DRAW") return 0 if (num % 4 == 1) or (n % 2 == 0): print("WIN") else: print("LOSE") for i in range(int(input())): solve() ```
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. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins. Submitted Solution: ``` d = {1:'WIN', 0:'LOSE', -1:'DRAW'} t=int(input()) for _ in range(t): n = int(input()) a = [int(x) for x in input().split()] f = [0] * 30 for x in a: for b in range(30): if (x >> b) & 1: f[b] += 1 ans = -1 for b in reversed(range(30)): if f[b] % 2 == 1: ans = 0 if f[b] % 4 == 3 and (n - f[b]) % 2 == 0 else 1 break print(d[ans]) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins. Submitted Solution: ``` import sys,os,io input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline for _ in range (int(input())): n = int(input()) a = [int(i) for i in input().split()] cnt = [0]*35 for i in a: bi = bin(i)[2:][::-1] for j in range (len(bi)): if bi[j]=='1': cnt[j]+=1 ans = "DRAW" for i in range (34,-1,-1): if cnt[i]%4==1 or (cnt[i]%4==3 and not n%2): ans = "WIN" break if cnt[i]%4==3: ans = "LOSE" break print(ans) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins. Submitted Solution: ``` from bisect import * from collections import * from math import gcd,ceil,sqrt,floor,inf from heapq import * from itertools import * from operator import add,mul,sub,xor,truediv,floordiv from functools import * #------------------------------------------------------------------------ import os import sys from io import BytesIO, IOBase # region fastio BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") #------------------------------------------------------------------------ def RL(): return map(int, sys.stdin.readline().rstrip().split()) def RLL(): return list(map(int, sys.stdin.readline().rstrip().split())) def N(): return int(input()) #------------------------------------------------------------------------ from types import GeneratorType def bootstrap(f, stack=[]): def wrappedfunc(*args, **kwargs): if stack: return f(*args, **kwargs) else: to = f(*args, **kwargs) while True: if type(to) is GeneratorType: stack.append(to) to = next(to) else: stack.pop() if not stack: break to = stack[-1].send(to) return to return wrappedfunc farr=[1] ifa=[] def fact(x,mod=0): if mod: while x>=len(farr): farr.append(farr[-1]*len(farr)%mod) else: while x>=len(farr): farr.append(farr[-1]*len(farr)) return farr[x] def ifact(x,mod): global ifa ifa.append(pow(farr[-1],mod-2,mod)) for i in range(x,0,-1): ifa.append(ifa[-1]*i%mod) ifa=ifa[::-1] def per(i,j,mod=0): if i<j: return 0 if not mod: return fact(i)//fact(i-j) return farr[i]*ifa[i-j]%mod def com(i,j,mod=0): if i<j: return 0 if not mod: return per(i,j)//fact(j) return per(i,j,mod)*ifa[j]%mod def catalan(n): return com(2*n,n)//(n+1) def linc(f,t,l,r): while l<r: mid=(l+r)//2 if t>f(mid): l=mid+1 else: r=mid return l def rinc(f,t,l,r): while l<r: mid=(l+r+1)//2 if t<f(mid): r=mid-1 else: l=mid return l def ldec(f,t,l,r): while l<r: mid=(l+r)//2 if t<f(mid): l=mid+1 else: r=mid return l def rdec(f,t,l,r): while l<r: mid=(l+r+1)//2 if t>f(mid): r=mid-1 else: l=mid return l def isprime(n): for i in range(2,int(n**0.5)+1): if n%i==0: return False return True def binfun(x): c=0 for w in arr: c+=ceil(w/x) return c def lowbit(n): return n&-n def inverse(a,m): a%=m if a<=1: return a return ((1-inverse(m,a)*m)//a)%m class BIT: def __init__(self,arr): self.arr=arr self.n=len(arr)-1 def update(self,x,v): while x<=self.n: self.arr[x]+=v x+=x&-x def query(self,x): ans=0 while x: ans+=self.arr[x] x&=x-1 return ans ''' class SMT: def __init__(self,arr): self.n=len(arr)-1 self.arr=[0]*(self.n<<2) self.lazy=[0]*(self.n<<2) def Build(l,r,rt): if l==r: self.arr[rt]=arr[l] return m=(l+r)>>1 Build(l,m,rt<<1) Build(m+1,r,rt<<1|1) self.pushup(rt) Build(1,self.n,1) def pushup(self,rt): self.arr[rt]=self.arr[rt<<1]+self.arr[rt<<1|1] def pushdown(self,rt,ln,rn):#lr,rn表区间数字数 if self.lazy[rt]: self.lazy[rt<<1]+=self.lazy[rt] self.lazy[rt<<1|1]=self.lazy[rt] self.arr[rt<<1]+=self.lazy[rt]*ln self.arr[rt<<1|1]+=self.lazy[rt]*rn self.lazy[rt]=0 def update(self,L,R,c,l=1,r=None,rt=1):#L,R表示操作区间 if r==None: r=self.n if L<=l and r<=R: self.arr[rt]+=c*(r-l+1) self.lazy[rt]+=c return m=(l+r)>>1 self.pushdown(rt,m-l+1,r-m) if L<=m: self.update(L,R,c,l,m,rt<<1) if R>m: self.update(L,R,c,m+1,r,rt<<1|1) self.pushup(rt) def query(self,L,R,l=1,r=None,rt=1): if r==None: r=self.n #print(L,R,l,r,rt) if L<=l and R>=r: return self.arr[rt] m=(l+r)>>1 self.pushdown(rt,m-l+1,r-m) ans=0 if L<=m: ans+=self.query(L,R,l,m,rt<<1) if R>m: ans+=self.query(L,R,m+1,r,rt<<1|1) return ans ''' class DSU:#容量+路径压缩 def __init__(self,n): self.c=[-1]*n def same(self,x,y): return self.find(x)==self.find(y) def find(self,x): if self.c[x]<0: return x self.c[x]=self.find(self.c[x]) return self.c[x] def union(self,u,v): u,v=self.find(u),self.find(v) if u==v: return False if self.c[u]<self.c[v]: u,v=v,u self.c[u]+=self.c[v] self.c[v]=u return True def size(self,x): return -self.c[self.find(x)] class UFS:#秩+路径 def __init__(self,n): self.parent=[i for i in range(n)] self.ranks=[0]*n def find(self,x): if x!=self.parent[x]: self.parent[x]=self.find(self.parent[x]) return self.parent[x] def union(self,u,v): pu,pv=self.find(u),self.find(v) if pu==pv: return False if self.ranks[pu]>=self.ranks[pv]: self.parent[pv]=pu if self.ranks[pv]==self.ranks[pu]: self.ranks[pu]+=1 else: self.parent[pu]=pv def Prime(n): c=0 prime=[] flag=[0]*(n+1) for i in range(2,n+1): if not flag[i]: prime.append(i) c+=1 for j in range(c): if i*prime[j]>n: break flag[i*prime[j]]=prime[j] if i%prime[j]==0: break return prime def dij(s,graph): d={} d[s]=0 heap=[(0,s)] seen=set() while heap: dis,u=heappop(heap) if u in seen: continue for v in graph[u]: if v not in d or d[v]>d[u]+graph[u][v]: d[v]=d[u]+graph[u][v] heappush(heap,(d[v],v)) return d def GP(it): return [(ch,len(list(g))) for ch,g in groupby(it)] class DLN: def __init__(self,val): self.val=val self.pre=None self.next=None t=N() for i in range(t): n=N() a=RLL() res=0 for x in a: res^=x if res==0: ans='DRAW' else: k=0 while res: res>>=1 k+=1 k-=1 c=0 for x in a: if x&(1<<k): c+=1 c//=2 #print(c) if c&1: if n&1: ans='LOSE' else: ans="WIN" else: ans="WIN" print(ans) ''' sys.setrecursionlimit(200000) import threading threading.stack_size(10**8) t=threading.Thread(target=main) t.start() t.join() ''' ```
instruction
0
6,772
19
13,544
Yes
output
1
6,772
19
13,545
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins. Submitted Solution: ``` d = { 1: 'WIN', 0: 'LOSE', -1: 'DRAW' } t = int(input()) for _ in range(t): n = int(input()) a = map(int, input().split()) f = [0] * 30 for x in a: for b in range(30): if x >> b & 1: f[b] += 1 ans = -1 for x in reversed(range(30)): if f[x] % 2 == 1: ans = 0 if f[x] % 4 == 3 and (n - f[x]) % 2 == 0 else 1 break print(d[ans]) ```
instruction
0
6,773
19
13,546
Yes
output
1
6,773
19
13,547
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins. Submitted Solution: ``` def run(n, a): for i in range(30, -1, -1): count = 0 for j in range(n): count += (a[j] >> i) & 1 if count == 1: return 'WIN' elif count % 2 == 1 and n % 2 == 1: return 'LOSE' elif count % 2 == 0: return 'WIN' return 'DRAW' def main(): t = int(input()) for _ in range(t): n = int(input()) a = list(map(int, input().split())) ans = run(n, a) print(ans) if __name__ == '__main__': main() ```
instruction
0
6,774
19
13,548
No
output
1
6,774
19
13,549
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins. Submitted Solution: ``` n=int(input()) l=list(map(int,input().split())) for i in range(30,-1,-1): cnt=0 for j in l: if j&(1<<i): cnt+=1 if cnt%4==1 or (n-cnt)&1: print("WIN") quit() elif cnt%4==3: print("LOSE") quit() print("DRAW") ```
instruction
0
6,775
19
13,550
No
output
1
6,775
19
13,551
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins. Submitted Solution: ``` for _ in range(int(input())): n=input() a=[int(o) for o in input().split()] ones=[0]*31 zeros= [0]*31 for i in a: ba=bin(i)[2:][::-1] j=-1 for k in ba: if k=='1': ones[j]+=1 else: zeros[j]+=1 j-=1 res="DEAW" for i in range(31): if ones[i]%2!=0: if ones[i]%4==3 and zeros[i]%2==0: res="LOSE" else: res="WIN" break print(res) ```
instruction
0
6,776
19
13,552
No
output
1
6,776
19
13,553
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Koa the Koala and her best friend want to play a game. The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts. Let's describe a move in the game: * During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player. More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Note that after a move element y is removed from a. * The game ends when the array is empty. At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw. If both players play optimally find out whether Koa will win, lose or draw the game. Input Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows. The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a. The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a. It is guaranteed that the sum of n over all test cases does not exceed 10^5. Output For each test case print: * WIN if Koa will win the game. * LOSE if Koa will lose the game. * DRAW if the game ends in a draw. Examples Input 3 3 1 2 2 3 2 2 3 5 0 0 0 2 2 Output WIN LOSE DRAW Input 4 5 4 1 5 1 3 4 1 0 1 6 1 0 2 5 4 Output WIN WIN DRAW WIN Note In testcase 1 of the first sample we have: a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins. Submitted Solution: ``` def run(n, a): for i in range(30, -1, -1): count = 0 for j in range(n): count += (a[j] >> i) & 1 if count == 1: return 'WIN' elif count % 2 == 1 and n % 2 == 1: return 'LOSE' elif count % 2 == 1: return 'WIN' return 'DRAW' def main(): t = int(input()) for _ in range(t): n = int(input()) a = list(map(int, input().split())) ans = run(n, a) print(ans) if __name__ == '__main__': main() ```
instruction
0
6,777
19
13,554
No
output
1
6,777
19
13,555
Provide tags and a correct Python 3 solution for this coding contest problem. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games.
instruction
0
6,794
19
13,588
Tags: greedy, implementation, sortings Correct Solution: ``` for t in range(int(input())): n,k=map(int,input().split()) s=input() if k>=n: print(n*2-1) continue l=0 inter=[] count=0 out=0 for i in s: if i=='L': l+=1 count+=1 else: if count!=0: inter.append(count) out+=1 else: out+=2 count=0 if s[0]=='W': out-=1 elif inter: inter.pop(0) if l<=k: print(n*2-1) elif l==n and k!=0: print(k*2-1) else: r=n-l inter.sort() for i in inter: if k>=i: out+=i*2+1 k-=i else: out+=k*2 k=0 break out+=k*2 print(out) ```
output
1
6,794
19
13,589
Provide tags and a correct Python 3 solution for this coding contest problem. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games.
instruction
0
6,795
19
13,590
Tags: greedy, implementation, sortings Correct Solution: ``` for _ in " "*int(input()): n,k=map(int,input().split()) s=list(input()) if "W" not in s: print(max((min(k,n)*2)-1,0)) elif k >= s.count("L"): print((n*2)-1) else: cnt,sm,ind=list(),s.count("W"),s.index("W") for i in range(ind+1,n): if s[i] == "W": cnt.append(i-ind-1) ind=i cnt.sort() for i in cnt: if k >= i: sm+=(2*i)+1 k-=i else: break; if k>0: sm+=(2*k) print(sm) ```
output
1
6,795
19
13,591
Provide tags and a correct Python 3 solution for this coding contest problem. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games.
instruction
0
6,796
19
13,592
Tags: greedy, implementation, sortings Correct Solution: ``` for _ in range(int(input())): n, k = map(int, input().split()) x = 1 X = [] ans = 0 y = 0 for s in input(): if s == 'W': y = 1 if x: X += [x] ans += 1 x = 0 else: ans += 2 else: x += 1 if y == 0: print(max(min(k, n) * 2 - 1, 0)) continue if x: X += [x + 10 ** 8] X[0] += 99999999 X.sort() X.reverse() while k > 0 and X: x = X.pop() if x >= 10 ** 7: x -= 10 ** 8 ans += 2 * min(x, k) k -= min(x, k) elif x > k: ans += 2 * k break else: ans += 2 * x + 1 k -= x print(ans) ```
output
1
6,796
19
13,593
Provide tags and a correct Python 3 solution for this coding contest problem. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games.
instruction
0
6,797
19
13,594
Tags: greedy, implementation, sortings Correct Solution: ``` nums = int(input().strip()) for _ in range(nums): n,k = map(int,input().strip().split()) s = input().strip() lw,rw = s.find("W"),s.rfind("W") res = cur_num = 0 if lw==rw: if lw==-1: res = 2*k-1 else: res = 2*k+1 res = min(2*len(s)-1,res) else: part = [] for i in range(lw,rw+1): if s[i]=="W": if i>lw and s[i-1]=="L": part.append(cur_num) cur_num = 0 if i>lw and s[i-1]=="W": res+=2 else: res+=1 else: cur_num+=1 if k>=(sum(part)+lw+len(s)-rw-1): res = 2*len(s)-1 else: part.sort() for i in range(len(part)): if k>=part[i]: res+=2*part[i]+1 k-=part[i] else: break res+=2*k print(max(res,0)) ```
output
1
6,797
19
13,595
Provide tags and a correct Python 3 solution for this coding contest problem. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games.
instruction
0
6,798
19
13,596
Tags: greedy, implementation, sortings Correct Solution: ``` for _ in range(int(input())): n,k=map(int,input().split()) s=input() s=list(s) cw=0 w=[] idx=-1 cl=0 fw=-1 lw=-1 ans = 0 for i in range(n): if(s[i]=='W'): if(i>0 and s[i-1]=='W'): ans+=2 else: ans+=1 if(fw==-1): fw=i lw=i cw+=1 if(idx!=-1): if(i-idx-1): w.append(i-idx-1) idx=i else: cl+=1 w.sort() for i in w: if(k==0): break if(i<=k): k-=i ans+=2*(i-1)+3 else: ans+=2*(k) k -= k if(k>0): if(k>=cl): ans=1+(n-1)*2 else: if(cw==0): if(k>=n): ans = 1 + (n - 1) * 2 k=0 else: ans=1+(k-1)*2 k=0 else: for i in range(lw+1,n): if(k==0): break ans+=2 k-=1 if(k>0): for i in range(fw-1,-1,-1): if(k==0): break ans+=2 k-=1 print(ans) ```
output
1
6,798
19
13,597
Provide tags and a correct Python 3 solution for this coding contest problem. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games.
instruction
0
6,799
19
13,598
Tags: greedy, implementation, sortings Correct Solution: ``` I=input for _ in[0]*int(I()): n,k=map(int,I().split());s=I();c=s.count('W');n=min(n,c+k);a=sorted(map(len,filter(None,s.strip('L').split('W')))) while a and c+a[0]<=n:c+=a.pop(0) print((2*n-len(a)or 1)-1) ```
output
1
6,799
19
13,599
Provide tags and a correct Python 3 solution for this coding contest problem. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games.
instruction
0
6,800
19
13,600
Tags: greedy, implementation, sortings Correct Solution: ``` def score(a,n): score = 0 if a[0]=='L' else 1 for i in range(1,n): if a[i]==a[i-1] =='W': score+=2 elif a[i]=='W': score+=1 return score t = int(input()) for _ in range(t): n,k = map(int,input().split()) s = input() mylist = [] x = 0 while(x<n and s[x]=='L'): x+=1 count = 0 while(x<n): if(s[x]=='W'): if count!=0: mylist.append(count) count=0 else: count+=1 x+=1 mylist.sort() ans = 0 for i in mylist: k-=i if k==0: ans+= 2*i + 1 break elif k>0: ans+=2*i+1 else: ans+=2*i break counter = 0 while(counter<n and s[counter]=='L'): counter+=1 scounter = 0 while( scounter<n and s[n-1-scounter]=='L' ): scounter+=1 ans+=score(s,n) if ans==0 and k>0: ans-=1 if k<=(scounter+counter): ans+=2*k else: ans+=2*(scounter+counter) # print("ans",ans) print(ans) ```
output
1
6,800
19
13,601
Provide tags and a correct Python 3 solution for this coding contest problem. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games.
instruction
0
6,801
19
13,602
Tags: greedy, implementation, sortings Correct Solution: ``` t = int(input()) for it in range(0, t): n, k = tuple(list(map(int, input().split(' ')))) results = [char for char in input()] initial_score = 0 loss_amount = 0 for i in range(0, len(results)): if i > 0 and results[i] == 'W' and results[i - 1] == 'W': initial_score += 1 if results[i] == 'L': loss_amount += 1 k = min(k, loss_amount) initial_score += (n - loss_amount) streak_increase_added_score = 2 * k if loss_amount == n and streak_increase_added_score > 0: streak_increase_added_score -= 1 streak_diffs = [] current_streak_diff = 0 streak_found = 0 for i in range(0, n): if results[i] == 'W': streak_found = True if current_streak_diff != 0: streak_diffs.append(current_streak_diff) current_streak_diff = 0 if results[i] == 'L' and streak_found: current_streak_diff += 1 sorted_streak_diffs = sorted(streak_diffs) disjoint_streak_decrease_added_score = 0 for i in range(0, len(sorted_streak_diffs)): if k >= sorted_streak_diffs[i]: disjoint_streak_decrease_added_score += 1 k -= sorted_streak_diffs[i] else: break final_score = (initial_score + streak_increase_added_score + disjoint_streak_decrease_added_score) print(final_score) ```
output
1
6,801
19
13,603
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games. Submitted Solution: ``` import sys input=sys.stdin.readline t=int(input()) for i in range(t): n,k=map(int,input().split()) state=input() state=[i for i in state] ans,prev=0,0 store=[] if state[0]=='W': rang=[-1] else: rang=[] for i in range(len(state)): if state[i]=='W': if len(rang)==1: if rang[0]==i-1: rang=[i] else: store.append((i-rang[0]-1,rang[0]+1,i)) rang=[i] else: rang=[i] last=(rang[0] if rang else 0) store.sort() if k>0: for i in store: for j in range(i[1],i[2]): state[j]='W' k-=1 if k==0: break if k==0: break if k>0: for i in range(last+1,len(state)): if state[i]=='L' : state[i]='W' k-=1 if k==0: break if k>0: for i in range(len(state)-1,-1,-1): if state[i]=='L' : state[i]='W' k-=1 if k==0: break if state[0]=='W': ans=1 else: ans=0 for i in range(1,len(state)): if state[i]=='W': if state[i-1]=='W': ans+=2 else: ans+=1 sys.stdout.write(str(ans)+'\n') ```
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. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games. Submitted Solution: ``` def solve(): n, k = map(int, input().split()) A = input() segs = [] s, t = 0, 0 while s < n and A[s] == 'L': s += 1 head = (0, s) nn = n while nn >= 1 and A[nn - 1] == 'L': nn -= 1 tail = (nn, n) while s < nn: if A[s] == 'W': s += 1 continue t = s while t < nn and A[t] == 'L': t += 1 segs.append((s, t)) s = t segs.sort(key=lambda x: x[1] - x[0]) B = list(A) for (s, t) in segs: if k <= 0: break w = min(t - s, k) B[s:s+w] = 'W' * w k -= w if k > 0 and tail[0] != n: s, t = tail w = min(t - s, k) B[s:s+w] = 'W' * w k -= w if k > 0 and head[1] > 0: s, t = head w = min(t - s, k) B[t - w: t] = 'W' * w k -= w score = 0 for i in range(n): if i >= 1 and B[i - 1] == 'W' and B[i] == 'W': score += 2 continue if B[i] == 'W': score += 1 continue return score TC = int(input()) for _ in range(TC): print(solve()) ```
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. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games. Submitted Solution: ``` for i in range(int(input())): n, k = map(int, input().split()) s = input() wins = s.count('W') + k if wins >= n: print(2 * n - 1) else: streaks = int(s[0] == 'W') + s.count('LW') or int(wins > 0) gaps = s.strip('L').replace('W', ' ').strip().split() for g in sorted(map(len, gaps)): if g > k: break k -= g streaks -= 1 print(wins * 2 - streaks) ```
instruction
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6,804
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13,608
Yes
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1
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19
13,609
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games. Submitted Solution: ``` from itertools import groupby for _ in range(int(input())): n, k = map(int, input().split()) s = input() if k >= s.count('L'): print(n * 2 - 1) else: s = s.strip("L") group = [] for i, g in groupby(s): if i == 'L': group.append(len(list(g))) group.sort() i, m = 0, len(group) r = k while i < m and r >= group[i]: r -= group[i] i += 1 ans = (s.count('W') + k) * 2 - (m + 1 - i) print(max(0, ans)) ```
instruction
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6,805
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13,610
Yes
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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. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games. Submitted Solution: ``` import os import sys from io import BytesIO, IOBase import math from itertools import permutations from decimal import * getcontext().prec = 25 MOD = pow(10, 9) + 7 BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # n, k = map(int, input().split(" ")) # l = list(map(int, input().split(" "))) for _ in range(int(input())): n, k = map(int, input().split(" ")) l = input() if n == k: print(2 * k - 1) else: t = 0 z = [] w = False le = pre = 0 for i in range(n): if l[i] == "L": pre += 1 else: break start = max(1, pre) if l[0]=="W": t+=1 for i in range(start, n): if l[i] == "W": w=True if le: z.append(le) le = 0 if l[i - 1] == "W": t += 2 else: t += 1 if l[i] == "L": le += 1 extra = le z.sort() if k == 0: print(t) elif not extra and not z: if not w: print(2*k -1) else: print(2*k+1) elif not z: t += 2 * (min(pre, k)) k = max(0, k - pre) t += 2 * (min(k, extra)) print(t) elif z: for i in range(len(z)): if z[i] <= k: k -= z[i] t += 2 * z[i] + 1 else: t += 2 * k k = 0 break if k: t += 2 * (min(pre, k)) k = max(0, k - pre) t += 2 * (min(k, extra)) print(t) ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games. Submitted Solution: ``` test_cases = int(input()) for i in range(0, test_cases): stats = [int(x) for x in input().split()] record = str(input()) g = stats[0] c = stats[1] score = 0 des = [] #irability indices = {} # of desirable locations indices[1] = [] indices[2] = [] indices[3] = [] for i in range(0, g): if record[i] == "W": des.append(0) score += 1 if i != 0 and record[i - 1] == "W": score += 1 else: d = 1 if i != 0 and record[i - 1] == "W": d += 1 if i != g - 1 and record[i + 1] == "W": d += 1 des.append(d) indices[d].append(i) for choice in range(0, c): # arbitrarily pick first top desirable index d = 3 while d > 0: if bool(indices[d]): break d -= 1 #des == 0: perfect game lol if d == 0: break ind = indices[d][0] # flip it! score += d des[ind] = 0 indices[d].remove(ind) if ind != 0 and des[ind - 1] > 0: indices[des[ind - 1] + 1].append(ind - 1) indices[des[ind - 1]].remove(ind - 1) des[ind - 1] += 1 if ind != g - 1 and des[ind + 1] > 0: indices[des[ind + 1] + 1].append(ind + 1) indices[des[ind + 1]].remove(ind + 1) des[ind + 1] += 1 print(score) ```
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. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games. Submitted Solution: ``` #!/usr/bin/env python import os import sys from io import BytesIO, IOBase #from bisect import bisect_left as bl #c++ lowerbound bl(array,element) #from bisect import bisect_right as br #c++ upperbound br(array,element) from functools import cmp_to_key def main(): for _ in range(int(input())): n,k=map(int,input().split(" ")) a=list(input()) start=-1 end=-1 temp=[] for x in range(n): if a[x]=='L': end+=1 else: if start!=end: temp.append([end-start,[start+1,end]]) start=x end=x if start!=end: temp.append([end-start,[start+1,end]]) #print(temp) def boss(a,b): if a[0]>b[0]: return 1 elif a[0]<b[0]: return -1 else: if a[1][0]==0 or a[1][1]==n-1: return 1 else: return -1 temp.sort(key=cmp_to_key(boss)) for x in temp: if k<=0: break for z in range(x[1][0],x[1][1]+1): a[z]='W' k-=1 if k<=0: break if k<=0: break ans=0 chk=-1 #print(a,temp) for x in range(n): if a[x]=='W': if chk==-1: ans+=1 chk=0 else: ans+=2 else: chk=-1 print(ans) #-----------------------------BOSS-------------------------------------! # region fastio BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # endregion if __name__ == "__main__": main() ```
instruction
0
6,808
19
13,616
No
output
1
6,808
19
13,617
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You like playing chess tournaments online. In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game"). The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game. After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug. Compute the maximum score you can get by cheating in the optimal way. Input Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows. The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change. The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L. It is guaranteed that the sum of n over all testcases does not exceed 200,000. Output For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way. Example Input 8 5 2 WLWLL 6 5 LLLWWL 7 1 LWLWLWL 15 5 WWWLLLWWWLLLWWW 40 7 LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL 1 0 L 1 1 L 6 1 WLLWLW Output 7 11 6 26 46 0 1 6 Note Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game). An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game. Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game). An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games. Submitted Solution: ``` #include <CodeforcesSolutions.h> #include <ONLINE_JUDGE <solution.cf(contestID = "1427",questionID = "A",method = "GET")>.h> """ Author : thekushalghosh Team : CodeDiggers I prefer Python language over the C++ language :p :D Visit my website : thekushalghosh.github.io """ import sys,math,cmath,time,collections start_time = time.time() ########################################################################## ################# ---- THE ACTUAL CODE STARTS BELOW ---- ################# def solve(): n,k = invr() s = list(insr()) if "W" not in s: if k == 0: c = 0 else: c = (2 * min(k,len(s))) - 1 else: i = s.index("W") while i < len(s): if k > 0 and s[i] == "L": s[i] = "W" k = k - 1 i = i + 1 i = s.index("W") while i >= 0: if k > 0 and s[i] == "L": s[i] = "W" k = k - 1 i = i - 1 c = 0 for i in range(len(s)): if s[i] == "W": if i != 0 and s[i - 1] == "W": c = c + 2 else: c = c + 1 print(c) ################## ---- THE ACTUAL CODE ENDS ABOVE ---- ################## ########################################################################## def main(): global tt if not ONLINE_JUDGE: sys.stdin = open("input.txt","r") sys.stdout = open("output.txt","w") t = 1 t = inp() for tt in range(1,t + 1): solve() if not ONLINE_JUDGE: print("Time Elapsed :",time.time() - start_time,"seconds") sys.stdout.close() #---------------------- USER DEFINED INPUT FUNCTIONS ----------------------# def inp(): return(int(input())) def inlt(): return(list(map(int,input().split()))) def insr(): return(input().strip()) def invr(): return(map(int,input().split())) #------------------ USER DEFINED PROGRAMMING FUNCTIONS ------------------# def counter(a): q = [0] * max(a) for i in range(len(a)): q[a[i] - 1] = q[a[i] - 1] + 1 return(q) def counter_elements(a): q = dict() for i in range(len(a)): if a[i] not in q: q[a[i]] = 0 q[a[i]] = q[a[i]] + 1 return(q) def string_counter(a): q = [0] * 26 for i in range(len(a)): q[ord(a[i]) - 97] = q[ord(a[i]) - 97] + 1 return(q) def factorial(n,m = 1000000007): q = 1 for i in range(n): q = (q * (i + 1)) % m return(q) def factors(n): q = [] for i in range(1,int(n ** 0.5) + 1): if n % i == 0: q.append(i); q.append(n // i) return(list(sorted(list(set(q))))) def prime_factors(n): q = [] while n % 2 == 0: q.append(2); n = n // 2 for i in range(3,int(n ** 0.5) + 1,2): while n % i == 0: q.append(i); n = n // i if n > 2: q.append(n) return(list(sorted(q))) def transpose(a): n,m = len(a),len(a[0]) b = [[0] * n for i in range(m)] for i in range(m): for j in range(n): b[i][j] = a[j][i] return(b) def power_two(x): return (x and (not(x & (x - 1)))) def ceil(a, b): return -(-a // b) def seive(n): a = [1] prime = [True for i in range(n+1)] p = 2 while (p * p <= n): if (prime[p] == True): for i in range(p ** 2,n + 1, p): prime[i] = False p = p + 1 for p in range(2,n + 1): if prime[p]: a.append(p) return(a) #-----------------------------------------------------------------------# ONLINE_JUDGE = __debug__ if ONLINE_JUDGE: #import io,os #input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline input = sys.stdin.readline main() ```
instruction
0
6,809
19
13,618
No
output
1
6,809
19
13,619
Provide tags and a correct Python 3 solution for this coding contest problem. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
instruction
0
6,977
19
13,954
Tags: games, greedy, sortings Correct Solution: ``` from sys import stdin from collections import deque import heapq n = int(stdin.readline()) piles = [] for x in range(n): a = [int(x) for x in stdin.readline().split()][1:] piles.append(a) cielTotal = 0 jiroTotal = 0 mids = [] for x in piles: cielTotal += sum(x[:len(x)//2]) jiroTotal += sum(x[len(x)//2+len(x)%2:]) #print(x) #print(cielTotal,jiroTotal) if len(x)%2 == 1: mids.append(x[len(x)//2]) mids.sort(reverse=True) turn = True for x in mids: if turn: cielTotal += x else: jiroTotal += x turn = not turn print(cielTotal,jiroTotal) ```
output
1
6,977
19
13,955
Provide tags and a correct Python 3 solution for this coding contest problem. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
instruction
0
6,978
19
13,956
Tags: games, greedy, sortings Correct Solution: ``` n = int(input()) a,b = 0,0 l = [] for _ in range(n): inpt = list(map(int,input().split()))[1:] li = len(inpt) if li%2: l.append(inpt[li//2]) a += sum((inpt[:li//2])) b += sum((inpt[(li + 1)//2:])) l.sort(reverse=True) a += sum(l[::2]) b += sum(l[1::2]) print(a, b) ```
output
1
6,978
19
13,957
Provide tags and a correct Python 3 solution for this coding contest problem. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
instruction
0
6,979
19
13,958
Tags: games, greedy, sortings Correct Solution: ``` #!/usr/bin/env python3 odd, even = [], [] player1_turn = True player1 = player2 = 0 pile_number = int(input()) for _ in range(pile_number): n, *pile = tuple(map(int, input().split())) if n % 2 == 0: even.append(pile) else: odd.append(pile) for pile in even: n = len(pile) player1 += sum(pile[:n//2]) player2 += sum(pile[n//2:]) for pile in sorted(odd, reverse=True, key=lambda x: x[len(x)//2]): n = len(pile) top, middle, bottom = pile[:n//2], pile[n//2], pile[n//2+1:] player1 += sum(top) player2 += sum(bottom) if player1_turn: player1 += middle player1_turn = not player1_turn else: player2 += middle player1_turn = not player1_turn print(player1, player2) ```
output
1
6,979
19
13,959
Provide tags and a correct Python 3 solution for this coding contest problem. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
instruction
0
6,980
19
13,960
Tags: games, greedy, sortings Correct Solution: ``` from functools import reduce n = int(input()) cards = [list(map(int, input().split()[1:])) for i in range(n)] mid = sorted((c[len(c) >> 1] for c in cards if len(c) & 1 == 1), reverse=True) add = lambda x=0, y=0: x + y a, b = reduce(add, mid[::2] or [0]), reduce(add, mid[1::2] or [0]) for c in cards: m = len(c) >> 1 a += reduce(add, c[:m] or [0]) b += reduce(add, c[m + (len(c) & 1):] or [0]) print(a, b) ```
output
1
6,980
19
13,961
Provide tags and a correct Python 3 solution for this coding contest problem. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
instruction
0
6,981
19
13,962
Tags: games, greedy, sortings Correct Solution: ``` n = int(input()) S = [0] * n ciel, giro = 0, 0 odd = [] for i in range(n): L = list(map(int, input().split())) k = L[0] L = L[1:] S[i] = sum(L) if k % 2: odd.append(L[k // 2]) ciel += sum(L[:k // 2]) giro += sum(L[(k + 1) // 2:]) odd.sort(reverse=True) for i, x in enumerate(odd): if i % 2: giro += x else: ciel += x print(ciel, giro) ```
output
1
6,981
19
13,963
Provide tags and a correct Python 3 solution for this coding contest problem. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
instruction
0
6,982
19
13,964
Tags: games, greedy, sortings Correct Solution: ``` n = int(input()) c = [list(map(int, input().split())) for _ in range(n)] a, b = 0, 0 d = [] for i in range(n): if len(c[i]) % 2: a += sum(c[i][1:c[i][0]//2+1]) b += sum(c[i][c[i][0]//2+1:]) else: a += sum(c[i][1:c[i][0]//2+1]) b += sum(c[i][c[i][0]//2+2:]) d.append(c[i][c[i][0]//2+1]) d.sort(reverse=True) print(a+sum(d[0::2]), b+sum(d[1::2])) ```
output
1
6,982
19
13,965
Provide tags and a correct Python 3 solution for this coding contest problem. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
instruction
0
6,983
19
13,966
Tags: games, greedy, sortings Correct Solution: ``` n = int(input()) a = b = 0 s = [] for _ in range(n): l = [*map(int, input().split())][1:] m = len(l) if m & 1: s.append(l[m//2]) a += sum((l[:m//2])) b += sum((l[(m + 1)//2:])) s.sort(reverse = True) a += sum(s[::2]) b += sum(s[1::2]) print(a, b) ```
output
1
6,983
19
13,967
Provide tags and a correct Python 3 solution for this coding contest problem. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3.
instruction
0
6,984
19
13,968
Tags: games, greedy, sortings Correct Solution: ``` p, n = [], int(input()) a = b = 0 for i in range(n): t = list(map(int, input().split())) k = t[0] // 2 + 1 a += sum(t[1: k]) if t[0] & 1: p.append(t[k]) b += sum(t[k + 1: ]) else: b += sum(t[k: ]) p.sort(reverse = True) print(a + sum(p[0 :: 2]), b + sum(p[1 :: 2])) ```
output
1
6,984
19
13,969
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. Submitted Solution: ``` n = int(input()) lista = [] aux = [] somaA = 0 somaB = 0 for i in range(n): a = [int(i) for i in input().split()][1:] if len(a) > 1: somaA += sum(a[0:len(a)//2]) somaB += sum(a[-(len(a)//2):]) if len(a) % 2 == 1: aux.append(a[len(a)//2]) aux.sort(reverse=True) for i in range(0, len(aux), 2): somaA += aux[i] for i in range(1, len(aux), 2): somaB += aux[i] print(somaA, somaB) ```
instruction
0
6,985
19
13,970
Yes
output
1
6,985
19
13,971
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. Submitted Solution: ``` N = int(input()) one = two = 0 middles = [] for i in range(N): array = list(map(int, input().split()))[1:] size = len(array)-1 middle = size//2 for i in range(middle): one += array[i] for i in range(middle+1, len(array)): two += array[i] if len(array)%2==1: middles.append(array[middle]) else: one += array[middle] middles = sorted(middles) ONE = True for i in range(len(middles)-1, -1, -1): if ONE: one += middles[i] ONE = False else: two += middles[i] ONE = True print(one, two) ```
instruction
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6,986
19
13,972
Yes
output
1
6,986
19
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. Submitted Solution: ``` from functools import reduce n = int(input()) cards = [list(map(int, input().split()[1:])) for i in range(n)] mid = [c[len(c) >> 1] for c in cards if len(c) & 1 == 1] a, b = 0, 0 add = lambda x=0, y=0: x + y for c in cards: m = len(c) >> 1 a += reduce(add, c[:m] or [0]) b += reduce(add, c[m + (len(c) & 1):] or [0]) mid.sort(reverse=True) a += reduce(add, mid[::2] or [0]) b += reduce(add, mid[1::2] or [0]) print(a, b) ```
instruction
0
6,987
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13,974
Yes
output
1
6,987
19
13,975
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. Submitted Solution: ``` n=int(input()) s1,s2=0,0 tab = [] for i in range(n): c = list(map(int,input().split())) for j in range(1,c[0]+1): if(j*2<=c[0]): s1+=c[j] else: s2+=c[j] if(c[0] & 1): s2-=c[(c[0]+1)//2] tab.append(c[(c[0]+1)//2]) if(len(tab)): tab.sort() tab.reverse() for i in range(len(tab)): if(i & 1): s2+=tab[i] else: s1+=tab[i] print(s1,s2) # Made By Mostafa_Khaled ```
instruction
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6,988
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13,976
Yes
output
1
6,988
19
13,977
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. Submitted Solution: ``` n = int(input()) S = [0] * n ciel, giro = [], [] a, b = 0, 0 for i in range(n): L = list(map(int, input().split())) k = L[0] L = L[1:] S[i] = sum(L) if k % 2: ciel.append((sum(L[:k // 2 + 1]), i)) giro.append((sum(L[k // 2:], i), i)) else: a += sum(L[:k // 2]) b += sum(L[k // 2:]) ciel.sort(reverse=True) giro.sort(reverse=True) vis = [False] * n k = len(ciel) i, j = 0, 0 finished = False while not finished: finished = True while i < k and vis[ciel[i][1]]: i += 1 if i < k: finished = False vis[ciel[i][1]] = True a += ciel[i][0] b += S[ciel[i][1]] - ciel[i][0] while j < k and vis[giro[j][1]]: j += 1 if j < k: finished = False vis[giro[j][1]] = True b += giro[j][0] a += S[giro[j][1]] - giro[j][0] print(a, b) ```
instruction
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6,989
19
13,978
No
output
1
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19
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. Submitted Solution: ``` from sys import stdin from collections import deque import heapq n = int(stdin.readline()) piles = [] for x in range(n): a = [int(x) for x in stdin.readline().split()][1:] piles.append(a) cielTotal = 0 jiroTotal = 0 mids = [] for x in piles: cielTotal += sum(x[:len(x)//2]) jiroTotal += sum(x[len(x)//2+len(x)%2:]) if len(x)%2 == 1: mids.append(x[len(x)//2]) mids.sort() turn = True for x in mids: if turn: cielTotal += x else: jiroTotal += x print(cielTotal,jiroTotal) ```
instruction
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6,990
19
13,980
No
output
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19
13,981
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. Submitted Solution: ``` from sys import stdin from collections import deque import heapq n = int(stdin.readline()) piles = [] for x in range(n): a = deque([int(x) for x in stdin.readline().split()][1:]) piles.append(a) ciel = [(-x[0],i) for i,x in enumerate(piles)] jiro = [(-x[-1],i) for i,x in enumerate(piles)] heapq.heapify(ciel) heapq.heapify(jiro) empty = set([-1]) cielTotal = 0 jiroTotal = 0 turn = True while True: if turn: ind = -1 while ind in empty and ciel: nxt,ind = heapq.heappop(ciel) nxt = -nxt if ind in empty: break piles[ind].popleft() cielTotal += nxt if not piles[ind]: empty.add(ind) else: heapq.heappush(ciel, (-piles[ind][0], ind)) else: ind = -1 while ind in empty and jiro: nxt,ind = heapq.heappop(jiro) nxt = -nxt if ind in empty: break piles[ind].pop() jiroTotal += nxt if not piles[ind]: empty.add(ind) else: heapq.heappush(jiro, (-piles[ind][-1], ind)) turn = not turn print(cielTotal,jiroTotal) ```
instruction
0
6,991
19
13,982
No
output
1
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19
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Fox Ciel is playing a card game with her friend Fox Jiro. There are n piles of cards on the table. And there is a positive integer on each card. The players take turns and Ciel takes the first turn. In Ciel's turn she takes a card from the top of any non-empty pile, and in Jiro's turn he takes a card from the bottom of any non-empty pile. Each player wants to maximize the total sum of the cards he took. The game ends when all piles become empty. Suppose Ciel and Jiro play optimally, what is the score of the game? Input The first line contain an integer n (1 ≤ n ≤ 100). Each of the next n lines contains a description of the pile: the first integer in the line is si (1 ≤ si ≤ 100) — the number of cards in the i-th pile; then follow si positive integers c1, c2, ..., ck, ..., csi (1 ≤ ck ≤ 1000) — the sequence of the numbers on the cards listed from top of the current pile to bottom of the pile. Output Print two integers: the sum of Ciel's cards and the sum of Jiro's cards if they play optimally. Examples Input 2 1 100 2 1 10 Output 101 10 Input 1 9 2 8 6 5 9 4 7 1 3 Output 30 15 Input 3 3 1 3 2 3 5 4 6 2 8 7 Output 18 18 Input 3 3 1000 1000 1000 6 1000 1000 1000 1000 1000 1000 5 1000 1000 1000 1000 1000 Output 7000 7000 Note In the first example, Ciel will take the cards with number 100 and 1, Jiro will take the card with number 10. In the second example, Ciel will take cards with numbers 2, 8, 6, 5, 9 and Jiro will take cards with numbers 4, 7, 1, 3. Submitted Solution: ``` #!/usr/bin/env python3 player1 = player2 = 0 player1_turn = True pile_number = int(input()) piles = [] for _ in range(pile_number): n, *pile = tuple(map(int, input().split())) piles.append(pile) for pile in sorted(piles, reverse=True): n = len(pile) if n % 2 == 0: player1 += sum(pile[:n//2]) player2 += sum(pile[n//2:]) else: top, middle, bottom = pile[:n//2], pile[n//2], pile[n//2+1:] player1 += sum(top) player2 += sum(bottom) if player1_turn: player1 += middle player1_turn = not player1_turn else: player2 += middle player1_turn = not player1_turn print(player1, player2) ```
instruction
0
6,992
19
13,984
No
output
1
6,992
19
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Provide tags and a correct Python 3 solution for this coding contest problem. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≤ n ≤ 350000) is given. Each game is represented by a pair of scores a, b (1 ≤ a, b ≤ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
instruction
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Tags: math, number theory Correct Solution: ``` # ---------------------------iye ha aam zindegi--------------------------------------------- import math import heapq, bisect import sys from collections import deque, defaultdict from fractions import Fraction mod = 10 ** 9 + 7 mod1 = 998244353 # ------------------------------warmup---------------------------- import os import sys from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") # -------------------game starts now----------------------------------------------------import math class TreeNode: def __init__(self, k, v): self.key = k self.value = v self.left = None self.right = None self.parent = None self.height = 1 self.num_left = 1 self.num_total = 1 class AvlTree: def __init__(self): self._tree = None def add(self, k, v): if not self._tree: self._tree = TreeNode(k, v) return node = self._add(k, v) if node: self._rebalance(node) def _add(self, k, v): node = self._tree while node: if k < node.key: if node.left: node = node.left else: node.left = TreeNode(k, v) node.left.parent = node return node.left elif node.key < k: if node.right: node = node.right else: node.right = TreeNode(k, v) node.right.parent = node return node.right else: node.value = v return @staticmethod def get_height(x): return x.height if x else 0 @staticmethod def get_num_total(x): return x.num_total if x else 0 def _rebalance(self, node): n = node while n: lh = self.get_height(n.left) rh = self.get_height(n.right) n.height = max(lh, rh) + 1 balance_factor = lh - rh n.num_total = 1 + self.get_num_total(n.left) + self.get_num_total(n.right) n.num_left = 1 + self.get_num_total(n.left) if balance_factor > 1: if self.get_height(n.left.left) < self.get_height(n.left.right): self._rotate_left(n.left) self._rotate_right(n) elif balance_factor < -1: if self.get_height(n.right.right) < self.get_height(n.right.left): self._rotate_right(n.right) self._rotate_left(n) else: n = n.parent def _remove_one(self, node): """ Side effect!!! Changes node. Node should have exactly one child """ replacement = node.left or node.right if node.parent: if AvlTree._is_left(node): node.parent.left = replacement else: node.parent.right = replacement replacement.parent = node.parent node.parent = None else: self._tree = replacement replacement.parent = None node.left = None node.right = None node.parent = None self._rebalance(replacement) def _remove_leaf(self, node): if node.parent: if AvlTree._is_left(node): node.parent.left = None else: node.parent.right = None self._rebalance(node.parent) else: self._tree = None node.parent = None node.left = None node.right = None def remove(self, k): node = self._get_node(k) if not node: return if AvlTree._is_leaf(node): self._remove_leaf(node) return if node.left and node.right: nxt = AvlTree._get_next(node) node.key = nxt.key node.value = nxt.value if self._is_leaf(nxt): self._remove_leaf(nxt) else: self._remove_one(nxt) self._rebalance(node) else: self._remove_one(node) def get(self, k): node = self._get_node(k) return node.value if node else -1 def _get_node(self, k): if not self._tree: return None node = self._tree while node: if k < node.key: node = node.left elif node.key < k: node = node.right else: return node return None def get_at(self, pos): x = pos + 1 node = self._tree while node: if x < node.num_left: node = node.left elif node.num_left < x: x -= node.num_left node = node.right else: return (node.key, node.value) raise IndexError("Out of ranges") @staticmethod def _is_left(node): return node.parent.left and node.parent.left == node @staticmethod def _is_leaf(node): return node.left is None and node.right is None def _rotate_right(self, node): if not node.parent: self._tree = node.left node.left.parent = None elif AvlTree._is_left(node): node.parent.left = node.left node.left.parent = node.parent else: node.parent.right = node.left node.left.parent = node.parent bk = node.left.right node.left.right = node node.parent = node.left node.left = bk if bk: bk.parent = node node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1 node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right) node.num_left = 1 + self.get_num_total(node.left) def _rotate_left(self, node): if not node.parent: self._tree = node.right node.right.parent = None elif AvlTree._is_left(node): node.parent.left = node.right node.right.parent = node.parent else: node.parent.right = node.right node.right.parent = node.parent bk = node.right.left node.right.left = node node.parent = node.right node.right = bk if bk: bk.parent = node node.height = max(self.get_height(node.left), self.get_height(node.right)) + 1 node.num_total = 1 + self.get_num_total(node.left) + self.get_num_total(node.right) node.num_left = 1 + self.get_num_total(node.left) @staticmethod def _get_next(node): if not node.right: return node.parent n = node.right while n.left: n = n.left return n avl=AvlTree() #-----------------------------------------------binary seacrh tree--------------------------------------- class SegmentTree1: def __init__(self, data, default='z', func=lambda a, b: min(a ,b)): """initialize the segment tree with data""" self._default = default self._func = func self._len = len(data) self._size = _size = 1 << (self._len - 1).bit_length() self.data = [default] * (2 * _size) self.data[_size:_size + self._len] = data for i in reversed(range(_size)): self.data[i] = func(self.data[i + i], self.data[i + i + 1]) def __delitem__(self, idx): self[idx] = self._default def __getitem__(self, idx): return self.data[idx + self._size] def __setitem__(self, idx, value): idx += self._size self.data[idx] = value idx >>= 1 while idx: self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) idx >>= 1 def __len__(self): return self._len def query(self, start, stop): if start == stop: return self.__getitem__(start) stop += 1 start += self._size stop += self._size res = self._default while start < stop: if start & 1: res = self._func(res, self.data[start]) start += 1 if stop & 1: stop -= 1 res = self._func(res, self.data[stop]) start >>= 1 stop >>= 1 return res def __repr__(self): return "SegmentTree({0})".format(self.data) # -------------------game starts now----------------------------------------------------import math class SegmentTree: def __init__(self, data, default=0, func=lambda a, b: a + b): """initialize the segment tree with data""" self._default = default self._func = func self._len = len(data) self._size = _size = 1 << (self._len - 1).bit_length() self.data = [default] * (2 * _size) self.data[_size:_size + self._len] = data for i in reversed(range(_size)): self.data[i] = func(self.data[i + i], self.data[i + i + 1]) def __delitem__(self, idx): self[idx] = self._default def __getitem__(self, idx): return self.data[idx + self._size] def __setitem__(self, idx, value): idx += self._size self.data[idx] = value idx >>= 1 while idx: self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1]) idx >>= 1 def __len__(self): return self._len def query(self, start, stop): if start == stop: return self.__getitem__(start) stop += 1 start += self._size stop += self._size res = self._default while start < stop: if start & 1: res = self._func(res, self.data[start]) start += 1 if stop & 1: stop -= 1 res = self._func(res, self.data[stop]) start >>= 1 stop >>= 1 return res def __repr__(self): return "SegmentTree({0})".format(self.data) # -------------------------------iye ha chutiya zindegi------------------------------------- class Factorial: def __init__(self, MOD): self.MOD = MOD self.factorials = [1, 1] self.invModulos = [0, 1] self.invFactorial_ = [1, 1] def calc(self, n): if n <= -1: print("Invalid argument to calculate n!") print("n must be non-negative value. But the argument was " + str(n)) exit() if n < len(self.factorials): return self.factorials[n] nextArr = [0] * (n + 1 - len(self.factorials)) initialI = len(self.factorials) prev = self.factorials[-1] m = self.MOD for i in range(initialI, n + 1): prev = nextArr[i - initialI] = prev * i % m self.factorials += nextArr return self.factorials[n] def inv(self, n): if n <= -1: print("Invalid argument to calculate n^(-1)") print("n must be non-negative value. But the argument was " + str(n)) exit() p = self.MOD pi = n % p if pi < len(self.invModulos): return self.invModulos[pi] nextArr = [0] * (n + 1 - len(self.invModulos)) initialI = len(self.invModulos) for i in range(initialI, min(p, n + 1)): next = -self.invModulos[p % i] * (p // i) % p self.invModulos.append(next) return self.invModulos[pi] def invFactorial(self, n): if n <= -1: print("Invalid argument to calculate (n^(-1))!") print("n must be non-negative value. But the argument was " + str(n)) exit() if n < len(self.invFactorial_): return self.invFactorial_[n] self.inv(n) # To make sure already calculated n^-1 nextArr = [0] * (n + 1 - len(self.invFactorial_)) initialI = len(self.invFactorial_) prev = self.invFactorial_[-1] p = self.MOD for i in range(initialI, n + 1): prev = nextArr[i - initialI] = (prev * self.invModulos[i % p]) % p self.invFactorial_ += nextArr return self.invFactorial_[n] class Combination: def __init__(self, MOD): self.MOD = MOD self.factorial = Factorial(MOD) def ncr(self, n, k): if k < 0 or n < k: return 0 k = min(k, n - k) f = self.factorial return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD # --------------------------------------iye ha combinations ka zindegi--------------------------------- def powm(a, n, m): if a == 1 or n == 0: return 1 if n % 2 == 0: s = powm(a, n // 2, m) return s * s % m else: return a * powm(a, n - 1, m) % m # --------------------------------------iye ha power ka zindegi--------------------------------- def sort_list(list1, list2): zipped_pairs = zip(list2, list1) z = [x for _, x in sorted(zipped_pairs)] return z # --------------------------------------------------product---------------------------------------- def product(l): por = 1 for i in range(len(l)): por *= l[i] return por # --------------------------------------------------binary---------------------------------------- def binarySearchCount(arr, n, key): left = 0 right = n - 1 count = 0 while (left <= right): mid = int((right + left)/ 2) # Check if middle element is # less than or equal to key if (arr[mid]<=key): count = mid+1 left = mid + 1 # If key is smaller, ignore right half else: right = mid - 1 return count # --------------------------------------------------binary---------------------------------------- def countdig(n): c = 0 while (n > 0): n //= 10 c += 1 return c def countGreater( arr,n, k): l = 0 r = n - 1 # Stores the index of the left most element # from the array which is greater than k leftGreater = n # Finds number of elements greater than k while (l <= r): m = int(l + (r - l) / 2) if (arr[m] >= k): leftGreater = m r = m - 1 # If mid element is less than # or equal to k update l else: l = m + 1 # Return the count of elements # greater than k return (n - leftGreater) # --------------------------------------------------binary------------------------------------ for i in range(int(input())): a,b=map(int,input().split()) c=a*b l=int(c**(1./3)+0.5) if l**3==a*b and a%l==0 and b%l==0: print("YES") else: print("NO") ```
output
1
7,206
19
14,413
Provide tags and a correct Python 3 solution for this coding contest problem. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≤ n ≤ 350000) is given. Each game is represented by a pair of scores a, b (1 ≤ a, b ≤ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
instruction
0
7,207
19
14,414
Tags: math, number theory Correct Solution: ``` import sys,os,io from sys import stdin from math import log, gcd, ceil from collections import defaultdict, deque, Counter from heapq import heappush, heappop, heapify from bisect import bisect_left , bisect_right import math def ii(): return int(input()) def li(): return list(map(int,input().split())) if(os.path.exists('input.txt')): sys.stdin = open("input.txt","r") ; sys.stdout = open("output.txt","w") else: input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline no = "No" yes = "Yes" def solve(): a,b = li() x = (pow(a*b,1/3)) x=round(x) if x*x*x==a*b and a%x==b%x==0: print(yes) else: print(no) t = 1 t = int(input()) for _ in range(t): solve() ```
output
1
7,207
19
14,415
Provide tags and a correct Python 3 solution for this coding contest problem. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≤ n ≤ 350000) is given. Each game is represented by a pair of scores a, b (1 ≤ a, b ≤ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
instruction
0
7,208
19
14,416
Tags: math, number theory Correct Solution: ``` import sys input = sys.stdin.readline print = sys.stdout.write cbrt = {i**3:i for i in range(1001)} n = int(input()) all_res = [] for _ in range(n): a, b = map(int, input().split()) if a == b: all_res.append('Yes' if a in cbrt else 'No') continue if a > b: a, b = b, a r = cbrt.get(a * a // b, 0) if r == 0 or a % (r * r) > 0: all_res.append('No') continue y = a //(r * r) if r * r * y == a and r * y * y == b: all_res.append('Yes') else: all_res.append('No') print('\n'.join(all_res)) ```
output
1
7,208
19
14,417
Provide tags and a correct Python 3 solution for this coding contest problem. <image> Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting. The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one. Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not. Input In the first string, the number of games n (1 ≤ n ≤ 350000) is given. Each game is represented by a pair of scores a, b (1 ≤ a, b ≤ 109) – the results of Slastyona and Pushok, correspondingly. Output For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise. You can output each letter in arbitrary case (upper or lower). Example Input 6 2 4 75 45 8 8 16 16 247 994 1000000000 1000000 Output Yes Yes Yes No No Yes Note First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won. The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
instruction
0
7,209
19
14,418
Tags: math, number theory Correct Solution: ``` #Code by Sounak, IIESTS #------------------------------warmup---------------------------- import os import sys import math from io import BytesIO, IOBase from fractions import Fraction BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = "x" in file.mode or "r" not in file.mode self.write = self.buffer.write if self.writable else None def read(self): while True: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) if not b: break ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines = 0 return self.buffer.read() def readline(self): while self.newlines == 0: b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)) self.newlines = b.count(b"\n") + (not b) ptr = self.buffer.tell() self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr) self.newlines -= 1 return self.buffer.readline() def flush(self): if self.writable: os.write(self._fd, self.buffer.getvalue()) self.buffer.truncate(0), self.buffer.seek(0) class IOWrapper(IOBase): def __init__(self, file): self.buffer = FastIO(file) self.flush = self.buffer.flush self.writable = self.buffer.writable self.write = lambda s: self.buffer.write(s.encode("ascii")) self.read = lambda: self.buffer.read().decode("ascii") self.readline = lambda: self.buffer.readline().decode("ascii") sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout) input = lambda: sys.stdin.readline().rstrip("\r\n") #-------------------game starts now----------------------------------------------------- for t in range (int(input())): a,b=map(int,input().split()) p=a*b #print(p) c=int(round(p**(1./3))) #print (c) if c**3==p and a%c==0 and b%c==0: print("Yes") else: print("No") ```
output
1
7,209
19
14,419