message
stringlengths
2
67k
message_type
stringclasses
2 values
message_id
int64
0
1
conversation_id
int64
463
109k
cluster
float64
19
19
__index_level_0__
int64
926
217k
Provide tags and a correct Python 3 solution for this coding contest problem. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW
instruction
0
19,938
19
39,876
Tags: dp, graphs Correct Solution: ``` def ma(): s=input() v=s.split(' ') n=int(v[0]) k=int(v[1]) s=input() dp=[[0,0] for _ in range(n+1)] flag=True mp={} mp['W']=1 mp['D']=0 mp['L']=-1 for i in range (1,n): c=s[i-1] if c=='?': dp[i][0]=min(dp[i-1][0]+1 ,k-1) dp[i][1]=max(dp[i-1][1]-1 ,-k+1) else: dp[i][0]=min(dp[i-1][0]+mp[c],k-1) dp[i][1]=max(dp[i-1][1]+mp[c],-k+1) if dp[i][1]==k or dp[i][0]==-k: flag=False ''' elif c=='D': dp[i][0]=dp[i-1][0] dp[i][1]=dp[i-1][1] elif c=='W': dp[i][0]=min(dp[i-1][0]+1 ,k-1) dp[i][1]=dp[i-1][1]+1 if dp[i][1]==k: flag=False elif c=='L': dp[i][0]=dp[i-1][0]-1 dp[i][1]=max(dp[i-1][1]-1 ,-k+1) if dp[i][0]==-k: flag=False ''' if not flag: print('NO') return i=n if s[i-1]=='?': dp[i][0]=dp[i-1][0]+1 dp[i][1]=dp[i-1][1]-1 else : dp[i][0]=dp[i-1][0]+mp[s[i-1]] dp[i][1]=dp[i-1][1]+mp[s[i-1]] ''' elif s[i-1]=='W': dp[i][0]=dp[i-1][0]+1 dp[i][1]=dp[i-1][1]+1 elif s[i-1]=='L': dp[i][0]=dp[i-1][0]-1 dp[i][1]=dp[i-1][1]-1 ''' res=['?']*n if dp[i][0]==k or dp[i][1]==-k: if dp[i][0]==k: cur=k else: cur=-k for i in range(n-1,-1,-1): c=s[i] if c=='?': if cur>dp[i][0]: res[i]='W' elif dp[i][1]<=cur<=dp[i][0]: res[i]='D' elif cur<dp[i][1]: res[i]='L' else: res[i]=c cur=cur-mp[res[i]] ''' elif c=='D': cur=cur res[i]=c elif c=='W': cur=cur-1 res[i]=c elif c=='L': cur=cur+1 res[i]=c ''' for i in range(n): print(res[i],end='') else: print('NO') ma() ```
output
1
19,938
19
39,877
Provide tags and a correct Python 3 solution for this coding contest problem. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW
instruction
0
19,939
19
39,878
Tags: dp, graphs Correct Solution: ``` # by the authority of GOD author: manhar singh sachdev # import os,sys from io import BytesIO,IOBase def main(): n,k = map(int,input().split()) s = input().strip() dp = [[0]*(2*k+5) for _ in range(n+1)] # diff ; win/draw/lose dp[0][0] = 1 prev = [[-1]*(2*k+5) for _ in range(n+1)] for i in range(1,n): for j in range(-k+1,k): if (s[i-1] == '?' or s[i-1] == 'L') and dp[i-1][j+1]: dp[i][j] = 1 prev[i][j] = 'L' if (s[i-1] == '?' or s[i-1] == 'D') and dp[i-1][j]: dp[i][j] = 1 prev[i][j] = 'D' if (s[i-1] == '?' or s[i-1] == 'W') and dp[i-1][j-1]: dp[i][j] = 1 prev[i][j] = 'W' for j in range(-k,k+1): if (s[n-1] == '?' or s[n-1] == 'L') and dp[n-1][j+1]: dp[n][j] = 1 prev[n][j] = 'L' if (s[n-1] == '?' or s[n-1] == 'D') and dp[n-1][j]: dp[n][j] = 1 prev[n][j] = 'D' if (s[n-1] == '?' or s[n-1] == 'W') and dp[n-1][j-1]: dp[n][j] = 1 prev[n][j] = 'W' if not dp[n][k] and not dp[n][-k]: print('NO') exit() elif dp[n][k]: st = k else: st = -k ans = [] dct = {'L':1,'W':-1,'D':0} for i in range(n,0,-1): l = prev[i][st] ans.append(l) st += dct[l] print(''.join(ans[::-1])) # Fast IO Region 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") if __name__ == "__main__": main() ```
output
1
19,939
19
39,879
Provide tags and a correct Python 3 solution for this coding contest problem. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW
instruction
0
19,940
19
39,880
Tags: dp, graphs Correct Solution: ``` # 803E import collections def do(): n, k = map(int, input().split(" ")) s = input() dp = collections.defaultdict(set) gap = {'W': 1, 'L': -1, 'D': 0} dp[-1].add(0) for i in range(n-1): if s[i] == '?': for pre in dp[i-1]: for g in gap.values(): t = pre + g if abs(t) != k: dp[i].add(t) else: for pre in dp[i-1]: t = pre + gap[s[i]] if abs(t) != k: dp[i].add(t) if s[n-1] == '?': for pre in dp[n-2]: for g in gap.values(): dp[n-1].add(pre + g) else: for pre in dp[n-2]: dp[n-1].add(pre + gap[s[n-1]]) # print(dp) if k not in dp[n-1] and -k not in dp[n-1]: return "NO" res = [c for c in s] cur = k if k in dp[n-1] else -k for i in range(n-1, 0, -1): if s[i] == '?': for c in gap: if abs(cur - gap[c]) != k and cur - gap[c] in dp[i-1]: res[i] = c cur -= gap[c] break else: cur -= gap[s[i]] if res[0] == '?': if cur == 0: res[0] = 'D' elif cur == 1: res[0] = 'W' else: res[0] = 'L' return "".join(res) print(do()) ```
output
1
19,940
19
39,881
Provide tags and a correct Python 3 solution for this coding contest problem. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW
instruction
0
19,941
19
39,882
Tags: dp, graphs Correct Solution: ``` N,k=list(map(int,input().strip().split(' '))) S=input() # num of W-num of L=j, j>k means k-j dp=[[0 for j in range(2*k+1)]for i in range(N)] #print(dp) for i in range(len(S)): if i==0: if S[0]=='W': dp[0][1]='W' elif S[0]=='L': dp[0][-1]='L' elif S[0]=='D': dp[0][0]='D' else: dp[0][1]='W' dp[0][-1]='L' dp[0][0]='D' elif i!=len(S)-1: if S[i]=='W': for j in range(0,k): if j==0: if dp[i-1][-1]!=0: dp[i][0]='W' else: if dp[i-1][j-1]!=0: dp[i][j]='W' for j in range(1,k): if j!=k-1: if dp[i-1][-j-1]!=0: dp[i][-j]='W' elif S[i]=='L': for j in range(0,k): if dp[i-1][j+1]!=0: dp[i][j]='L' for j in range(1,k): if j==1: if dp[i-1][0]!=0: dp[i][-1]='L' else: if dp[i-1][-j+1]!=0: dp[i][-j]='L' elif S[i]=='D': for j in range(0,2*k+1): if dp[i-1][j]!=0: dp[i][j]='D' else: for j in range(0,k): if j==0: if dp[i-1][-1]!=0: dp[i][j]='W' elif dp[i-1][1]!=0: dp[i][j]='L' elif dp[i-1][0]!=0: dp[i][j]='D' else: if dp[i-1][j-1]!=0: dp[i][j]='W' elif dp[i-1][j+1]!=0: dp[i][j]='L' elif dp[i-1][j]!=0: dp[i][j]='D' for j in range(1,k): if j==1: if dp[i-1][0]!=0: dp[i][-1]='L' elif dp[i-1][-1]!=0: dp[i][-1]='D' elif dp[i-1][-2]!=0: dp[i][-1]='W' else: if dp[i-1][-(j-1)]!=0: dp[i][-j]='L' elif dp[i-1][-j]!=0: dp[i][-j]='D' elif dp[i-1][-(j+1)]!=0: dp[i][-j]='W' else: if S[i]=='W': if dp[i-1][k-1]!=0: dp[i][k]='W' elif S[i]=='L': if dp[i-1][-(k-1)]!=0: dp[i][-k]='L' elif S[i]=='D': 1 else: if dp[i-1][k-1]!=0: dp[i][k]='W' elif dp[i-1][-(k-1)]!=0: dp[i][-k]='L' #print(dp) if k>1 and N>=k: if dp[len(S)-1][k]==0 and dp[len(S)-1][-k]==0: print('NO') else: if dp[len(S)-1][k]!=0: ans='' cur=k for j in range(1,len(S)+1): temp=dp[len(S)-j][cur] if temp=='W': ans+=temp cur-=1 elif temp=='D': ans+=temp elif temp=='L': ans+=temp cur+=1 elif dp[len(S)-1][-k]!=0: ans='' cur=-k for j in range(1,len(S)+1): temp=dp[len(S)-j][cur] if temp=='W': ans+=temp cur-=1 elif temp=='D': ans+=temp elif temp=='L': ans+=temp cur+=1 ans=ans[::-1] print(ans) elif N<k: print('NO') elif k==1: shit=0 for i in range(len(S)): if i<len(S)-1: if S[i]!='?': shit=1 break if shit==1: print('NO') else: temp='' for i in range(len(S)-1): temp+='D' if S[-1]=='D': print('NO') elif S[-1]=='L': temp+='L' print(temp) else: temp+='W' print(temp) ```
output
1
19,941
19
39,883
Provide tags and a correct Python 3 solution for this coding contest problem. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW
instruction
0
19,942
19
39,884
Tags: dp, graphs Correct Solution: ``` n, k = [int(i) for i in input().split()] s = input() dp = [[False] * 2010 for i in range(1001)] dp[0][0] = True for i in range(n): l = -k + 1 r = k if i == n - 1: l -= 1 r += 1 for b in range(l, r): if s[i] == 'L': dp[i + 1][b] = dp[i][b + 1] elif s[i] == 'W': dp[i + 1][b] = dp[i][b - 1] elif s[i] == 'D': dp[i + 1][b] = dp[i][b] else: dp[i + 1][b] = dp[i][b + 1] or dp[i][b - 1] or dp[i][b] ans = [0] * n i = n b = -1 if dp[i][k]: b = k elif dp[i][-k]: b = -k if b == -1: print("NO") else: while i > 0: if (s[i - 1] == 'L' or s[i - 1] == '?') and dp[i][b] == dp[i - 1][b + 1]: ans[i - 1] = 'L' b += 1 elif (s[i - 1] == 'W' or s[i - 1] == '?') and dp[i][b] == dp[i - 1][b - 1]: ans[i - 1] = 'W' b -= 1 else: ans[i - 1] = 'D' i -= 1 for j in ans: print(j, end='') ```
output
1
19,942
19
39,885
Provide tags and a correct Python 3 solution for this coding contest problem. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW
instruction
0
19,943
19
39,886
Tags: dp, graphs Correct Solution: ``` # Legends Always Come Up with Solution # Author: Manvir Singh import os import sys from io import BytesIO, IOBase def main(): n,k=map(int,input().split()) s=list(input().rstrip()) dp,ans=[['0']*(2*k+2) for _ in range(n+1)],[] dp[0][0]='.' for i in range(1,n+1): for j in range(k+1): if j==k and i!=n: continue if s[i-1]=='W': dp[i][j]=('W' if dp[i-1][j-1]!='0' else '0') elif s[i-1]=='D': dp[i][j]=('D' if dp[i-1][j]!='0' else '0') elif s[i-1]=='L': dp[i][j]=('L' if dp[i-1][j+1]!='0' else '0') else: if dp[i-1][j-1]!='0': dp[i][j]='W' elif dp[i-1][j]!='0': dp[i][j]='D' elif dp[i-1][j+1]!='0': dp[i][j]='L' for j in range(-1,-(k+1),-1): if j==-k and i!=n: continue if s[i - 1] == 'W': dp[i][j] = ('W' if dp[i - 1][j - 1] != '0' else '0') elif s[i - 1] == 'D': dp[i][j] = ('D' if dp[i - 1][j] != '0' else '0') elif s[i - 1] == 'L': dp[i][j] = ('L' if dp[i - 1][j + 1] != '0' else '0') else: if dp[i - 1][j - 1] != '0': dp[i][j] = 'W' elif dp[i - 1][j] != '0': dp[i][j] = 'D' elif dp[i - 1][j + 1] != '0': dp[i][j] = 'L' if dp[n][k]!='0' or dp[n][-k]!='0': i,j=n,k if dp[n][k]=='0': j=-k while len(ans)!=n: ans.append(dp[i][j]) if dp[i][j]=='W': i,j=i-1,j-1 elif dp[i][j]=='D': i-=1 elif dp[i][j]=='L': i,j=i-1,j+1 ans.reverse() print("".join(ans)) else: print('NO') # 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") if __name__ == "__main__": main() ```
output
1
19,943
19
39,887
Provide tags and a correct Python 3 solution for this coding contest problem. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW
instruction
0
19,944
19
39,888
Tags: dp, graphs Correct Solution: ``` n, k = [int(i) for i in input().split()] s = input() dp = [[False] * 2100 for i in range(1001)] dp[0][0] = True for i in range(n): l = -k + 1 r = k if i == n - 1: l -= 1 r += 1 for b in range(l, r): if s[i] == 'L': dp[i + 1][b] = dp[i][b + 1] elif s[i] == 'W': dp[i + 1][b] = dp[i][b - 1] elif s[i] == 'D': dp[i + 1][b] = dp[i][b] else: dp[i + 1][b] = dp[i][b + 1] or dp[i][b - 1] or dp[i][b] ans = [] i = n b = -1 if dp[i][k]: b = k elif dp[i][-k]: b = -k if b == -1: print("NO") else: while i > 0: if (s[i - 1] == 'L' or s[i - 1] == '?') and dp[i][b] == dp[i - 1][b + 1]: ans.append('L') b += 1 elif (s[i - 1] == 'W' or s[i - 1] == '?') and dp[i][b] == dp[i - 1][b - 1]: ans.append('W') b -= 1 else: ans.append('D') i -= 1 for j in reversed(ans): print(j, end='') ```
output
1
19,944
19
39,889
Provide tags and a correct Python 3 solution for this coding contest problem. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW
instruction
0
19,945
19
39,890
Tags: dp, graphs Correct Solution: ``` import sys n, k = map(int, input().split()) s = list(input()) if s[-1] == 'D': print('NO') exit() size, zero = 2*k-1, k-1 dp = [[0]*size for _ in range(n)] dp[0][zero] = 1 for i in range(n-1): for j in range(size): if j and (s[i] == 'W' or s[i] == '?'): dp[i+1][j] |= dp[i][j-1] if s[i] == 'D' or s[i] == '?': dp[i+1][j] |= dp[i][j] if j+1 < size and (s[i] == 'L' or s[i] == '?'): dp[i+1][j] |= dp[i][j+1] j = -1 if (s[-1] == 'W' or s[-1] == '?') and dp[-1][-1]: j = size-1 s[-1] = 'W' elif (s[-1] == 'L' or s[-1] == '?') and dp[-1][0]: j = 0 s[-1] = 'L' if j == -1: print('NO') exit() for i in range(n-2, -1, -1): if s[i] == 'W': assert dp[i][j-1] == 1 j -= 1 elif s[i] == 'L': assert dp[i][j+1] == 1 j += 1 elif s[i] == '?': if dp[i][j]: s[i] = 'D' elif j > 0 and dp[i][j-1]: s[i] = 'W' j -= 1 else: s[i] = 'L' j += 1 assert j == zero print(*s, sep='') ```
output
1
19,945
19
39,891
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW Submitted Solution: ``` N, K = map( int, input().split() ) S = input() offset = K + 1 dp = [ [ False for i in range( offset * 2 ) ] for j in range( N + 1 ) ] pre = [ [ 0 for i in range( offset * 2 ) ] for j in range( N + 1 ) ] # previous state dp[ 0 ][ offset ] = True for i in range( N ): for j in range( offset * 2 ): if not dp[ i ][ j ]: continue if ( S[ i ] == 'W' or S[ i ] == '?' ) and not ( i + 1 < N and j + 1 >= offset + K ): if not dp[ i + 1 ][ j + 1 ]: dp[ i + 1 ][ j + 1 ] = True pre[ i + 1 ][ j + 1 ] = j if ( S[ i ] == 'L' or S[ i ] == '?' ) and not ( i + 1 < N and j - 1 <= offset - K ): if not dp[ i + 1 ][ j - 1 ]: dp[ i + 1 ][ j - 1 ] = True pre[ i + 1 ][ j - 1 ] = j if S[ i ] == 'D' or S[ i ] == '?': if not dp[ i + 1 ][ j ]: dp[ i + 1 ][ j ] = True pre[ i + 1 ][ j ] = j if not dp[ N ][ offset + K ] and not dp[ N ][ offset - K ]: print( "NO" ) else: ans = "" i, j = N, offset + K if dp[ N ][ offset + K ] else offset - K while i: pj = pre[ i ][ j ] if S[ i - 1 ] == '?': if pj + 1 == j: ans += "W" elif pj - 1 == j: ans += "L" else: ans += "D" else: ans += S[ i - 1 ] i, j = i - 1, pj print( ans[ : : -1 ] ) ```
instruction
0
19,946
19
39,892
Yes
output
1
19,946
19
39,893
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW Submitted Solution: ``` def ma(): s=input() v=s.split(' ') n=int(v[0]) k=int(v[1]) s=input() dp=[[0,0] for _ in range(n+1)] flag=True for i in range (1,n): c=s[i-1] if c=='?': dp[i][0]=min(dp[i-1][0]+1 ,k-1) dp[i][1]=max(dp[i-1][1]-1 ,-k+1) elif c=='D': dp[i][0]=dp[i-1][0] dp[i][1]=dp[i-1][1] elif c=='W': dp[i][0]=min(dp[i-1][0]+1 ,k-1) dp[i][1]=dp[i-1][1]+1 if dp[i][1]==k: flag=False elif c=='L': dp[i][0]=dp[i-1][0]-1 dp[i][1]=max(dp[i-1][1]-1 ,-k+1) if dp[i][0]==-k: flag=False if not flag: print('NO') return i=n if s[i-1]=='?': dp[i][0]=dp[i-1][0]+1 dp[i][1]=dp[i-1][1]-1 elif s[i-1]=='D': dp[i][0]=dp[i-1][0] dp[i][1]=dp[i-1][1] elif s[i-1]=='W': dp[i][0]=dp[i-1][0]+1 dp[i][1]=dp[i-1][1]+1 elif s[i-1]=='L': dp[i][0]=dp[i-1][0]-1 dp[i][1]=dp[i-1][1]-1 res=['?']*n if dp[i][0]==k or dp[i][1]==-k: if dp[i][0]==k: cur=k else: cur=-k for i in range(n-1,-1,-1): c=s[i] if c=='?': if cur>dp[i][0]: cur=cur-1 res[i]='W' elif dp[i][1]<=cur<=dp[i][0]: cur=cur res[i]='D' elif cur<dp[i][1]: cur=cur+1 res[i]='L' elif c=='D': cur=cur res[i]=c elif c=='W': cur=cur-1 res[i]=c elif c=='L': cur=cur+1 res[i]=c for i in range(n): print(res[i],end='') else: print('NO') ma() ```
instruction
0
19,947
19
39,894
Yes
output
1
19,947
19
39,895
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW Submitted Solution: ``` def ma(): s=input() v=s.split(' ') n=int(v[0]) k=int(v[1]) s=input() dp=[[0,0] for _ in range(n+1)] flag=True mp={} mp['W']=1 mp['D']=0 mp['L']=-1 for i in range (1,n): c=s[i-1] if c=='?': dp[i][0]=min(dp[i-1][0]+1 ,k-1) dp[i][1]=max(dp[i-1][1]-1 ,-k+1) else: dp[i][0]=min(dp[i-1][0]+mp[c],k-1) dp[i][1]=max(dp[i-1][1]+mp[c],-k+1) if dp[i][1]==k or dp[i][0]==-k: flag=False break if not flag: print('NO') return i=n if s[i-1]=='?': dp[i][0]=dp[i-1][0]+1 dp[i][1]=dp[i-1][1]-1 else : dp[i][0]=dp[i-1][0]+mp[s[i-1]] dp[i][1]=dp[i-1][1]+mp[s[i-1]] res=['?']*n if dp[i][0]==k or dp[i][1]==-k: if dp[i][0]==k: cur=k else: cur=-k for i in range(n-1,-1,-1): c=s[i] if c=='?': if cur>dp[i][0]: res[i]='W' elif dp[i][1]<=cur<=dp[i][0]: res[i]='D' elif cur<dp[i][1]: res[i]='L' else: res[i]=c cur=cur-mp[res[i]] for i in range(n): print(res[i],end='') else: print('NO') ma() ```
instruction
0
19,948
19
39,896
Yes
output
1
19,948
19
39,897
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW Submitted Solution: ``` n, k = map(int, input().split()) *v, l = input() sets = [(0, 0)] d = {'W' : +1, 'D': 0, 'L': -1} for c in v: ms, mx = sets[-1] ns = max(1 - k, ms + d.get(c, -1)) nx = min(k - 1, mx + d.get(c, +1)) if ns > nx: print('NO') exit(0) sets.append((ns, nx)) ms, mx = sets[-1] if mx == k - 1 and l in '?W': cur = k - 1 ans = ['W'] elif ms == 1 - k and l in '?L': cur = 1 - k ans = ['L'] else: print('NO') exit(0) ans += list(reversed(v)) for i, (c, (s, x)) in enumerate(zip(reversed(v), sets[-2::-1])): if c == '?': ans[i + 1] = next(p for p, q in d.items() if s <= cur - q and cur - q <= x) cur -= d[ans[i + 1]] print(''.join(reversed(ans))) ```
instruction
0
19,949
19
39,898
Yes
output
1
19,949
19
39,899
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW Submitted Solution: ``` #Bhargey Mehta (Sophomore) #DA-IICT, Gandhinagar import sys, math, queue #sys.stdin = open("input.txt", "r") MOD = 10**9+7 sys.setrecursionlimit(1000000) def solve(n, k): if abs(k) > K or (k == K and n < N): return False if dp[n][k] is not None: return dp[n][k] #print(s[n-1], n, k) if s[n-1] == 'W': dp[n][k] = solve(n-1, k-1) elif s[n-1] == 'L': dp[n][k] = solve(n-1, k+1) elif s[n-1] == 'D': dp[n][k] = solve(n-1, k) else: dp[n][k] = solve(n-1, k-1) or solve(n-1, k+1) or solve(n-1, k) return dp[n][k] def back(n, k): if n == 0: return if s[n-1] == 'W': back(n-1, k-1) print('W', end="") elif s[n-1] == 'L': back(n-1, k+1) print('L', end="") elif s[n-1] == 'D': back(n-1, k) print('D', end="") else: if solve(n-1, k-1): back(n-1, k-1) print('W', end="") elif solve(n-1, k+1): back(n-1, k+1) print('L', end="") else: back(n-1, k) print('D', end="") N, K = map(int, input().split()) s = input() dp = [[None for i in range(2*K+1)] for j in range(N+1)] for i in range(2*K+1): dp[0][i] = False dp[0][0] = True for i in range(-K, K+1): if solve(N, i): ans = "" back(N, i) print(ans) exit() print("NO") ```
instruction
0
19,950
19
39,900
No
output
1
19,950
19
39,901
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW Submitted Solution: ``` # Legends Always Come Up with Solution # Author: Manvir Singh import os import sys from io import BytesIO, IOBase from collections import deque def main(): n,k=map(int,input().split()) s=list(input().rstrip()) l,r,q=0,0,deque() for i in range(n-1): if s[i]=='W': r+=1 elif s[i]=='L': l+=1 elif s[i]=='?': q.append(i) if abs(r-l)==k: if r>l and q: s[q.popleft()]='L' elif l>r and q: s[q.popleft()]='W' else: print("NO") return l,r,q=s.count('L'),s.count('W'),s.count('?') if abs(r-l)>k: print("NO") else: z=k-abs(r-l) c='W' if r>=l else 'L' for i in range(n-1,-1,-1): if s[i]=='?': if z: s[i]=c z-=1 else: s[i]='D' if not z: print("".join(s)) else: print("NO") # 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") if __name__ == "__main__": main() ```
instruction
0
19,951
19
39,902
No
output
1
19,951
19
39,903
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW Submitted Solution: ``` import sys n, k = map(int, input().split()) s = list(input()) size, zero = 2*k-1, k-1 dp = [[0]*size for _ in range(n)] dp[0][zero] = 1 for i in range(n-1): for j in range(size): if dp[i][j] == 0: continue if j+1 < size and (s[i] == 'W' or s[i] == '?'): dp[i+1][j+1] = 1 if s[i] == 'D' or s[i] == '?': dp[i+1][j] = 1 if j and (s[i] == 'L' or s[i] == '?'): dp[i+1][j-1] = 1 j = -1 if (s[-1] == 'W' or s[-1] == '?') and dp[-1][-1]: j = size-1 s[-1] = 'W' elif (s[-1] == 'L' or s[-1] == '?') and dp[-1][0]: j = 0 s[-1] = 'L' if j == -1: print('NO') exit() for i in range(n-2, -1, -1): if s[i] == 'W': j -= 1 elif s[i] == 'L': j += 1 elif s[i] == '?': if dp[i][j]: s[i] = 'D' elif j > 0 and dp[i][j-1]: s[i] = 'W' j -= 1 else: s[i] = 'D' j += 1 print(*s, sep='') ```
instruction
0
19,952
19
39,904
No
output
1
19,952
19
39,905
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Each evening Roma plays online poker on his favourite website. The rules of poker on this website are a bit strange: there are always two players in a hand, there are no bets, and the winner takes 1 virtual bourle from the loser. Last evening Roma started to play poker. He decided to spend no more than k virtual bourles — he will stop immediately if the number of his loses exceeds the number of his wins by k. Also Roma will leave the game if he wins enough money for the evening, i.e. if the number of wins exceeds the number of loses by k. Next morning Roma found a piece of paper with a sequence on it representing his results. Roma doesn't remember the results exactly, and some characters in the sequence are written in a way such that it's impossible to recognize this character, so Roma can't recall whether he won k bourles or he lost. The sequence written by Roma is a string s consisting of characters W (Roma won the corresponding hand), L (Roma lost), D (draw) and ? (unknown result). Roma wants to restore any valid sequence by changing all ? characters to W, L or D. The sequence is called valid if all these conditions are met: * In the end the absolute difference between the number of wins and loses is equal to k; * There is no hand such that the absolute difference before this hand was equal to k. Help Roma to restore any such sequence. Input The first line contains two numbers n (the length of Roma's sequence) and k (1 ≤ n, k ≤ 1000). The second line contains the sequence s consisting of characters W, L, D and ?. There are exactly n characters in this sequence. Output If there is no valid sequence that can be obtained from s by replacing all ? characters by W, L or D, print NO. Otherwise print this sequence. If there are multiple answers, print any of them. Examples Input 3 2 L?? Output LDL Input 3 1 W?? Output NO Input 20 5 ?LLLLLWWWWW????????? Output WLLLLLWWWWWWWWLWLWDW Submitted Solution: ``` from sys import exit from copy import deepcopy n, k = [int(i) for i in input().split()] s = [i for i in input()] p = [0] * (n + 1) qind = -1 def check(): global s b = 0 for i in range(len(s)): if s[i] == 'L': b -= 1 elif s[i] == 'W': b += 1 if i != len(s) - 1 and abs(b) >= k: return False return abs(b) == k def solved(): for i in s: if i == '?': print('D', end='') else: print(i, end='') exit(0) def no_ans(): print('NO') exit(0) for i in range(len(s)): p[i + 1] = p[i] if s[i] == 'L': p[i + 1] -= 1 elif s[i] == 'W': p[i + 1] += 1 if abs(p[i + 1]) >= k and i != len(s) - 1: while qind < i and (qind == -1 or s[qind] != '?'): qind += 1 if qind == i and s[i] != '?': no_ans() s[qind] = 'L' if p[i + 1] > 0 else 'W' p[i + 1] = k - 1 if p[i + 1] > 0 else -k + 1 scpy = deepcopy(s) rest = k - p[n] j = n - 1 while j >= 0 and rest > 0: if s[j] == '?': s[j] = 'W' rest -= 1 j -= 1 ok = (rest == 0) and check() if ok: solved() s = deepcopy(scpy) rest = (p[n] + k) j = n - 1 while j >= 0 and rest > 0: if s[j] == '?': s[j] = 'L' rest -= 1 j -= 1 ok = (rest == 0) and check() if not ok: no_ans() solved() ```
instruction
0
19,953
19
39,906
No
output
1
19,953
19
39,907
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N boxes arranged in a circle. The i-th box contains A_i stones. Determine whether it is possible to remove all the stones from the boxes by repeatedly performing the following operation: * Select one box. Let the box be the i-th box. Then, for each j from 1 through N, remove exactly j stones from the (i+j)-th box. Here, the (N+k)-th box is identified with the k-th box. Note that the operation cannot be performed if there is a box that does not contain enough number of stones to be removed. Constraints * 1 ≦ N ≦ 10^5 * 1 ≦ A_i ≦ 10^9 Input The input is given from Standard Input in the following format: N A_1 A_2 … A_N Output If it is possible to remove all the stones from the boxes, print `YES`. Otherwise, print `NO`. Examples Input 5 4 5 1 2 3 Output YES Input 5 6 9 12 10 8 Output YES Input 4 1 2 3 1 Output NO Submitted Solution: ``` import sys input = sys.stdin.readline N = int(input()) A = list(map(int,input().split())) ''' import random N = 3 A = [0]*N for i in range(1000): n = random.randint(1,N) for j in range(N): A[(n-1+j)%N] += j+1 ''' M = N*(N+1)//2 sumA = sum(A) if sumA % M != 0: print('NO') exit() diff = [x-y for x,y in zip(A[1:] + [A[0]], A)] all_cnt = 0 while min(diff) < 0: cnt = 0 for i in range(N): if diff[i] < 0: t = -(diff[i]//(N-1)) cnt += t diff[i] += t*N diff = [d-cnt for d in diff] all_cnt += cnt N2 = sumA - all_cnt * M if N2 % (M*N) == 0: print('YES') else: print('NO') ```
instruction
0
20,161
19
40,322
No
output
1
20,161
19
40,323
Provide a correct Python 3 solution for this coding contest problem. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60
instruction
0
20,994
19
41,988
"Correct Solution: ``` #!/usr/bin/env python3 from bisect import bisect N, Q = map(int, input().split()) A = [0] * (N % 2) + list(map(int, input().split())) HF = len(A) // 2 li = [] cumsum = [sum(A[HF:])] for i in range(HF - 1): left = A[2 * i + 1] right = A[i + HF] li += [(left + right) // 2 + 1] cumsum += [cumsum[-1] + left - right] for _ in range(Q): X = int(input()) print(cumsum[bisect(li, X)]) ```
output
1
20,994
19
41,989
Provide a correct Python 3 solution for this coding contest problem. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60
instruction
0
20,995
19
41,990
"Correct Solution: ``` # http://kmjp.hatenablog.jp/entry/2019/01/13/0930 import sys input = sys.stdin.readline from bisect import bisect_left n, q = map(int, input().split()) a = list(map(int, input().split())) xs = [int(input()) for i in range(q)] s = [0]*(n+1) se = [0]*(n+1) for i in range(n): s[i+1] = s[i] + a[i] if i : se[i+1] = se[i-1] se[i+1] += a[i] def check(x, k): if k > n: return False Tk = (k+1)//2 i = bisect_left(a, x- (a[n-Tk]-x)) return i+k <= n for x in xs: left = 0 right = n+1 while right-left > 1: mid = (left+right)//2 if check(x, mid): left = mid else: right = mid top = (left+1)//2 ans = 0 ans += s[n] - s[n-top] if left%2: left += 1 ans += se[n-left] if n-left>=0 else 0 print(ans) ```
output
1
20,995
19
41,991
Provide a correct Python 3 solution for this coding contest problem. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60
instruction
0
20,996
19
41,992
"Correct Solution: ``` import sys input = sys.stdin.readline def calc(x): l, r = 0, (N+1)//2 while r - l > 1: m = (l+r) // 2 if A[m] + A[2*m] >= 2 * x: l = m else: r = m return l N, Q = map(int, input().split()) A = [int(a) for a in input().split()][::-1] B = [A[0]] + [0] * (N-1) for i in range(1, N): B[i] = B[i-1] + A[i] C = [A[0]] + [0] * (N-1) for i in range(2, N, 2): C[i] = C[i-2] + A[i] C[-1] += C[-2] for _ in range(Q): x = int(input()) c = calc(x) print(B[c] + (C[-1] - C[2*c] if c*2<=N else 0)) ```
output
1
20,996
19
41,993
Provide a correct Python 3 solution for this coding contest problem. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60
instruction
0
20,997
19
41,994
"Correct Solution: ``` from bisect import bisect_left import sys if sys.version_info[0:2] >= (3, 3): from collections.abc import Sequence else: from collections import Sequence class LazySequence(Sequence): def __init__(self, f, n): self.f = f self.n = n def __len__(self): return self.n def __getitem__(self, i): if not (0 <= i < self.n): raise IndexError return self.f(i) N, Q = map(int, input().split()) A = [int(s) for s in input().split()] X = [] for _ in range(Q): X.append(int(input())) # A.sort() s = [0] * (N + 1) for i in range(1, N + 1): s[i] = s[i - 1] + A[i - 1] t = [0, A[0]] + [0] * (N - 1) for i in range(2, N + 1): t[i] = t[i - 2] + A[i - 1] def index_left(x, i): val = 2 * x - A[i] return bisect_left(A, val) def nankaime(x, i): """requires x <= A[i]""" return i - index_left(x, i) + 1 def npi(x, i): return nankaime(x, i) + i def index_right(x, istart): ls = LazySequence(lambda i: npi(x, i + istart), N - istart) return istart + bisect_left(ls, N) - 1 def getans(x): istart = bisect_left(A, x) if istart == N: return t[N] j = index_right(x, istart) turn = N - 1 - j i = j - turn + 1 return s[N] - s[j + 1] + (t[i] if i > 0 else 0) for i in range(Q): print(getans(X[i])) ```
output
1
20,997
19
41,995
Provide a correct Python 3 solution for this coding contest problem. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60
instruction
0
20,998
19
41,996
"Correct Solution: ``` # -*- coding: utf-8 -*- import sys, re from collections import deque, defaultdict, Counter from math import sqrt, hypot, factorial, pi, sin, cos, radians if sys.version_info.minor >= 5: from math import gcd else: from fractions import gcd from heapq import heappop, heappush, heapify, heappushpop from bisect import bisect_left, bisect_right from itertools import permutations, combinations, product from operator import itemgetter, mul from copy import deepcopy from functools import reduce, partial from fractions import Fraction from string import ascii_lowercase, ascii_uppercase, digits def input(): return sys.stdin.readline().strip() def list2d(a, b, c): return [[c] * b for i in range(a)] def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)] def ceil(x, y=1): return int(-(-x // y)) def round(x): return int((x*2+1) // 2) def fermat(x, y, MOD): return x * pow(y, MOD-2, MOD) % MOD def lcm(x, y): return (x * y) // gcd(x, y) def lcm_list(nums): return reduce(lcm, nums, 1) def gcd_list(nums): return reduce(gcd, nums, nums[0]) def INT(): return int(input()) def MAP(): return map(int, input().split()) def LIST(): return list(map(int, input().split())) sys.setrecursionlimit(10 ** 9) INF = float('inf') MOD = 10 ** 9 + 7 N, Q = MAP() A = LIST() sm = sum([A[i] for i in range(N-1, -1, -2)]) borders = [(INF, sm)] j = N-3 for i in range(N-2, N//2-1, -1): border = (A[j] + A[i]) // 2 val = A[i] - A[j] sm += val borders.append((border, sm)) j -= 2 borders.sort() for _ in range(Q): x = INT() idx = bisect_left(borders, (x, 0)) print(borders[idx][1]) ```
output
1
20,998
19
41,997
Provide a correct Python 3 solution for this coding contest problem. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60
instruction
0
20,999
19
41,998
"Correct Solution: ``` from bisect import bisect_left N, Q = map(int, input().split()) A = [int(i) for i in input().split()] X = [int(input()) for _ in range(Q)] i = (N & 1) ^ 1 j = N // 2 st = sum(A[j:]) ret_k = [] ret_v = [] while i < j : ret_k.append((A[i] + A[j]) // 2) ret_v.append(st) st = st - A[j] + A[i] i += 2 j += 1 ret_k.append(1e+12) ret_v.append(st) for x in X : print(ret_v[bisect_left(ret_k, x)]) ```
output
1
20,999
19
41,999
Provide a correct Python 3 solution for this coding contest problem. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60
instruction
0
21,000
19
42,000
"Correct Solution: ``` import bisect n,q = map(int, input().split()) aList = list(map(int, input().split())) sumList=[] sep2SumList=[] for i in range(n): if i==0: sumList.append(aList[i]) else: sumList.append(sumList[-1]+aList[i]) if n%2==0: if i%2==1: if i==1: sep2SumList.append(aList[i]) else: sep2SumList.append(sep2SumList[-1]+aList[i]) else: if i%2==0: if i==0: sep2SumList.append(aList[i]) else: sep2SumList.append(sep2SumList[-1]+aList[i]) sakaime=[] anskazu=(n+1)//2 for i in range(anskazu): sakaime.append((aList[n-(i+1+1)]+aList[n-((i+1+1)*2-1)])//2) sakaime.reverse() sakaime=sakaime[1:] def kotae(x): bisect.bisect_left(sakaime,x) num=len(sakaime)+1-bisect.bisect_left(sakaime,x) if num==len(sakaime)+1: ans=sumList[-1]-sumList[-1-num] else: ans=sumList[-1]-sumList[-1-num]+sep2SumList[(n-num*2+1)//2-1] #+1することで奇数を吸収 return ans for i in range(q): x=int(input()) print(kotae(x)) ```
output
1
21,000
19
42,001
Provide a correct Python 3 solution for this coding contest problem. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60
instruction
0
21,001
19
42,002
"Correct Solution: ``` # coding: utf-8 # Your code here! import bisect n,q = [int(i) for i in input().split()] a = [int(i) for i in input().split()] if n%2 == 1: n+=1 a.insert(0, 0) sikiri = [(a[2*i+1] + a[i+n//2])//2 for i in range(n//2-1)] s = sum(a[n//2:]) ans = [s] for i in range(n//2-1): s = s - a[i+n//2] + a[2*i+1] ans.append(s) #print(a) #print(sikiri) #print(ans) for _ in range(q): x = int(input()) i = bisect.bisect_left(sikiri,x) print(ans[i]) ```
output
1
21,001
19
42,003
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60 Submitted Solution: ``` import itertools import sys def input(): return sys.stdin.readline() def inpl(): return [int(i) for i in input().split()] def f(y): return abs(x-A[y]) N, Q = inpl() A = inpl() SA = list(itertools.accumulate(A)) if N%2 : B = [v for i, v in enumerate(A) if not i%2] B = [0] + list(itertools.accumulate(B)) else: B = [v for i, v in enumerate(A) if i%2] B = [0] + list(itertools.accumulate(B)) for _ in range(Q): x = int(input()) lo = 1 hi = -(-N//2) + 1 while hi - lo >1: mid = (lo+hi)//2 if mid == 1: continue if max(f(N-mid-1), f(N-2*mid+1)) <= f(N-mid): lo = mid else: hi = mid print(SA[N-1] - SA[N-lo-1] + B[-((2*lo-N)//2)]) ```
instruction
0
21,002
19
42,004
Yes
output
1
21,002
19
42,005
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60 Submitted Solution: ``` from collections import defaultdict, Counter from itertools import product, groupby, count, permutations, combinations from math import pi, sqrt from collections import deque from bisect import bisect, bisect_left, bisect_right from string import ascii_lowercase from functools import lru_cache import sys sys.setrecursionlimit(10000) INF = float("inf") YES, Yes, yes, NO, No, no = "YES", "Yes", "yes", "NO", "No", "no" dy4, dx4 = [0, 1, 0, -1], [1, 0, -1, 0] dy8, dx8 = [0, -1, 0, 1, 1, -1, -1, 1], [1, 0, -1, 0, 1, 1, -1, -1] def inside(y, x, H, W): return 0 <= y < H and 0 <= x < W def ceil(a, b): return (a + b - 1) // b # aとbの最大公約数 def gcd(a, b): if b == 0: return a return gcd(b, a % b) # aとbの最小公倍数 def lcm(a, b): g = gcd(a, b) return a / g * b def solve(A, Q): N = len(A) A = A[::-1] s, es = [0] * (N + 1), [0] * (N + 1) for i in range(N): s[i + 1] = s[i] + A[i] es[i + 1] = es[i] + (A[i] if i % 2 == 0 else 0) x_list, sum_t_list = [], [] for n in range((N - 1) // 2): x = (A[n + 1] + A[n * 2 + 2]) // 2 + 1 sum_t = s[n + 1] + (es[N] - es[n * 2 + 2]) x_list.append(x) sum_t_list.append(sum_t) x_list = x_list[::-1] sum_t_list = sum_t_list[::-1] for _ in range(Q): x = int(input()) p = bisect_right(x_list, x) if p == 0: print(s[(N + 1) // 2]) else: print(sum_t_list[p - 1]) def main(): N, Q = map(int, input().split()) A = list(map(int, input().split())) solve(A, Q) if __name__ == '__main__': main() ```
instruction
0
21,003
19
42,006
Yes
output
1
21,003
19
42,007
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60 Submitted Solution: ``` #!/usr/bin/env python3 from collections import defaultdict,deque from heapq import heappush, heappop from bisect import bisect_left, bisect_right import sys, random, itertools, math sys.setrecursionlimit(10**5) input = sys.stdin.readline sqrt = math.sqrt def LI(): return list(map(int, input().split())) def LF(): return list(map(float, input().split())) def LI_(): return list(map(lambda x: int(x)-1, input().split())) def II(): return int(input()) def IF(): return float(input()) def LS(): return list(map(list, input().split())) def S(): return list(input().rstrip()) def IR(n): return [II() for _ in range(n)] def LIR(n): return [LI() for _ in range(n)] def FR(n): return [IF() for _ in range(n)] def LFR(n): return [LI() for _ in range(n)] def LIR_(n): return [LI_() for _ in range(n)] def SR(n): return [S() for _ in range(n)] def LSR(n): return [LS() for _ in range(n)] mod = 1000000007 inf = 1e10 #solve def solve(): n, q = LI() a = LI() odd = [0] * n even = [0] * n def f(mid): return abs(a[mid] - x) < abs(a[mid - (n - mid - 1)] - x) for i in range(n): if i & 1: odd[i] += odd[i - 1] + a[i] else: odd[i] += odd[i - 1] acc = list(itertools.accumulate(a)) for _ in range(q): x = II() ok = 0 ng = n while abs(ng - ok) > 1: mid = (ok + ng) // 2 if f(mid): ok = mid else: ng = mid ok = ng - (n - ng) ng -= 1 ans = acc[-1] - acc[ng] if ok < 0: pass elif n & 1: ans += acc[ok]-odd[ok] else: ans += odd[ok] print(ans) return #main if __name__ == '__main__': solve() ```
instruction
0
21,004
19
42,008
Yes
output
1
21,004
19
42,009
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60 Submitted Solution: ``` #参考 #https://atcoder.jp/contests/aising2019/submissions/3995168 import bisect N,Q=map(int,input().split()) A=list(map(int,input().split())) Asum=[0]*N Asum2=[0]*N total=0 for i in range(N): total+=A[i] Asum[i]=total if i>1: Asum2[i]=A[i]+Asum2[i-2] else: Asum2[i]=A[i] X=[] for i in range(Q): X.append((int(input()),i)) X.sort(key=lambda x :x[0]) #yで高橋くんと青木くんの取りたいカードが初めて衝突すると考える。 #このようなyは半分より小さい所にはないので初期値を半分のところとする。 #yがNまで来た時は最初から交互に取る #Xを小さい順から計算することで、yの値が単調増加になる y=N//2-1 ans=[0]*Q for x,i in X: #条件式はy<=N-1を最初に持ってこないとA[y]の参照でエラーの可能性 while y<=N-1 and x>A[y]: y+=1 while y<=N-1: takahashi=N-y aoki=y+1-bisect.bisect_left(A,x-(A[y]-x)) if takahashi>aoki: y+=1 else: break #右端からA[y]までは全て高橋くんが取る ans[i]+=Asum[N-1]-Asum[y-1] #青木くんはyからN-y個取っているので、その下のところから交互に取る if y-(N-y)-1<0: continue ans[i]+=Asum2[y-(N-y)-1] for i in range(Q): print(ans[i]) ```
instruction
0
21,005
19
42,010
Yes
output
1
21,005
19
42,011
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60 Submitted Solution: ``` from bisect import bisect_left, bisect_right import sys input = sys.stdin.readline N, Q = map(int, input().split()) A = list(map(int, input().split())) A.sort() cum1 = [0] * N cum1[0], cum1[1] = A[0], A[1] for i in range(2, N): cum1[i] = cum1[i-2] + A[i] cum2 = [0] * N cum2[-1] = A[-1] for i in range(N-1)[::-1]: cum2[i] = cum2[i+1] + A[i] for _ in range(Q): x = int(input()) lb, ub = 0, 10**9 while ub - lb > 1: m = (lb + ub) // 2 i = bisect_left(A, x - m) j = bisect_right(A, x + m) cnt = j - i if cnt <= N - j: lb = m else: ub = m i = bisect_left(A, x - lb) j = bisect_right(A, x + lb) i -= (N - j) - (j - i) ans = (cum1[i-1] if i > 0 else 0) + (cum2[j] if j < N else 0) print(ans) ```
instruction
0
21,006
19
42,012
No
output
1
21,006
19
42,013
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60 Submitted Solution: ``` from itertools import accumulate import bisect n,q = map(int,input().split()) if n%2: a = [0]+list(map(int,input().split())) n += 1 else: a = list(map(int,input().split())) fs = [a[i] if i%2 else 0 for i in range(n)] accss = [0]*n accff = list(accumulate(a)) accfs = list(accumulate(fs)) xls = [] xpt = [] for i in range(n//2): xls.append((a[2*i+1]+a[i+n//2])/2) if i == 0: xpt.append(accff[n-1]-accff[n//2-1]) else: xpt.append(accff[n-1]-accff[i+n//2-1]+accfs[2*i-1]) for _ in range(q): x = bisect.bisect_left(xls,int(input())) if x >= n-1: print(xpt[-1]) else: print(xpt[x]) ```
instruction
0
21,007
19
42,014
No
output
1
21,007
19
42,015
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60 Submitted Solution: ``` N, Q = map(int, input().split()) A = [int(a) for a in input().split()][::-1] for _ in range(Q): x = int(input()) l, r = 0, (N+1)//2 while r - l > 1: m = (l+r) // 2 if A[m] + A[2*m] >= 2 * x: l = m else: r = m l += 1 print(sum(A[:l] + A[2*l::2])) ```
instruction
0
21,008
19
42,016
No
output
1
21,008
19
42,017
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N cards. The i-th card has an integer A_i written on it. For any two cards, the integers on those cards are different. Using these cards, Takahashi and Aoki will play the following game: * Aoki chooses an integer x. * Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner: * Takahashi should take the card with the largest integer among the remaining card. * Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards. * The game ends when there is no card remaining. You are given Q candidates for the value of x: X_1, X_2, ..., X_Q. For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i. Constraints * 2 \leq N \leq 100 000 * 1 \leq Q \leq 100 000 * 1 \leq A_1 < A_2 < ... < A_N \leq 10^9 * 1 \leq X_i \leq 10^9 (1 \leq i \leq Q) * All values in input are integers. Input Input is given from Standard Input in the following format: N Q A_1 A_2 ... A_N X_1 X_2 : X_Q Output Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i. Examples Input 5 5 3 5 7 11 13 1 4 9 10 13 Output 31 31 27 23 23 Input 4 3 10 20 30 40 2 34 34 Output 70 60 60 Submitted Solution: ``` import bisect import sys input = sys.stdin.readline INF = 10**12 n, q = [int(item) for item in input().split()] a = [int(item) for item in input().split()] # Calc cumrative sum sum_even = [0] * (n + 1) sum_odd = [0] * (n + 1) sum_all = [0] * (n + 1) for i, item in enumerate(a): if i % 2 == 0: sum_odd[i+1] = sum_odd[i] + a[i] sum_even[i+1] = sum_even[i] else: sum_even[i+1] = sum_even[i] + a[i] sum_odd[i+1] = sum_odd[i] sum_all[i+1] = sum_all[i] + a[i] # Iterate in query a.append(INF) ans = [] for i in range(q): x = int(input()) # Get div of aoki - takahashi # l: aoki takes, r: takahashi takes l = 0; r = n - 1 while r - l > 1: m = (r + l) // 2 rng = abs(x - a[m]) t_num = n - m a_num = n - t_num - (bisect.bisect_left(a, x - rng)) if t_num <= a_num + 1: r = m else: l = m rng = abs(x - a[r]) t_num = n - r rest = n - 2 * t_num t_sum = sum_all[n] - sum_all[n - t_num] a_sum = sum_all[r] - sum_all[r - t_num] # Add stripe area if n - t_num * 2 > 0: if rest % 2 == 0: t_sum += sum_even[rest] a_sum += sum_odd[rest] else: t_sum += sum_odd[rest] a_sum += sum_even[rest] ans.append(t_sum) print("\n".join([str(item) for item in ans])) ```
instruction
0
21,009
19
42,018
No
output
1
21,009
19
42,019
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N boxes arranged in a row from left to right. The i-th box from the left contains a_i manju (buns stuffed with bean paste). Sugim and Sigma play a game using these boxes. They alternately perform the following operation. Sugim goes first, and the game ends when a total of N operations are performed. * Choose a box that still does not contain a piece and is adjacent to the box chosen in the other player's last operation, then put a piece in that box. If there are multiple such boxes, any of them can be chosen. * If there is no box that satisfies the condition above, or this is Sugim's first operation, choose any one box that still does not contain a piece, then put a piece in that box. At the end of the game, each player can have the manju in the boxes in which he put his pieces. They love manju, and each of them is wise enough to perform the optimal moves in order to have the maximum number of manju at the end of the game. Find the number of manju that each player will have at the end of the game. Constraints * 2 \leq N \leq 300 000 * 1 \leq a_i \leq 1000 * All values in input are integers. Input Input is given from Standard Input in the following format: N a_1 a_2 ... a_N Output Print the numbers of Sugim's manju and Sigma's manju at the end of the game, in this order, with a space in between. Examples Input 5 20 100 10 1 10 Output 120 21 Input 6 4 5 1 1 4 5 Output 11 9 Input 5 1 10 100 10 1 Output 102 20 Submitted Solution: ``` from os import sys sys.setrecursionlimit(1000000000) n = int(input()) l = list(map(int, input().split())) def completo(l): for e in l: if e != 0: return False return True def solve(turno, a, b, l, index,n): if completo(l): print(a,b) return if turno == n: print(a,b) return if index == -1: m = max(l) index = l.index(m) elif l[index-1] == 0 and l[index+1] == 0: solve(turno,a,b,l,-1,n) elif l[index-1] > l[index+1]: m = l[index-1] index = index-1 else: m = l[index+1] index = index+1 l[index] = 0 if turno % 2 == 0: if index == 0 or index == len(l)-1: solve(turno+1,a+m,b,l,-1,n) else: solve(turno+1,a+m,b,l,index,n) else: if index == 0 or index == len(l)-1: solve(turno+1,a,b+m,l,-1,n) else: solve(turno+1,a,b+m,l,index,n) solve(0,0,0,l,-1,n) ```
instruction
0
21,010
19
42,020
No
output
1
21,010
19
42,021
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N boxes arranged in a row from left to right. The i-th box from the left contains a_i manju (buns stuffed with bean paste). Sugim and Sigma play a game using these boxes. They alternately perform the following operation. Sugim goes first, and the game ends when a total of N operations are performed. * Choose a box that still does not contain a piece and is adjacent to the box chosen in the other player's last operation, then put a piece in that box. If there are multiple such boxes, any of them can be chosen. * If there is no box that satisfies the condition above, or this is Sugim's first operation, choose any one box that still does not contain a piece, then put a piece in that box. At the end of the game, each player can have the manju in the boxes in which he put his pieces. They love manju, and each of them is wise enough to perform the optimal moves in order to have the maximum number of manju at the end of the game. Find the number of manju that each player will have at the end of the game. Constraints * 2 \leq N \leq 300 000 * 1 \leq a_i \leq 1000 * All values in input are integers. Input Input is given from Standard Input in the following format: N a_1 a_2 ... a_N Output Print the numbers of Sugim's manju and Sigma's manju at the end of the game, in this order, with a space in between. Examples Input 5 20 100 10 1 10 Output 120 21 Input 6 4 5 1 1 4 5 Output 11 9 Input 5 1 10 100 10 1 Output 102 20 Submitted Solution: ``` n = int(input()) l = list(map(int, input().split())) def completo(l): for e in l: if e != 0: return False return True def solve(turno, a, b, l, index,n): if completo(l): print(a,b) return if turno == n: print(a,b) return if index == -1: m = max(l) index = l.index(m) elif l[index-1] == 0 and l[index+1] == 0: solve(turno,a,b,l,-1,n) elif l[index-1] > l[index+1]: m = l[index-1] index = index-1 else: m = l[index+1] index = index+1 l[index] = 0 if turno % 2 == 0: if index == 0 or index == len(l)-1: solve(turno+1,a+m,b,l,-1,n) else: solve(turno+1,a+m,b,l,index,n) else: if index == 0 or index == len(l)-1: solve(turno+1,a,b+m,l,-1,n) else: solve(turno+1,a,b+m,l,index,n) solve(0,0,0,l,-1,n) ```
instruction
0
21,011
19
42,022
No
output
1
21,011
19
42,023
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N boxes arranged in a row from left to right. The i-th box from the left contains a_i manju (buns stuffed with bean paste). Sugim and Sigma play a game using these boxes. They alternately perform the following operation. Sugim goes first, and the game ends when a total of N operations are performed. * Choose a box that still does not contain a piece and is adjacent to the box chosen in the other player's last operation, then put a piece in that box. If there are multiple such boxes, any of them can be chosen. * If there is no box that satisfies the condition above, or this is Sugim's first operation, choose any one box that still does not contain a piece, then put a piece in that box. At the end of the game, each player can have the manju in the boxes in which he put his pieces. They love manju, and each of them is wise enough to perform the optimal moves in order to have the maximum number of manju at the end of the game. Find the number of manju that each player will have at the end of the game. Constraints * 2 \leq N \leq 300 000 * 1 \leq a_i \leq 1000 * All values in input are integers. Input Input is given from Standard Input in the following format: N a_1 a_2 ... a_N Output Print the numbers of Sugim's manju and Sigma's manju at the end of the game, in this order, with a space in between. Examples Input 5 20 100 10 1 10 Output 120 21 Input 6 4 5 1 1 4 5 Output 11 9 Input 5 1 10 100 10 1 Output 102 20 Submitted Solution: ``` import numpy as np def main(): n = int(input()) a = list(map(int, input().split())) a = np.array(a) s1 = 0 s2 = 0 for i in range(n): z = i % 2 if (i == 0): index = np.argmax(a) s1 = a[index] a[index] = -1 continue else: if (z == 0): [s1, a, index] = auto(s1, a, index) else: [s2, a, index] = auto(s2, a, index) print('{} {}'.format(s1, s2)) def auto(s, a, index): left = 0 right = 0 if (index == 0): left = -1 right = a[index+1] elif (index == len(a)-1): left = a[index-1] right = -1 else: left = a[index - 1] right = a[index + 1] if (left == -1 and right == -1): index = np.argmax(a) s += a[index] a[index] = -1 elif (left >= right): s += left index = index-1 a[index] = -1 elif (left < right): s += right index = index+1 a[index] = -1 return [s, a, index] if __name__ == '__main__': main() ```
instruction
0
21,012
19
42,024
No
output
1
21,012
19
42,025
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There are N boxes arranged in a row from left to right. The i-th box from the left contains a_i manju (buns stuffed with bean paste). Sugim and Sigma play a game using these boxes. They alternately perform the following operation. Sugim goes first, and the game ends when a total of N operations are performed. * Choose a box that still does not contain a piece and is adjacent to the box chosen in the other player's last operation, then put a piece in that box. If there are multiple such boxes, any of them can be chosen. * If there is no box that satisfies the condition above, or this is Sugim's first operation, choose any one box that still does not contain a piece, then put a piece in that box. At the end of the game, each player can have the manju in the boxes in which he put his pieces. They love manju, and each of them is wise enough to perform the optimal moves in order to have the maximum number of manju at the end of the game. Find the number of manju that each player will have at the end of the game. Constraints * 2 \leq N \leq 300 000 * 1 \leq a_i \leq 1000 * All values in input are integers. Input Input is given from Standard Input in the following format: N a_1 a_2 ... a_N Output Print the numbers of Sugim's manju and Sigma's manju at the end of the game, in this order, with a space in between. Examples Input 5 20 100 10 1 10 Output 120 21 Input 6 4 5 1 1 4 5 Output 11 9 Input 5 1 10 100 10 1 Output 102 20 Submitted Solution: ``` n = input() slimes = map(int, input().split()) res = 0 last = -1 cnt = 0 for slime in slimes: if slime != last: res += cnt // 2 last = slime cnt = 1 else: cnt += 1 res += cnt // 2 print(res) ```
instruction
0
21,013
19
42,026
No
output
1
21,013
19
42,027
Provide a correct Python 3 solution for this coding contest problem. D --Invisible Problem Statement You are trying to play a card game called "Invisible" with your friends. This card game uses two types of cards, a "scoring card" and a "jamming card". A positive value is written on each score card. The rules of this card game are as follows. * The game is played by two players, player 1 and player 2. The game starts on player 1's turn. * There is one stack and two decks in the field. The stack consists of cards placed by two players. In addition, the deck possessed by each player consists of the score card and the obstruction card possessed by that player. Players can check the order of cards in themselves or in their opponent's deck at any time. There are no cards on the stack at the beginning of the game. * The two players alternately perform one of the following two actions exactly once. * Put the top card of your deck on the top of the stack. However, this action cannot be performed when there are no cards in your deck. * Pass your turn. * When the player passes the turn, the following processing is performed. * Each player gets all the scoring cards in the stack that meet the following two conditions. The score card obtained is removed from the field. 1. This is the score card you put on the stack. 2. Above any disturbing cards placed by your opponent (when there are no disturbing cards in your stack, the player gets all the cards he or she puts on the stack). * Remove all cards in the stack. If both players pass in succession with no cards on the stack, the game ends. The final score of each player is the sum of the numbers written on the score card obtained by each player. Each player takes the best action to maximize the value obtained by subtracting the opponent's score from his own score. Your job is to calculate the difference between Player 1's score and Player 2's score when each player behaves optimally for each player's deck given. Input The input consists of a single test case of the form: $ n $ $ m $ $ a_1 $ $ a_2 $ $ \ dots $ $ a_n $ $ b_1 $ $ b_2 $ $ \ dots $ $ b_m $ The first line consists of positive integers $ n $, $ m $ ($ 1 \ le n, m \ le 50 $) representing the number of decks. The second line consists of $ n $ integers, where $ a_i $ represents the $ i $ th card from the top of player 1's deck ($ 1 \ le i \ le n $). $ a_i $ is more than $ 1 $, less than $ 1 {,} 000 {,} 000 $, or $ -1 $. The third line consists of $ m $ integers, where $ b_j $ represents the $ j $ th card from the top of player 2's deck ($ 1 \ le j \ le m $). $ b_j $ is more than $ 1 $, less than $ 1 {,} 000 {,} 000 $, or $ -1 $. When $ a_i $ and $ b_j $ are positive integers, it represents a scoring card, and when it is $ -1 $, it represents a jamming card. Output Output (Score of Player 1)-(Score of Player 2) when each player behaves optimally. Sample Input 1 twenty two 100 -1 200 300 Output for the Sample Input 1 -100 <image> <image> <image> Sample Input 2 3 5 10 30 -1 -1 90 20 10 -1 Output for the Sample Input 2 0 Sample Input 3 4 5 15 20 10 30 50 30 10 20 25 Output for the Sample Input 3 -60 Example Input 2 2 100 -1 200 300 Output -100
instruction
0
21,131
19
42,262
"Correct Solution: ``` n, m = [int(i) for i in input().split()] A = [int(i) for i in input().split()] B = [int(i) for i in input().split()] memo = dict() def calc(A, i): if A[i] != -1: return 0 point = 0 for j in range(i - 1, -1, -1): if A[j] == -1: break point += A[j] return point def dfs(a, b, skip, turn, a_stack, b_stack): key = (a, b, skip, turn, a_stack, b_stack) if key in memo: return memo[key] if skip == 3: return 0 if turn % 2 == 0: memo[key] = dfs(a, b, skip + 1, (turn + 1) % 2, 0, 0) + a_stack - b_stack if len(A) == a: return memo[key] if A[a] == -1: b_stack = 0 else: a_stack += A[a] memo[key] = max(memo[key], dfs(a + 1, b, 0, (turn + 1) % 2, a_stack, b_stack)) else: memo[key] = dfs(a, b, skip + 1, (turn + 1) % 2, 0, 0) - b_stack + a_stack if len(B) == b: return memo[key] if B[b] == -1: a_stack = 0 else: b_stack += B[b] memo[key] = min(memo[key], dfs(a, b + 1, 0, (turn + 1) % 2, a_stack, b_stack)) return memo[key] print(dfs(0, 0, 0, 0, 0, 0)) ```
output
1
21,131
19
42,263
Provide a correct Python 3 solution for this coding contest problem. D --Invisible Problem Statement You are trying to play a card game called "Invisible" with your friends. This card game uses two types of cards, a "scoring card" and a "jamming card". A positive value is written on each score card. The rules of this card game are as follows. * The game is played by two players, player 1 and player 2. The game starts on player 1's turn. * There is one stack and two decks in the field. The stack consists of cards placed by two players. In addition, the deck possessed by each player consists of the score card and the obstruction card possessed by that player. Players can check the order of cards in themselves or in their opponent's deck at any time. There are no cards on the stack at the beginning of the game. * The two players alternately perform one of the following two actions exactly once. * Put the top card of your deck on the top of the stack. However, this action cannot be performed when there are no cards in your deck. * Pass your turn. * When the player passes the turn, the following processing is performed. * Each player gets all the scoring cards in the stack that meet the following two conditions. The score card obtained is removed from the field. 1. This is the score card you put on the stack. 2. Above any disturbing cards placed by your opponent (when there are no disturbing cards in your stack, the player gets all the cards he or she puts on the stack). * Remove all cards in the stack. If both players pass in succession with no cards on the stack, the game ends. The final score of each player is the sum of the numbers written on the score card obtained by each player. Each player takes the best action to maximize the value obtained by subtracting the opponent's score from his own score. Your job is to calculate the difference between Player 1's score and Player 2's score when each player behaves optimally for each player's deck given. Input The input consists of a single test case of the form: $ n $ $ m $ $ a_1 $ $ a_2 $ $ \ dots $ $ a_n $ $ b_1 $ $ b_2 $ $ \ dots $ $ b_m $ The first line consists of positive integers $ n $, $ m $ ($ 1 \ le n, m \ le 50 $) representing the number of decks. The second line consists of $ n $ integers, where $ a_i $ represents the $ i $ th card from the top of player 1's deck ($ 1 \ le i \ le n $). $ a_i $ is more than $ 1 $, less than $ 1 {,} 000 {,} 000 $, or $ -1 $. The third line consists of $ m $ integers, where $ b_j $ represents the $ j $ th card from the top of player 2's deck ($ 1 \ le j \ le m $). $ b_j $ is more than $ 1 $, less than $ 1 {,} 000 {,} 000 $, or $ -1 $. When $ a_i $ and $ b_j $ are positive integers, it represents a scoring card, and when it is $ -1 $, it represents a jamming card. Output Output (Score of Player 1)-(Score of Player 2) when each player behaves optimally. Sample Input 1 twenty two 100 -1 200 300 Output for the Sample Input 1 -100 <image> <image> <image> Sample Input 2 3 5 10 30 -1 -1 90 20 10 -1 Output for the Sample Input 2 0 Sample Input 3 4 5 15 20 10 30 50 30 10 20 25 Output for the Sample Input 3 -60 Example Input 2 2 100 -1 200 300 Output -100
instruction
0
21,132
19
42,264
"Correct Solution: ``` import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools sys.setrecursionlimit(10**7) inf = 10**20 eps = 1.0 / 10**13 mod = 10**9+7 dd = [(-1,0),(0,1),(1,0),(0,-1)] ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)] def LI(): return [int(x) for x in sys.stdin.readline().split()] def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()] def LF(): return [float(x) for x in sys.stdin.readline().split()] def LS(): return sys.stdin.readline().split() def I(): return int(sys.stdin.readline()) def F(): return float(sys.stdin.readline()) def S(): return input() def pf(s): return print(s, flush=True) def main(): n,m = LI() a = LI() b = LI() fm = {} def f(ai,bi,pt,sa,sb,t): if pt > 2: return 0 key = (ai,bi,pt,sa,sb,t) if key in fm: return fm[key] r = f(ai,bi,pt+1,0,0,not t) + sa - sb tr = 0 if t: if ai < n: if a[ai] < 0: tr = f(ai+1,bi,0,sa,0,not t) else: tr = f(ai+1,bi,0,sa+a[ai],sb,not t) if r < tr: r = tr else: if bi < m: if b[bi] < 0: tr = f(ai,bi+1,0,0,sb,not t) else: tr = f(ai,bi+1,0,sa,sb+b[bi],not t) if r > tr: r = tr fm[key] = r return r r = f(0,0,0,0,0,True) return r print(main()) ```
output
1
21,132
19
42,265
Provide a correct Python 3 solution for this coding contest problem. D --Invisible Problem Statement You are trying to play a card game called "Invisible" with your friends. This card game uses two types of cards, a "scoring card" and a "jamming card". A positive value is written on each score card. The rules of this card game are as follows. * The game is played by two players, player 1 and player 2. The game starts on player 1's turn. * There is one stack and two decks in the field. The stack consists of cards placed by two players. In addition, the deck possessed by each player consists of the score card and the obstruction card possessed by that player. Players can check the order of cards in themselves or in their opponent's deck at any time. There are no cards on the stack at the beginning of the game. * The two players alternately perform one of the following two actions exactly once. * Put the top card of your deck on the top of the stack. However, this action cannot be performed when there are no cards in your deck. * Pass your turn. * When the player passes the turn, the following processing is performed. * Each player gets all the scoring cards in the stack that meet the following two conditions. The score card obtained is removed from the field. 1. This is the score card you put on the stack. 2. Above any disturbing cards placed by your opponent (when there are no disturbing cards in your stack, the player gets all the cards he or she puts on the stack). * Remove all cards in the stack. If both players pass in succession with no cards on the stack, the game ends. The final score of each player is the sum of the numbers written on the score card obtained by each player. Each player takes the best action to maximize the value obtained by subtracting the opponent's score from his own score. Your job is to calculate the difference between Player 1's score and Player 2's score when each player behaves optimally for each player's deck given. Input The input consists of a single test case of the form: $ n $ $ m $ $ a_1 $ $ a_2 $ $ \ dots $ $ a_n $ $ b_1 $ $ b_2 $ $ \ dots $ $ b_m $ The first line consists of positive integers $ n $, $ m $ ($ 1 \ le n, m \ le 50 $) representing the number of decks. The second line consists of $ n $ integers, where $ a_i $ represents the $ i $ th card from the top of player 1's deck ($ 1 \ le i \ le n $). $ a_i $ is more than $ 1 $, less than $ 1 {,} 000 {,} 000 $, or $ -1 $. The third line consists of $ m $ integers, where $ b_j $ represents the $ j $ th card from the top of player 2's deck ($ 1 \ le j \ le m $). $ b_j $ is more than $ 1 $, less than $ 1 {,} 000 {,} 000 $, or $ -1 $. When $ a_i $ and $ b_j $ are positive integers, it represents a scoring card, and when it is $ -1 $, it represents a jamming card. Output Output (Score of Player 1)-(Score of Player 2) when each player behaves optimally. Sample Input 1 twenty two 100 -1 200 300 Output for the Sample Input 1 -100 <image> <image> <image> Sample Input 2 3 5 10 30 -1 -1 90 20 10 -1 Output for the Sample Input 2 0 Sample Input 3 4 5 15 20 10 30 50 30 10 20 25 Output for the Sample Input 3 -60 Example Input 2 2 100 -1 200 300 Output -100
instruction
0
21,133
19
42,266
"Correct Solution: ``` n, m = map(int, input().split()) *A, = map(int, input().split()) *B, = map(int, input().split()) memo = {} def dfs(p, q, s, t, turn, pss): if (p, q, s, t, turn, pss) in memo: return memo[p, q, s, t, turn, pss] if p == len(A) and q == len(B): return s-t res = 0 if turn: # first if pss < 2: if s+t: res = (s - t) + dfs(p, q, 0, 0, 0, 0) else: res = dfs(p, q, 0, 0, 0, pss+1) else: return 0 if p < len(A): if A[p] == -1: res = max(res, dfs(p+1, q, s, 0, 0, 0)) else: res = max(res, dfs(p+1, q, s+A[p], t, 0, 0)) else: # second if pss < 2: if s+t: res = (s - t) + dfs(p, q, 0, 0, 1, 0) else: res = dfs(p, q, 0, 0, 1, pss+1) else: return 0 if q < len(B): if B[q] == -1: res = min(res, dfs(p, q+1, 0, t, 1, 0)) else: res = min(res, dfs(p, q+1, s, t+B[q], 1, 0)) memo[p, q, s, t, turn, pss] = res return res print(dfs(0, 0, 0, 0, 1, 0)) ```
output
1
21,133
19
42,267
Provide tags and a correct Python 3 solution for this coding contest problem. As we all know, Max is the best video game player among her friends. Her friends were so jealous of hers, that they created an actual game just to prove that she's not the best at games. The game is played on a directed acyclic graph (a DAG) with n vertices and m edges. There's a character written on each edge, a lowercase English letter. <image> Max and Lucas are playing the game. Max goes first, then Lucas, then Max again and so on. Each player has a marble, initially located at some vertex. Each player in his/her turn should move his/her marble along some edge (a player can move the marble from vertex v to vertex u if there's an outgoing edge from v to u). If the player moves his/her marble from vertex v to vertex u, the "character" of that round is the character written on the edge from v to u. There's one additional rule; the ASCII code of character of round i should be greater than or equal to the ASCII code of character of round i - 1 (for i > 1). The rounds are numbered for both players together, i. e. Max goes in odd numbers, Lucas goes in even numbers. The player that can't make a move loses the game. The marbles may be at the same vertex at the same time. Since the game could take a while and Lucas and Max have to focus on finding Dart, they don't have time to play. So they asked you, if they both play optimally, who wins the game? You have to determine the winner of the game for all initial positions of the marbles. Input The first line of input contains two integers n and m (2 ≤ n ≤ 100, <image>). The next m lines contain the edges. Each line contains two integers v, u and a lowercase English letter c, meaning there's an edge from v to u written c on it (1 ≤ v, u ≤ n, v ≠ u). There's at most one edge between any pair of vertices. It is guaranteed that the graph is acyclic. Output Print n lines, a string of length n in each one. The j-th character in i-th line should be 'A' if Max will win the game in case her marble is initially at vertex i and Lucas's marble is initially at vertex j, and 'B' otherwise. Examples Input 4 4 1 2 b 1 3 a 2 4 c 3 4 b Output BAAA ABAA BBBA BBBB Input 5 8 5 3 h 1 2 c 3 1 c 3 2 r 5 1 r 4 3 z 5 4 r 5 2 h Output BABBB BBBBB AABBB AAABA AAAAB Note Here's the graph in the first sample test case: <image> Here's the graph in the second sample test case: <image>
instruction
0
21,721
19
43,442
Tags: dfs and similar, dp, games, graphs Correct Solution: ``` # python3 from functools import lru_cache def readline(): return list(map(int, input().split())) def main(): n, m = readline() edges = [list() for __ in range(n)] for __ in range(m): tokens = input().split() begin, end = map(int, tokens[:2]) weight = ord(tokens[2]) edges[begin - 1].append((end - 1, weight)) @lru_cache(maxsize=None) def first_wins(first, second, lower=0): for (nxt, w) in edges[first]: if w >= lower: if not first_wins(second, nxt, w): return True return False for i in range(n): print("".join("BA"[first_wins(i, j)] for j in range(n))) main() ```
output
1
21,721
19
43,443
Provide tags and a correct Python 3 solution for this coding contest problem. As we all know, Max is the best video game player among her friends. Her friends were so jealous of hers, that they created an actual game just to prove that she's not the best at games. The game is played on a directed acyclic graph (a DAG) with n vertices and m edges. There's a character written on each edge, a lowercase English letter. <image> Max and Lucas are playing the game. Max goes first, then Lucas, then Max again and so on. Each player has a marble, initially located at some vertex. Each player in his/her turn should move his/her marble along some edge (a player can move the marble from vertex v to vertex u if there's an outgoing edge from v to u). If the player moves his/her marble from vertex v to vertex u, the "character" of that round is the character written on the edge from v to u. There's one additional rule; the ASCII code of character of round i should be greater than or equal to the ASCII code of character of round i - 1 (for i > 1). The rounds are numbered for both players together, i. e. Max goes in odd numbers, Lucas goes in even numbers. The player that can't make a move loses the game. The marbles may be at the same vertex at the same time. Since the game could take a while and Lucas and Max have to focus on finding Dart, they don't have time to play. So they asked you, if they both play optimally, who wins the game? You have to determine the winner of the game for all initial positions of the marbles. Input The first line of input contains two integers n and m (2 ≤ n ≤ 100, <image>). The next m lines contain the edges. Each line contains two integers v, u and a lowercase English letter c, meaning there's an edge from v to u written c on it (1 ≤ v, u ≤ n, v ≠ u). There's at most one edge between any pair of vertices. It is guaranteed that the graph is acyclic. Output Print n lines, a string of length n in each one. The j-th character in i-th line should be 'A' if Max will win the game in case her marble is initially at vertex i and Lucas's marble is initially at vertex j, and 'B' otherwise. Examples Input 4 4 1 2 b 1 3 a 2 4 c 3 4 b Output BAAA ABAA BBBA BBBB Input 5 8 5 3 h 1 2 c 3 1 c 3 2 r 5 1 r 4 3 z 5 4 r 5 2 h Output BABBB BBBBB AABBB AAABA AAAAB Note Here's the graph in the first sample test case: <image> Here's the graph in the second sample test case: <image>
instruction
0
21,722
19
43,444
Tags: dfs and similar, dp, games, graphs Correct Solution: ``` # int(input()) # [int(i) for i in input().split()] import sys sys.setrecursionlimit(20000) def go(v,w,last): if game[v][w][last] >= 0: return(game[v][w][last]) flag = 0 move = 0 for p in edges_out[v]: if p[1] >= last: move = 1 if not go(w,p[0],p[1]): flag = 1 break if not move or not flag: game[v][w][last] = 0 return(0) else: game[v][w][last] = 1 return(1) n,m = [int(i) for i in input().split()] edges_in = [] edges_out = [] for i in range(n): edges_in.append([]) edges_out.append([]) for i in range(m): s1,s2,s3 = input().split() v = int(s1)-1 w = int(s2)-1 weight = ord(s3[0]) - ord('a') + 1 edges_out[v].append((w,weight)) edges_in[w].append((v,weight)) game = [] for i in range(n): tmp1 = [] for j in range(n): tmp2 = [] for c in range(27): tmp2.append(-1) tmp1.append(tmp2) game.append(tmp1) ##for v in range(n): ## for w in range(n): ## for last in range(27): ## go(v,w,last) for v in range(n): s = '' for w in range(n): if go(v,w,0): s = s + 'A' else: s = s + 'B' print(s) ```
output
1
21,722
19
43,445
Provide tags and a correct Python 3 solution for this coding contest problem. As we all know, Max is the best video game player among her friends. Her friends were so jealous of hers, that they created an actual game just to prove that she's not the best at games. The game is played on a directed acyclic graph (a DAG) with n vertices and m edges. There's a character written on each edge, a lowercase English letter. <image> Max and Lucas are playing the game. Max goes first, then Lucas, then Max again and so on. Each player has a marble, initially located at some vertex. Each player in his/her turn should move his/her marble along some edge (a player can move the marble from vertex v to vertex u if there's an outgoing edge from v to u). If the player moves his/her marble from vertex v to vertex u, the "character" of that round is the character written on the edge from v to u. There's one additional rule; the ASCII code of character of round i should be greater than or equal to the ASCII code of character of round i - 1 (for i > 1). The rounds are numbered for both players together, i. e. Max goes in odd numbers, Lucas goes in even numbers. The player that can't make a move loses the game. The marbles may be at the same vertex at the same time. Since the game could take a while and Lucas and Max have to focus on finding Dart, they don't have time to play. So they asked you, if they both play optimally, who wins the game? You have to determine the winner of the game for all initial positions of the marbles. Input The first line of input contains two integers n and m (2 ≤ n ≤ 100, <image>). The next m lines contain the edges. Each line contains two integers v, u and a lowercase English letter c, meaning there's an edge from v to u written c on it (1 ≤ v, u ≤ n, v ≠ u). There's at most one edge between any pair of vertices. It is guaranteed that the graph is acyclic. Output Print n lines, a string of length n in each one. The j-th character in i-th line should be 'A' if Max will win the game in case her marble is initially at vertex i and Lucas's marble is initially at vertex j, and 'B' otherwise. Examples Input 4 4 1 2 b 1 3 a 2 4 c 3 4 b Output BAAA ABAA BBBA BBBB Input 5 8 5 3 h 1 2 c 3 1 c 3 2 r 5 1 r 4 3 z 5 4 r 5 2 h Output BABBB BBBBB AABBB AAABA AAAAB Note Here's the graph in the first sample test case: <image> Here's the graph in the second sample test case: <image>
instruction
0
21,723
19
43,446
Tags: dfs and similar, dp, games, graphs Correct Solution: ``` from functools import lru_cache def readline(): return list(map(int, input().split())) def main(): n, m = readline() edges = [list() for __ in range(n)] for __ in range(m): tokens = input().split() begin, end = map(int, tokens[:2]) weight = ord(tokens[2]) edges[begin - 1].append((end - 1, weight)) @lru_cache(maxsize=None) def first_wins(first, second, lower=0): for (nxt, w) in edges[first]: if w >= lower: if not first_wins(second, nxt, w): return True return False for i in range(n): print("".join("BA"[first_wins(i, j)] for j in range(n))) main() ```
output
1
21,723
19
43,447
Provide a correct Python 3 solution for this coding contest problem. There is an infinitely large pond, which we consider as a number line. In this pond, there are N lotuses floating at coordinates 0, 1, 2, ..., N-2 and N-1. On the lotus at coordinate i, an integer s_i is written. You are standing on the lotus at coordinate 0. You will play a game that proceeds as follows: * 1. Choose positive integers A and B. Your score is initially 0. * 2. Let x be your current coordinate, and y = x+A. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 3. Let x be your current coordinate, and y = x-B. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 4. Go back to step 2. You want to end the game with as high a score as possible. What is the score obtained by the optimal choice of A and B? Constraints * 3 \leq N \leq 10^5 * -10^9 \leq s_i \leq 10^9 * s_0=s_{N-1}=0 * All values in input are integers. Input Input is given from Standard Input in the following format: N s_0 s_1 ...... s_{N-1} Output Print the score obtained by the optimal choice of A and B. Examples Input 5 0 2 5 1 0 Output 3 Input 6 0 10 -7 -4 -13 0 Output 0 Input 11 0 -4 0 -99 31 14 -15 -39 43 18 0 Output 59
instruction
0
21,820
19
43,640
"Correct Solution: ``` n = int(input()) s = list(map(int, input().split())) ans = 0 for i in range(1, n): l = 0 r = n-1 cur = 0 while True: l += i r -= i if l>=n or r<=i or (r%i==0 and r<=l): break cur += s[l] + s[r] ans = max(ans, cur) print(ans) ```
output
1
21,820
19
43,641
Provide a correct Python 3 solution for this coding contest problem. There is an infinitely large pond, which we consider as a number line. In this pond, there are N lotuses floating at coordinates 0, 1, 2, ..., N-2 and N-1. On the lotus at coordinate i, an integer s_i is written. You are standing on the lotus at coordinate 0. You will play a game that proceeds as follows: * 1. Choose positive integers A and B. Your score is initially 0. * 2. Let x be your current coordinate, and y = x+A. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 3. Let x be your current coordinate, and y = x-B. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 4. Go back to step 2. You want to end the game with as high a score as possible. What is the score obtained by the optimal choice of A and B? Constraints * 3 \leq N \leq 10^5 * -10^9 \leq s_i \leq 10^9 * s_0=s_{N-1}=0 * All values in input are integers. Input Input is given from Standard Input in the following format: N s_0 s_1 ...... s_{N-1} Output Print the score obtained by the optimal choice of A and B. Examples Input 5 0 2 5 1 0 Output 3 Input 6 0 10 -7 -4 -13 0 Output 0 Input 11 0 -4 0 -99 31 14 -15 -39 43 18 0 Output 59
instruction
0
21,821
19
43,642
"Correct Solution: ``` n=int(input()) S=tuple(map(int,input().split())) ans=0 for c in range(1,n-1): k=1 tmp=0 while c*k<n-1: a=n-1-k*c if a<=c or (a<=k*c and a%c==0): break tmp+=S[n-1-k*c]+S[k*c] k+=1 ans=max(ans,tmp) print(ans) ```
output
1
21,821
19
43,643
Provide a correct Python 3 solution for this coding contest problem. There is an infinitely large pond, which we consider as a number line. In this pond, there are N lotuses floating at coordinates 0, 1, 2, ..., N-2 and N-1. On the lotus at coordinate i, an integer s_i is written. You are standing on the lotus at coordinate 0. You will play a game that proceeds as follows: * 1. Choose positive integers A and B. Your score is initially 0. * 2. Let x be your current coordinate, and y = x+A. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 3. Let x be your current coordinate, and y = x-B. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 4. Go back to step 2. You want to end the game with as high a score as possible. What is the score obtained by the optimal choice of A and B? Constraints * 3 \leq N \leq 10^5 * -10^9 \leq s_i \leq 10^9 * s_0=s_{N-1}=0 * All values in input are integers. Input Input is given from Standard Input in the following format: N s_0 s_1 ...... s_{N-1} Output Print the score obtained by the optimal choice of A and B. Examples Input 5 0 2 5 1 0 Output 3 Input 6 0 10 -7 -4 -13 0 Output 0 Input 11 0 -4 0 -99 31 14 -15 -39 43 18 0 Output 59
instruction
0
21,822
19
43,644
"Correct Solution: ``` import sys sys.setrecursionlimit(2147483647) INF=float("inf") MOD=10**9+7 input=lambda :sys.stdin.readline().rstrip() def resolve(): n=int(input()) S=list(map(int,input().split())) ans=0 for d in range(1,n): score=0 P=set() for x in range(n//d): a=(n-1)-x*d if(a<=d): break if((x*d in P) or (n-1-x*d in P)): break if(x*d==n-1-x*d): break score+=S[x*d] score+=S[n-1-x*d] P.add(x*d) P.add(n-1-x*d) ans=max(ans,score) print(ans) resolve() ```
output
1
21,822
19
43,645
Provide a correct Python 3 solution for this coding contest problem. There is an infinitely large pond, which we consider as a number line. In this pond, there are N lotuses floating at coordinates 0, 1, 2, ..., N-2 and N-1. On the lotus at coordinate i, an integer s_i is written. You are standing on the lotus at coordinate 0. You will play a game that proceeds as follows: * 1. Choose positive integers A and B. Your score is initially 0. * 2. Let x be your current coordinate, and y = x+A. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 3. Let x be your current coordinate, and y = x-B. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 4. Go back to step 2. You want to end the game with as high a score as possible. What is the score obtained by the optimal choice of A and B? Constraints * 3 \leq N \leq 10^5 * -10^9 \leq s_i \leq 10^9 * s_0=s_{N-1}=0 * All values in input are integers. Input Input is given from Standard Input in the following format: N s_0 s_1 ...... s_{N-1} Output Print the score obtained by the optimal choice of A and B. Examples Input 5 0 2 5 1 0 Output 3 Input 6 0 10 -7 -4 -13 0 Output 0 Input 11 0 -4 0 -99 31 14 -15 -39 43 18 0 Output 59
instruction
0
21,823
19
43,646
"Correct Solution: ``` import sys def single_input(F): return F.readline().strip("\n") def line_input(F): return F.readline().strip("\n").split() def solve(): F = sys.stdin N = int(single_input(F)) S = [int(s) for s in line_input(F)] maxpoint = 0 for c in range(1, N//2): s, l = 0, N-1 point = 0 if (N-1) % c == 0: while l > s and l > c: point += S[s] + S[l] maxpoint = max(point, maxpoint) s += c l -= c else: while l != s and l > c: point += S[s] + S[l] maxpoint = max(point, maxpoint) s += c l -= c print(maxpoint) return 0 if __name__ == "__main__": solve() ```
output
1
21,823
19
43,647
Provide a correct Python 3 solution for this coding contest problem. There is an infinitely large pond, which we consider as a number line. In this pond, there are N lotuses floating at coordinates 0, 1, 2, ..., N-2 and N-1. On the lotus at coordinate i, an integer s_i is written. You are standing on the lotus at coordinate 0. You will play a game that proceeds as follows: * 1. Choose positive integers A and B. Your score is initially 0. * 2. Let x be your current coordinate, and y = x+A. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 3. Let x be your current coordinate, and y = x-B. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 4. Go back to step 2. You want to end the game with as high a score as possible. What is the score obtained by the optimal choice of A and B? Constraints * 3 \leq N \leq 10^5 * -10^9 \leq s_i \leq 10^9 * s_0=s_{N-1}=0 * All values in input are integers. Input Input is given from Standard Input in the following format: N s_0 s_1 ...... s_{N-1} Output Print the score obtained by the optimal choice of A and B. Examples Input 5 0 2 5 1 0 Output 3 Input 6 0 10 -7 -4 -13 0 Output 0 Input 11 0 -4 0 -99 31 14 -15 -39 43 18 0 Output 59
instruction
0
21,824
19
43,648
"Correct Solution: ``` N = int(input()) S = list(map(int,input().split())) ans = 0 for d in range(1,N): max_now = 0 if (N-1) % d == 0: now = 0 i, j = 0, N-1 while i < j: now += S[i] + S[j] max_now = max(now, max_now) i += d j -= d else: now = 0 i, j = 0, N-1 while i < N-1 and j > d: now += S[i] + S[j] max_now = max(now, max_now) i += d j -= d ans = max(max_now, ans) print(ans) ```
output
1
21,824
19
43,649
Provide a correct Python 3 solution for this coding contest problem. There is an infinitely large pond, which we consider as a number line. In this pond, there are N lotuses floating at coordinates 0, 1, 2, ..., N-2 and N-1. On the lotus at coordinate i, an integer s_i is written. You are standing on the lotus at coordinate 0. You will play a game that proceeds as follows: * 1. Choose positive integers A and B. Your score is initially 0. * 2. Let x be your current coordinate, and y = x+A. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 3. Let x be your current coordinate, and y = x-B. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 4. Go back to step 2. You want to end the game with as high a score as possible. What is the score obtained by the optimal choice of A and B? Constraints * 3 \leq N \leq 10^5 * -10^9 \leq s_i \leq 10^9 * s_0=s_{N-1}=0 * All values in input are integers. Input Input is given from Standard Input in the following format: N s_0 s_1 ...... s_{N-1} Output Print the score obtained by the optimal choice of A and B. Examples Input 5 0 2 5 1 0 Output 3 Input 6 0 10 -7 -4 -13 0 Output 0 Input 11 0 -4 0 -99 31 14 -15 -39 43 18 0 Output 59
instruction
0
21,825
19
43,650
"Correct Solution: ``` N = int(input()) s = [int(i) for i in input().split()] ans = 0 for i in range(1, N-2): p = 0 a = N-1 k = 0 while True: k += 1 a -= i b = a-i if b>0 and a!= N-1-a and a!=N-1-a-i: p += (s[a] + s[N-1-a]) ans = max(ans, p) else: break print(ans) ```
output
1
21,825
19
43,651
Provide a correct Python 3 solution for this coding contest problem. There is an infinitely large pond, which we consider as a number line. In this pond, there are N lotuses floating at coordinates 0, 1, 2, ..., N-2 and N-1. On the lotus at coordinate i, an integer s_i is written. You are standing on the lotus at coordinate 0. You will play a game that proceeds as follows: * 1. Choose positive integers A and B. Your score is initially 0. * 2. Let x be your current coordinate, and y = x+A. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 3. Let x be your current coordinate, and y = x-B. The lotus at coordinate x disappears, and you move to coordinate y. * If y = N-1, the game ends. * If y \neq N-1 and there is a lotus floating at coordinate y, your score increases by s_y. * If y \neq N-1 and there is no lotus floating at coordinate y, you drown. Your score decreases by 10^{100} points, and the game ends. * 4. Go back to step 2. You want to end the game with as high a score as possible. What is the score obtained by the optimal choice of A and B? Constraints * 3 \leq N \leq 10^5 * -10^9 \leq s_i \leq 10^9 * s_0=s_{N-1}=0 * All values in input are integers. Input Input is given from Standard Input in the following format: N s_0 s_1 ...... s_{N-1} Output Print the score obtained by the optimal choice of A and B. Examples Input 5 0 2 5 1 0 Output 3 Input 6 0 10 -7 -4 -13 0 Output 0 Input 11 0 -4 0 -99 31 14 -15 -39 43 18 0 Output 59
instruction
0
21,826
19
43,652
"Correct Solution: ``` n = int(input()) s = list(map(int, input().split())) MINUS_INF = -float("inf") ans = 0 for c in range(1, n): k = 1 tmp_ans = 0 while k * c < n - 1: a = (n - 1) - k * c b = a - c if a <= b or b <= 0: tmp_ans = MINUS_INF if a % c == 0 and a // c <= k: tmp_ans = MINUS_INF tmp_ans += s[n-1-k*c] + s[k*c] ans = max(ans, tmp_ans) k += 1 print(ans) ```
output
1
21,826
19
43,653