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Provide a correct Python 3 solution for this coding contest problem. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A
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"Correct Solution: ``` n, a, b, c = map(int, input().split()) variables = [a, b, c] alph = ["A", "B", "C"] s = [[] for _ in range(n)] for i in range(n): u, v = map(lambda x: alph.index(x) , list(input())) s[i] = [u, v] # print(s) can_do = True ans = [] for i in range(n): u, v = s[i][0], s[i][1] if variables[u] + variables[v] == 0: can_do = False elif variables[v] == 0: variables[u] -= 1 variables[v] += 1 ans.append(alph[v]) elif variables[u] == 0: variables[v] -= 1 variables[u] += 1 ans.append(alph[u]) else: # both are > 0 if i == n-1: # do whatever you want variables[u] -= 1 variables[v] += 1 ans.append(alph[v]) else: # need to think about next step if variables[u] > 0 and variables[v] > 0: next_u, next_v = s[i+1][0], s[i+1][1] if variables[next_u] + variables[next_v] >= 2: # can subsctact and whatever if variables[u] < variables[v]: u, v = v, u variables[u] -= 1 variables[v] += 1 ans.append(alph[v]) else: # need to sponsor common = list( {u, v}.intersection({next_u, next_v}) )[0] # print("common", common) not_common = u + v - common variables[common] += 1 variables[not_common] -= 1 ans.append(alph[common]) if can_do: print("Yes") for item in ans: print(item) else: print("No") ```
output
1
40,192
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Provide a correct Python 3 solution for this coding contest problem. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A
instruction
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"Correct Solution: ``` #!/usr/bin/env python3 # Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools import sys YES = "Yes" # type: str NO = "No" # type: str def solve(N: int, A: int, B: int, C: int, s: "List[int]"): v = [A, B, C] ans = [] for i in range(N): l, r = s[i] if v[l] + v[r] == 0: return None if v[l] > v[r] or v[l] == v[r] and i != N - 1 and r in s[i + 1]: ans.append(r) v[l] -= 1 v[r] += 1 else: ans.append(l) v[l] += 1 v[r] -= 1 return ans def main(): def iterate_tokens(): for line in sys.stdin: for word in line.split(): yield word def s2index(s: "List[str]"): return [ord(c)-ord('A') for c in s] def index2s(i: int): return chr(i + ord('A')) tokens = iterate_tokens() N = int(next(tokens)) # type: int A = int(next(tokens)) # type: int B = int(next(tokens)) # type: int C = int(next(tokens)) # type: int s = [s2index(next(tokens)) for _ in range(N)] # type: "List[int]" ans = solve(N, A, B, C, s) if ans == None: print(NO) else: print(YES) print("\n".join(list(map(index2s, ans)))) if __name__ == '__main__': main() ```
output
1
40,193
5
80,387
Provide a correct Python 3 solution for this coding contest problem. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A
instruction
0
40,195
5
80,390
"Correct Solution: ``` n,a,b,c = map(int,input().split()) s = [] for i in range(n): tmp_s = input() s.append(tmp_s) ans = [] for i,val in enumerate(s): if val == 'AB': if a == b == 0: print('No') exit(0) elif a < b or (a == b and i != n-1 and 'A' in s[i+1]): ans.append('A') a += 1 b -= 1 else: ans.append('B') a -= 1 b += 1 elif val == 'BC': if b == c == 0: print('No') exit(0) elif b < c or (b == c and i != n-1 and 'B' in s[i+1]): ans.append('B') b += 1 c -= 1 else: ans.append('C') b -= 1 c += 1 else: if c == a == 0: print('No') exit(0) elif c < a or (c == a and i != n-1 and 'C' in s[i+1]): ans.append('C') c += 1 a -= 1 else: ans.append('A') c -= 1 a += 1 print('Yes') print(*ans,sep='\n') ```
output
1
40,195
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80,391
Provide a correct Python 3 solution for this coding contest problem. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A
instruction
0
40,196
5
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"Correct Solution: ``` N,A,B,C=map(int,input().split()) S=[] d={'A':A, 'B':B, 'C':C} for i in range(N): S.append(input()) out=[] for i in range(N): s=S[i] s0=s[0] s1=s[1] if d[s0]==d[s1]==0: print('No') break elif d[s0]==0: d[s0]+=1 d[s1]-=1 out.append(s0) elif d[s1]==0: d[s0]-=1 d[s1]+=1 out.append(s1) elif i == N-1: out.append(s0) elif s0 in S[i+1]: d[s0]+=1 d[s1]-=1 out.append(s0) else: d[s0]-=1 d[s1]+=1 out.append(s1) else: print('Yes') for o in out: print(o) ```
output
1
40,196
5
80,393
Provide a correct Python 3 solution for this coding contest problem. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A
instruction
0
40,197
5
80,394
"Correct Solution: ``` #!python3 # input N, A, B, C = list(map(int, input().split())) S = [input() for _ in range(N)] def main(): l = [A, B, C] d = {"AB": (0, 1, 2), "AC": (0, 2, 1), "BC": (1, 2, 0)} dl = ["A", "B", "C"] ans = [] for n in range(N): i, j, k = d[S[n]] if l[i] < l[j]: l[i] += 1 l[j] -= 1 ans.append(dl[i]) elif l[i] > l[j]: l[i] -= 1 l[j] += 1 ans.append(dl[j]) elif l[i] == 0: print("No") return else: if n < N - 1 and j == d[S[n + 1]][2]: i, j = j, i l[i] -= 1 l[j] += 1 ans.append(dl[j]) print("Yes") print("\n".join(ans)) if __name__ == "__main__": main() ```
output
1
40,197
5
80,395
Provide a correct Python 3 solution for this coding contest problem. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A
instruction
0
40,198
5
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"Correct Solution: ``` def solve(): ans = [] for i, (x, y) in enumerate(s): if num[x]>num[y]: x, y = y, x if num[x]==num[y] and i < n-1: if y == s[i+1][0] or y == s[i+1][1]: x, y = y, x num[x]+=1 num[y]-=1 ans.append(x) if num[y]<0: return False return ans from collections import defaultdict import sys n, a, b, c = map(int, input().split()) num = defaultdict(int) s = [input() for _ in range(n)] num['A'] = a num['B'] = b num['C'] = c id = ['A', 'B', 'C'] ans = solve() if ans: print('Yes') print(*ans, sep = '\n') else: print('No') ```
output
1
40,198
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80,397
Provide a correct Python 3 solution for this coding contest problem. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A
instruction
0
40,199
5
80,398
"Correct Solution: ``` from collections import deque from copy import copy n, a, b, c = map(int, input().split()) s = [input().rstrip() for _ in range(n)] m = {'A': a, 'B': b, 'C': c} ans = [] for i in range(n): if m[s[i][0]] > m[s[i][1]]: ans.append(s[i][1]) m[s[i][0]] -= 1 m[s[i][1]] += 1 elif m[s[i][0]] < m[s[i][1]]: ans.append(s[i][0]) m[s[i][0]] += 1 m[s[i][1]] -= 1 else: if m[s[i][0]] == 0: print('No') exit() if i != n-1: if s[i][0] in s[i+1]: ans.append(s[i][0]) m[s[i][0]] += 1 m[s[i][1]] -= 1 else: ans.append(s[i][1]) m[s[i][0]] -= 1 m[s[i][1]] += 1 else: ans.append(s[i][0]) print('Yes') print('\n'.join(ans)) ```
output
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A Submitted Solution: ``` n,a,b,c = map(int,input().split()) s = [input() for i in range(n)] dic = {'A':a,'B':b,'C':c} ans = ["Yes"] for i in range(n): if dic[s[i][0]] == 0 and dic[s[i][1]] == 0: print("No") exit() elif dic[s[i][0]] == 0: dic[s[i][0]] += 1 dic[s[i][1]] -= 1 ans.append(s[i][0]) elif dic[s[i][1]] == 0: dic[s[i][1]] += 1 dic[s[i][0]] -= 1 ans.append(s[i][1]) elif i != n-1: if s[i][0] in s[i+1]: dic[s[i][0]] += 1 dic[s[i][1]] -= 1 ans.append(s[i][0]) else: dic[s[i][1]] += 1 dic[s[i][0]] -= 1 ans.append(s[i][1]) else: dic[s[i][0]] += 1 dic[s[i][1]] -= 1 ans.append(s[i][0]) print(*ans,sep="\n") ```
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Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A Submitted Solution: ``` import sys, copy, math, heapq, bisect from itertools import accumulate from collections import deque, defaultdict, Counter sys.setrecursionlimit(500000) N,A,B,C = map(int,input().split()) ABC = [A,B,C] S = [] SS = ('A','B','C') d = [0,0,0] flag = True for i in range(N): s = input() if s=="AB": S.append(2) d[0] += 1 d[1] += 1 elif s=="BC": S.append(0) d[1] += 1 d[2] += 1 else: S.append(1) d[2] += 1 d[0] += 1 ans = [] for i in range(N): x,y = (S[i]+1)%3,(S[i]+2)%3 if ABC[x]<ABC[y]: ans.append(SS[x]) ABC[y] -= 1 ABC[x] += 1 elif ABC[x]>ABC[y]: ans.append(SS[y]) ABC[y] += 1 ABC[x] -= 1 else: if i < N-1: if S[i+1]==y: ans.append(SS[x]) ABC[y] -= 1 ABC[x] += 1 else: ans.append(SS[y]) ABC[y] += 1 ABC[x] -= 1 else: ans.append(SS[y]) ABC[y] += 1 ABC[x] -= 1 if ABC[0]<0 or ABC[1]<0 or ABC[2]<0: flag = False break if flag: print('Yes') print(*ans,sep='\n') else: print('No') ```
instruction
0
40,201
5
80,402
Yes
output
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40,201
5
80,403
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A Submitted Solution: ``` n,*abc=map(int,input().split()) ip=[0]*n for i in range(n): tmp=input() if tmp=="AB": ip[i]=[0,1] elif tmp=="BC": ip[i]=[1,2] else: ip[i]=[0,2] ans="Yes" res=[0]*n s=sum(abc) if s==0: ans="No" elif s==1: for i in range(n): i1=ip[i][0] i2=ip[i][1] if abc[i1]+abc[i2]==0: ans="No" elif abc[i1]+abc[i2]==1: if abc[i1]==0: abc[i1]+=1 abc[i2]-=1 res[i]=i1 else: abc[i1]-=1 abc[i2]+=1 res[i]=i2 else: i1=ip[0][0] i2=ip[0][1] if abc[i1]+abc[i2]==0: ans="No" else: for i in range(n): i1=ip[i][0] i2=ip[i][1] if abc[i1]*abc[i2]==0: if abc[i1]==0: abc[i1]+=1 abc[i2]-=1 res[i]=i1 else: abc[i1]-=1 abc[i2]+=1 res[i]=i2 elif i+1<n and ip[i+1]!=ip[i]: c=list(set(ip[i])&set(ip[i+1]))[0] if i1==c: abc[i1]+=1 abc[i2]-=1 res[i]=i1 else: abc[i1]-=1 abc[i2]+=1 res[i]=i2 else: abc[i1]+=1 abc[i2]-=1 res[i]=i1 print(ans) dic={0:"A",1:"B",2:"C"} if ans=="Yes": for i in range(n): ''' if res[i]==0: print("A") elif res[i]==1: print("B") else: print("C") ''' print(dic[res[i]]) ```
instruction
0
40,202
5
80,404
Yes
output
1
40,202
5
80,405
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A Submitted Solution: ``` import sys n,a,b,c = map(int,input().split()) abc = {"A":a,"B":b,"C":c} s = [input() for _ in range(n)] ans = [None]*n i = 0 while i <n: x = s[i][0] y = s[i][1] if abc[x] == 0 and abc[y] ==0: print("No") sys.exit() elif abc[x] == 1 and abc[y] ==1 and i<n-1: if s[i] == s[i+1]: ans[i] = x ans[i+1] = y i += 1 elif x in s[i+1]: ans[i] = x abc[x] += 1 abc[y] -= 1 else: ans[i] = y abc[x] -= 1 abc[y] += 1 else: if abc[x]<=abc[y]: ans[i] = x abc[x] += 1 abc[y] -= 1 else: ans[i] = y abc[x] -= 1 abc[y] += 1 i += 1 print("Yes") print("\n".join(ans)) ```
instruction
0
40,203
5
80,406
Yes
output
1
40,203
5
80,407
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A Submitted Solution: ``` import sys read = sys.stdin.buffer.read readline = sys.stdin.buffer.readline readlines = sys.stdin.buffer.readlines Q, A, B, C = map(int, readline().split()) N = A + B + C S = read().split() S = tuple(0 if s == b'BC' else 1 if s == b'AC' else 2 for s in S) def solve_1(N, A, B, C, S): nums = [A, B, C] for s in S: if nums[s] == N: raise Exception i, j = (0, 1) if s == 2 else (0, 2) if s == 1 else (1, 2) if nums[i] < nums[j]: i, j = j, i yield j nums[j] += 1 nums[i] -= 1 def solve_2(N, A, B, C, S): nums = [A, B, C] s = S[0] # 初手で死亡 if nums[s] == N: raise Exception # あとはできる。きわどいときは 2 手読み S = S + (0, ) for s, t in zip(S, S[1:]): i, j = (0, 1) if s == 2 else (0, 2) if s == 1 else (1, 2) if (nums[i], nums[j]) != (1, 1): if nums[i] < nums[j]: i, j = j, i elif s != t: i, j = t, 3 - s - t yield j nums[j] += 1 nums[i] -= 1 def large(N, A, B, C, S): nums = [A, B, C] for s in S: if nums[s] == N: raise Exception i, j = (0, 1) if s == 2 else (0, 2) if s == 1 else (1, 2) if nums[i] < nums[j]: i, j = j, i yield j nums[j] += 1 nums[i] -= 1 print(s, nums) N = 2 A, B, C = 1, 1, 0 S = (0, 1, 2, 1, 2, 2, 2, 1, 2, 1) f = solve_1 if N == 1 else solve_2 if N == 2 else large try: cmds = list(f(N, A, B, C, S)) print('Yes') answer = ('ABC' [i] for i in cmds) print('\n'.join(answer)) except Exception: print('No') ```
instruction
0
40,204
5
80,408
No
output
1
40,204
5
80,409
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A Submitted Solution: ``` n,a,b,c = map(int, input().split()) d = {} d["A"] = a d["B"] = b d["C"] = c al = [0]*(n+1) bl = [0]*(n+1) cl = [0]*(n+1) pl = [] for i in range(n): p = input() pl.append(p) al[i+1] = al[i] bl[i+1] = bl[i] cl[i+1] = cl[i] if p[0]=="A" or p[1]=="A": al[i+1] += 1 if p[0]=="B" or p[1]=="B": bl[i+1] += 1 if p[0]=="C" or p[1]=="C": cl[i+1] += 1 dp = {} dp["A"] = al dp["B"] = bl dp["C"] = cl res = [] for i in range(n): p = pl[i] if d[p[0]]>d[p[1]]: if d[p[0]]<=0: print("No") exit() res.append(p[1]) d[p[0]] -= 1 d[p[1]] += 1 elif d[p[0]]<d[p[1]]: if d[p[1]]<=0: print("No") exit() res.append(p[0]) d[p[0]] += 1 d[p[1]] -= 1 else: if dp[p[0]][-1] - dp[p[0]][i] > dp[p[1]][-1] - dp[p[1]][i]: if d[p[1]]<=0: print("No") exit() res.append(p[0]) d[p[0]] += 1 d[p[1]] -= 1 else: if d[p[0]]<=0: print("No") exit() res.append(p[1]) d[p[0]] -= 1 d[p[1]] += 1 print("Yes") for p in res: print(p) ```
instruction
0
40,205
5
80,410
No
output
1
40,205
5
80,411
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A Submitted Solution: ``` import sys read = sys.stdin.read readline = sys.stdin.readline readlines = sys.stdin.readlines def main(): n,A,B,C = map(int, readline().split()) N = A + B + C S = [readline().strip() for _ in range(n)] ans = [] possible = True for i, s in enumerate(S): if s == "AB": if A + B == 0: print("No") possible = False break if i < n - 1 and A == B: if S[i+1] == "AC": A += 1 B -= 1 ans.append("A") elif S[i+1] == "BC": A -= 1 B += 1 ans.append("B") else: A += 1 B -= 1 ans.append("A") else: if A < B: A += 1 B -= 1 ans.append("A") else: A -= 1 B += 1 ans.append("B") elif s == "AC": if A + C == 0: print("No") possible = False break if i < n - 1 and A == C: if S[i+1] == "AB": A += 1 B -= 1 ans.append("A") elif S[i+1] == "BC": A -= 1 C += 1 ans.append("C") else: A += 1 B -= 1 ans.append("A") else: if A < C: A += 1 C -= 1 ans.append("A") else: A -= 1 C += 1 ans.append("C") else: if B + C == 0: print("No") possible = False break if i < n - 1 and B == C: if S[i+1] == "AB": B += 1 C -= 1 ans.append("B") elif S[i+1] == "AC": B -= 1 C += 1 ans.append("C") else: B += 1 C -= 1 ans.append("B") else: if B < C: B += 1 C -= 1 ans.append("B") else: B -= 1 C += 1 ans.append("C") if possible: print("Yes") print("\n".join(ans)) if __name__ == "__main__": main() ```
instruction
0
40,206
5
80,412
No
output
1
40,206
5
80,413
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. There is a game that involves three variables, denoted A, B, and C. As the game progresses, there will be N events where you are asked to make a choice. Each of these choices is represented by a string s_i. If s_i is `AB`, you must add 1 to A or B then subtract 1 from the other; if s_i is `AC`, you must add 1 to A or C then subtract 1 from the other; if s_i is `BC`, you must add 1 to B or C then subtract 1 from the other. After each choice, none of A, B, and C should be negative. Determine whether it is possible to make N choices under this condition. If it is possible, also give one such way to make the choices. Constraints * 1 \leq N \leq 10^5 * 0 \leq A,B,C \leq 10^9 * N, A, B, C are integers. * s_i is `AB`, `AC`, or `BC`. Input Input is given from Standard Input in the following format: N A B C s_1 s_2 : s_N Output If it is possible to make N choices under the condition, print `Yes`; otherwise, print `No`. Also, in the former case, show one such way to make the choices in the subsequent N lines. The (i+1)-th line should contain the name of the variable (`A`, `B`, or `C`) to which you add 1 in the i-th choice. Examples Input 2 1 3 0 AB AC Output Yes A C Input 3 1 0 0 AB BC AB Output No Input 1 0 9 0 AC Output No Input 8 6 9 1 AC BC AB BC AC BC AB AB Output Yes C B B C C B A A Submitted Solution: ``` import sys l = sys.stdin.readline().strip() N, A, B, C = map(int, l.split()) history = [] for _ in range(N): cmd = sys.stdin.readline().strip() history.append(cmd) if A+B+C == 0: print("No") elif A+B+C == 1: fail = False path = "" for one in history: if one == "AB": if A == 0 and B==0: fail = True break else: if A == 0: A = 1 B = 0 path += "A" else: A = 0 B = 1 path += "B" if one == "AC": if A== 0 and C == 0: fail = True break else: if A==0: A = 1 C = 0 path += "A" else: A = 0 C = 1 path += "C" if one == "BC": if B == 0 and C == 0: fail = True break else: if B == 0: B = 1 C = 0 path += "B" else: C,B = 1,0 path += "C" if fail: print("No") else: print ("Yes") for one in path: print(one) else: fail = False path = "" for idx, one in enumerate(history): if A < 0 or B < 0 or C<0: fail = True break if one == "AB": if A <= 0 and B<=0: fail = True break else: if idx == N-1 or history[idx+1] == "AB": if A > B: A, B,path = A-1, B+1, path +"B" else: A, B, path = A+1, B-1, path+"A" else: if "A" in history[idx+1]: if B > 0: A, B, path = A+1, B-1, path+"A" else: A, B, path = A-1, B+1, path+"A" else: if A > 0: A, B,path = A-1, B+1, path +"B" else: A, B, path = A+1, B-1, path+"A" elif one =="AC": if A<=0 and C<=0: fail =True break else: if idx == N-1 or history[idx+1] == "AC": if A > C: A, C, path = A -1, C+1, path+"C" else: A,C,path = A+1, C-1, path +"A" else: if "A" in history[idx+1]: if C > 0: A,C,path = A+1, C-1, path +"A" else: A, C, path = A -1, C+1, path+"C" else: if A > 0: A, C, path = A -1, C+1, path+"C" else: A,C,path = A+1, C-1, path +"A" else: if B<=0 and C<=0: fail = True break else: if idx == N-1 or history[idx+1] == "BC": if B > C: B,C,path = B-1,C+1, path+"C" else: B,C,path = B+1,C-1,path+"B" else: if "B" in history[idx+1]: if C > 0: B,C,path = B+1,C-1,path+"B" else: B,C,path = B-1,C+1, path+"C" else: if B > 0: B,C,path = B-1,C+1, path+"C" else: B,C,path = B+1,C-1,path+"B" if fail: print("No") else: print("Yes") for one in path: print(one) ```
instruction
0
40,207
5
80,414
No
output
1
40,207
5
80,415
Provide a correct Python 3 solution for this coding contest problem. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394
instruction
0
40,224
5
80,448
"Correct Solution: ``` A, B = map(int, input().split()) print((A + B) // 2 if not (A + B) % 2 else "IMPOSSIBLE") ```
output
1
40,224
5
80,449
Provide a correct Python 3 solution for this coding contest problem. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394
instruction
0
40,225
5
80,450
"Correct Solution: ``` a,b=map(int,input().split()) print("IMPOSSIBLE" if abs(a-b)%2==1 else (a+b)//2) ```
output
1
40,225
5
80,451
Provide a correct Python 3 solution for this coding contest problem. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394
instruction
0
40,226
5
80,452
"Correct Solution: ``` a,b=map(int,input().split()) print (int((a+b)/2) if (a-b)%2==0 else "IMPOSSIBLE") ```
output
1
40,226
5
80,453
Provide a correct Python 3 solution for this coding contest problem. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394
instruction
0
40,227
5
80,454
"Correct Solution: ``` a,b = map(int, input().split()) ans="IMPOSSIBLE" if (a+b)%2==0: ans=(a+b)//2 print(ans) ```
output
1
40,227
5
80,455
Provide a correct Python 3 solution for this coding contest problem. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394
instruction
0
40,228
5
80,456
"Correct Solution: ``` A,B = map(int,input().split()) K = 'IMPOSSIBLE' if (A+B) % 2 != 0 else (A+B) // 2 print(K) ```
output
1
40,228
5
80,457
Provide a correct Python 3 solution for this coding contest problem. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394
instruction
0
40,229
5
80,458
"Correct Solution: ``` A,B=map(int,input().split()) print((A+B)//2 if (A+B)%2==0 else "IMPOSSIBLE") ```
output
1
40,229
5
80,459
Provide a correct Python 3 solution for this coding contest problem. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394
instruction
0
40,230
5
80,460
"Correct Solution: ``` a,b = map(int, input().split()) x = a +b print(int(x/2) if x%2 == 0 else "IMPOSSIBLE") ```
output
1
40,230
5
80,461
Provide a correct Python 3 solution for this coding contest problem. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394
instruction
0
40,231
5
80,462
"Correct Solution: ``` a, b = map(int,input().split()) print('IMPOSSIBLE' if (a+b)%2 else abs((a+b)//2)) ```
output
1
40,231
5
80,463
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394 Submitted Solution: ``` A,B = map(int,input().split()) print("IMPOSSIBLE" if (A+B)%2!=0 else int((A+B)/2)) ```
instruction
0
40,232
5
80,464
Yes
output
1
40,232
5
80,465
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394 Submitted Solution: ``` a,b=map(int,input().split()) print((a+b)//2 if (a+b)//2 == (a+b)/2 else 'IMPOSSIBLE') ```
instruction
0
40,233
5
80,466
Yes
output
1
40,233
5
80,467
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394 Submitted Solution: ``` a,b = map(int, input().split()) print(int(a+((b-a)/2)) if (b-a)%2 == 0 else "IMPOSSIBLE") ```
instruction
0
40,234
5
80,468
Yes
output
1
40,234
5
80,469
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394 Submitted Solution: ``` a,b=map(int,input().split()) print(int(min(a,b)+abs(a-b)/2) if (a-b)%2==0 else "IMPOSSIBLE") ```
instruction
0
40,235
5
80,470
Yes
output
1
40,235
5
80,471
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394 Submitted Solution: ``` a,b=int(input().split()) print(a+b //2 if a+b % 2==0 else 'IMPSSIBLE') ```
instruction
0
40,236
5
80,472
No
output
1
40,236
5
80,473
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394 Submitted Solution: ``` n, m = map(int, input().split()) if (n+m)%2 == 0:print((n+m)/2) else:print("IMPOSSIBLE") ```
instruction
0
40,237
5
80,474
No
output
1
40,237
5
80,475
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394 Submitted Solution: ``` p,q=map(int,input().split()) if (p-q)%2==1: print("IMPOSSIBLE") else: print(abs((p-q)//2)) ```
instruction
0
40,238
5
80,476
No
output
1
40,238
5
80,477
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. We have two distinct integers A and B. Print the integer K such that |A - K| = |B - K|. If such an integer does not exist, print `IMPOSSIBLE` instead. Constraints * All values in input are integers. * 0 \leq A,\ B \leq 10^9 * A and B are distinct. Input Input is given from Standard Input in the following format: A B Output Print the integer K satisfying the condition. If such an integer does not exist, print `IMPOSSIBLE` instead. Examples Input 2 16 Output 9 Input 0 3 Output IMPOSSIBLE Input 998244353 99824435 Output 549034394 Submitted Solution: ``` import sys stdin = sys.stdin sys.setrecursionlimit(10 ** 7) def li(): return map(int, stdin.readline().split()) def li_(): return map(lambda x: int(x) - 1, stdin.readline().split()) def lf(): return map(float, stdin.readline().split()) def ls(): return stdin.readline().split() def ns(): return stdin.readline().rstrip() def lc(): return list(ns()) def ni(): return int(stdin.readline()) def nf(): return float(stdin.readline()) A, B = li() if A + B % 2 == 1: print("IMPOSSIBLE") else: C = (A + B)/2 print(int(C)) ```
instruction
0
40,239
5
80,478
No
output
1
40,239
5
80,479
Provide a correct Python 3 solution for this coding contest problem. Let M be a positive integer. You are given 2 N integers a_1, a_2, \ldots, a_{2 N}, where 0 \leq a_i < M for each i. Consider dividing the 2 N integers into N pairs. Here, each integer must belong to exactly one pair. We define the ugliness of a pair (x, y) as (x + y) \mod M. Let Z be the largest ugliness of the N pairs. Find the minimum possible value of Z. Constraints * All values in input are integers. * 1 \leq N \leq 10^5 * 1 \leq M \leq 10^9 * 0 \leq a_i < M Input Input is given from Standard Input in the following format: N M a_1 a_2 \cdots a_{2N} Output Print the minimum possible value of Z, where Z is the largest ugliness of the N pairs. Examples Input 3 10 0 2 3 4 5 9 Output 5 Input 2 10 1 9 1 9 Output 0
instruction
0
40,241
5
80,482
"Correct Solution: ``` n, m = map(int, input().split()) a = sorted([int(x) for x in input().split()]) def chk(x): for i in range(2*x, 2*n): if i != 2*n - 1 - (i - 2*x) and a[i] + a[2*n-1-(i-2*x)] < m: return False return True bottom = -1 top = n while top - bottom > 1: mid = (top + bottom)//2 if chk(mid): top = mid else: bottom = mid ans = -1 for i in range(2*top, 2*n): ans = max(ans, (a[i]+a[2*n-1-(i-2*top)]) % m) for i in range(2*top): ans = max(ans, (a[i] + a[2*top-1-i]) % m) print(ans) ```
output
1
40,241
5
80,483
Provide a correct Python 3 solution for this coding contest problem. Let M be a positive integer. You are given 2 N integers a_1, a_2, \ldots, a_{2 N}, where 0 \leq a_i < M for each i. Consider dividing the 2 N integers into N pairs. Here, each integer must belong to exactly one pair. We define the ugliness of a pair (x, y) as (x + y) \mod M. Let Z be the largest ugliness of the N pairs. Find the minimum possible value of Z. Constraints * All values in input are integers. * 1 \leq N \leq 10^5 * 1 \leq M \leq 10^9 * 0 \leq a_i < M Input Input is given from Standard Input in the following format: N M a_1 a_2 \cdots a_{2N} Output Print the minimum possible value of Z, where Z is the largest ugliness of the N pairs. Examples Input 3 10 0 2 3 4 5 9 Output 5 Input 2 10 1 9 1 9 Output 0
instruction
0
40,242
5
80,484
"Correct Solution: ``` def check(k): ret = 0 b = 2 * k - 1 for j in range(k): t = aaa[j] + aaa[b - j] if t >= m: return -1 ret = max(ret, t) b = 2 * k c = 2 * n - 1 for j in range(n - k): t = aaa[b + j] + aaa[c - j] if t < m: return -2 ret = max(ret, t - m) return ret n, m = map(int, input().split()) aaa = sorted(map(int, input().split())) l, r = 0, n ans = -1 while l < r: mid = (l + r) // 2 res = check(mid) if res == -1: r = mid elif res == -2: l = mid + 1 else: ans = res r = mid if ans == -1: ans = check(n) print(ans) ```
output
1
40,242
5
80,485
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let M be a positive integer. You are given 2 N integers a_1, a_2, \ldots, a_{2 N}, where 0 \leq a_i < M for each i. Consider dividing the 2 N integers into N pairs. Here, each integer must belong to exactly one pair. We define the ugliness of a pair (x, y) as (x + y) \mod M. Let Z be the largest ugliness of the N pairs. Find the minimum possible value of Z. Constraints * All values in input are integers. * 1 \leq N \leq 10^5 * 1 \leq M \leq 10^9 * 0 \leq a_i < M Input Input is given from Standard Input in the following format: N M a_1 a_2 \cdots a_{2N} Output Print the minimum possible value of Z, where Z is the largest ugliness of the N pairs. Examples Input 3 10 0 2 3 4 5 9 Output 5 Input 2 10 1 9 1 9 Output 0 Submitted Solution: ``` n = int(input()) list = [] a = [] for i in range(n): list.append(int(input)) for i in range(1, n): for j in range(1, i): if list[i] == j: a.insert(j, j) if a == list: for i in range(n): print(list[i]) else: print(-1) ```
instruction
0
40,243
5
80,486
No
output
1
40,243
5
80,487
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let M be a positive integer. You are given 2 N integers a_1, a_2, \ldots, a_{2 N}, where 0 \leq a_i < M for each i. Consider dividing the 2 N integers into N pairs. Here, each integer must belong to exactly one pair. We define the ugliness of a pair (x, y) as (x + y) \mod M. Let Z be the largest ugliness of the N pairs. Find the minimum possible value of Z. Constraints * All values in input are integers. * 1 \leq N \leq 10^5 * 1 \leq M \leq 10^9 * 0 \leq a_i < M Input Input is given from Standard Input in the following format: N M a_1 a_2 \cdots a_{2N} Output Print the minimum possible value of Z, where Z is the largest ugliness of the N pairs. Examples Input 3 10 0 2 3 4 5 9 Output 5 Input 2 10 1 9 1 9 Output 0 Submitted Solution: ``` n, m = map(int, input().split()) a = [int(i) for i in input().split()] med = m / 2 a = [i if (i <= med) else (i - m) for i in a] a = sorted(a) ans = [] for i in range(n): temp = a[i] + a[-i-1] ans.append(temp) ans = [i % m for i in ans] print(max(ans)) ```
instruction
0
40,244
5
80,488
No
output
1
40,244
5
80,489
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let M be a positive integer. You are given 2 N integers a_1, a_2, \ldots, a_{2 N}, where 0 \leq a_i < M for each i. Consider dividing the 2 N integers into N pairs. Here, each integer must belong to exactly one pair. We define the ugliness of a pair (x, y) as (x + y) \mod M. Let Z be the largest ugliness of the N pairs. Find the minimum possible value of Z. Constraints * All values in input are integers. * 1 \leq N \leq 10^5 * 1 \leq M \leq 10^9 * 0 \leq a_i < M Input Input is given from Standard Input in the following format: N M a_1 a_2 \cdots a_{2N} Output Print the minimum possible value of Z, where Z is the largest ugliness of the N pairs. Examples Input 3 10 0 2 3 4 5 9 Output 5 Input 2 10 1 9 1 9 Output 0 Submitted Solution: ``` import sys import numpy as np from itertools import combinations from itertools import permutations ### 方針 ### 実行時間は最大でも2N!で収まる気がする ### 最悪全ての組み合わせの数列に対して、上から2桁ずつ足し算してあまりを求め続けてその時の最大値を全部とって比較すればいい ### 流石に↑は嘘っぽいので、ひとつの数列を作成したい気がする ### a[0]:N a[1]:M a = list(map(int,input().split())) input = list(map(int,input().split())) min=4 for i in permutations(input,len(input)): max=0 for j in range(0,len(i),2): mod = (i[j]+i[j+1])%a[1] if max < mod: max=mod if min > max: min = max print(min) ```
instruction
0
40,245
5
80,490
No
output
1
40,245
5
80,491
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Let M be a positive integer. You are given 2 N integers a_1, a_2, \ldots, a_{2 N}, where 0 \leq a_i < M for each i. Consider dividing the 2 N integers into N pairs. Here, each integer must belong to exactly one pair. We define the ugliness of a pair (x, y) as (x + y) \mod M. Let Z be the largest ugliness of the N pairs. Find the minimum possible value of Z. Constraints * All values in input are integers. * 1 \leq N \leq 10^5 * 1 \leq M \leq 10^9 * 0 \leq a_i < M Input Input is given from Standard Input in the following format: N M a_1 a_2 \cdots a_{2N} Output Print the minimum possible value of Z, where Z is the largest ugliness of the N pairs. Examples Input 3 10 0 2 3 4 5 9 Output 5 Input 2 10 1 9 1 9 Output 0 Submitted Solution: ``` n, m = map(int, input().split()) a = sorted([int(x) for x in input().split()]) if n == 1: print(sum(a) % m) exit() def chk(x): for i in range(2*x, 2*n): if i != 2*n - 1 - (i - 2*x) and a[i] + a[2*n-1-(i-2*x)] < m: return False for i in range(2*x): if i != 2*x-1-i and a[i] + a[2*x-1-i] >= m: return False return True bottom = -1 top = n while top - bottom > 1: mid = (top + bottom)//2 if chk(mid): top = mid else: bottom = mid if top == 0: break ans = -1 for i in range(2*top, 2*n): ans = max(ans, (a[i]+a[2*n-1-(i-2*top)]) % m) for i in range(2*top): ans = max(ans, (a[i] + a[2*top-1-i]) % m) print(ans) ```
instruction
0
40,246
5
80,492
No
output
1
40,246
5
80,493
Provide a correct Python 3 solution for this coding contest problem. Problem statement Real variables $ x_1, x_2, ..., x_N $ satisfy the following conditions. 1. $ 0 \ leq x_i \ leq 1 $ ($ 1 \ leq i \ leq N $) 2. $ w_1x_1 + w_2x_2 + ... + w_Nx_N \ leq W $ At this time, find the maximum value that $ v_1x_1 + v_2x_2 + ... + v_Nx_N $ can take. It is known that such a maximum actually exists. Constraint * $ 1 \ leq N \ leq 10 ^ 5 $ * $ 1 \ leq W \ leq 10 ^ 5 $ * $ -10 ^ 4 \ leq w_i \ leq 10 ^ 4 $ * $ -10 ^ 4 \ leq v_i \ leq 10 ^ 4 $ input Input follows the following format. All given numbers are integers. $ N $ $ W $ $ w_1 $ $ v_1 $ $ w_2 $ $ v_2 $ $ ... $ $ w_N $ $ v_N $ output Output the maximum possible value of $ v_1x_1 + v_2x_2 + ... + v_Nx_N $ on one line. The output must not have an error greater than $ 10 ^ {-3} $. Examples Input 1 1 3 1 Output 0.333333 Input 2 3 3 3 1 2 Output 4.000000 Input 2 1 -1 -3 3 10 Output 3.666667
instruction
0
40,396
5
80,792
"Correct Solution: ``` import heapq N, W = [int(n) for n in input().split()] tmpw = 0 tmpv = 0 minheap = [] for i in range(N): w, v = [int(n) for n in input().split()] if(w < 0): tmpw += w tmpv += v w *= -1 v *= -1 if(v > 0): if w == 0: tmpv += v else: heapq.heappush(minheap, (-(v/w), w, v)) while(W-tmpw > 1e-9 and not minheap == []): p = heapq.heappop(minheap) w = p[1] v = p[2] x = min(1, (W-tmpw)/w) tmpw += x*w tmpv += x*v print(tmpv) ```
output
1
40,396
5
80,793
Provide a correct Python 3 solution for this coding contest problem. Example Input R?????,2?) Output 29
instruction
0
40,401
5
80,802
"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(): s = S() l = len(s) fm = {} fm[''] = -1 def f(s): if s in fm: return fm[s] l = len(s) r = -1 if l > 5 and s[1] in '(?' and s[-1] in ')?': if s[0] in 'R?': for i in range(3,l-2): if s[i] not in ',?': continue tl = f(s[2:i]) tr = f(s[i+1:-1]) if tl >= 0 and tr >= 0 and r < tr: r = tr if s[0] in 'L?': for i in range(3,l-2): if s[i] not in ',?': continue tl = f(s[2:i]) tr = f(s[i+1:-1]) if tl >= 0 and tr >= 0 and r < tl: r = tl ff = True if s[0] == '0' and l > 1: ff = False for tc in 'RL,()': if tc in s: ff = False break if ff: r = int(s.replace('?', '9')) fm[s] = r return r r = f(s) if r < 0: return 'invalid' return r print(main()) ```
output
1
40,401
5
80,803
Provide a correct Python 3 solution for this coding contest problem. Oranges on Cans square1001 You put a $ N $ can of aluminum on the table. E869120 You put $ M $ of oranges on each aluminum can on the table. How many oranges are on the aluminum can? input Input is given from standard input in the following format. $ N $ $ M $ output Output the number of oranges on the aluminum can in one line. However, insert a line break at the end. Constraint * $ 1 \ leq N \ leq 9 $ * $ 1 \ leq M \ leq 9 $ * All inputs are integers. Input example 1 3 4 Output example 1 12 Input example 2 7 7 Output example 2 49 Example Input 3 4 Output 12
instruction
0
40,403
5
80,806
"Correct Solution: ``` n, m = [int(i) for i in input().split()] print(n*m) ```
output
1
40,403
5
80,807
Provide a correct Python 3 solution for this coding contest problem. Oranges on Cans square1001 You put a $ N $ can of aluminum on the table. E869120 You put $ M $ of oranges on each aluminum can on the table. How many oranges are on the aluminum can? input Input is given from standard input in the following format. $ N $ $ M $ output Output the number of oranges on the aluminum can in one line. However, insert a line break at the end. Constraint * $ 1 \ leq N \ leq 9 $ * $ 1 \ leq M \ leq 9 $ * All inputs are integers. Input example 1 3 4 Output example 1 12 Input example 2 7 7 Output example 2 49 Example Input 3 4 Output 12
instruction
0
40,404
5
80,808
"Correct Solution: ``` def nums(): return list(map(int,input().split())) N,M = nums() print(N*M) ```
output
1
40,404
5
80,809
Provide a correct Python 3 solution for this coding contest problem. Oranges on Cans square1001 You put a $ N $ can of aluminum on the table. E869120 You put $ M $ of oranges on each aluminum can on the table. How many oranges are on the aluminum can? input Input is given from standard input in the following format. $ N $ $ M $ output Output the number of oranges on the aluminum can in one line. However, insert a line break at the end. Constraint * $ 1 \ leq N \ leq 9 $ * $ 1 \ leq M \ leq 9 $ * All inputs are integers. Input example 1 3 4 Output example 1 12 Input example 2 7 7 Output example 2 49 Example Input 3 4 Output 12
instruction
0
40,405
5
80,810
"Correct Solution: ``` a,b=map(int,input().split()) print(a*b) ```
output
1
40,405
5
80,811
Provide a correct Python 3 solution for this coding contest problem. Oranges on Cans square1001 You put a $ N $ can of aluminum on the table. E869120 You put $ M $ of oranges on each aluminum can on the table. How many oranges are on the aluminum can? input Input is given from standard input in the following format. $ N $ $ M $ output Output the number of oranges on the aluminum can in one line. However, insert a line break at the end. Constraint * $ 1 \ leq N \ leq 9 $ * $ 1 \ leq M \ leq 9 $ * All inputs are integers. Input example 1 3 4 Output example 1 12 Input example 2 7 7 Output example 2 49 Example Input 3 4 Output 12
instruction
0
40,406
5
80,812
"Correct Solution: ``` print(eval(input().replace(" ", "*"))) ```
output
1
40,406
5
80,813
Provide a correct Python 3 solution for this coding contest problem. Oranges on Cans square1001 You put a $ N $ can of aluminum on the table. E869120 You put $ M $ of oranges on each aluminum can on the table. How many oranges are on the aluminum can? input Input is given from standard input in the following format. $ N $ $ M $ output Output the number of oranges on the aluminum can in one line. However, insert a line break at the end. Constraint * $ 1 \ leq N \ leq 9 $ * $ 1 \ leq M \ leq 9 $ * All inputs are integers. Input example 1 3 4 Output example 1 12 Input example 2 7 7 Output example 2 49 Example Input 3 4 Output 12
instruction
0
40,407
5
80,814
"Correct Solution: ``` n,m=map(int,input().split()) print(n*m) ```
output
1
40,407
5
80,815
Provide a correct Python 3 solution for this coding contest problem. Oranges on Cans square1001 You put a $ N $ can of aluminum on the table. E869120 You put $ M $ of oranges on each aluminum can on the table. How many oranges are on the aluminum can? input Input is given from standard input in the following format. $ N $ $ M $ output Output the number of oranges on the aluminum can in one line. However, insert a line break at the end. Constraint * $ 1 \ leq N \ leq 9 $ * $ 1 \ leq M \ leq 9 $ * All inputs are integers. Input example 1 3 4 Output example 1 12 Input example 2 7 7 Output example 2 49 Example Input 3 4 Output 12
instruction
0
40,408
5
80,816
"Correct Solution: ``` N,M = map(int,input().split()) print(N*M) ```
output
1
40,408
5
80,817
Provide a correct Python 3 solution for this coding contest problem. Write a program which manipulates a sequence $A$ = {$a_0, a_1, ..., a_{n-1}$} with the following operations: * $add(s, t, x)$ : add $x$ to $a_s, a_{s+1}, ..., a_t$. * $find(s, t)$ : report the minimum value in $a_s, a_{s+1}, ..., a_t$. Note that the initial values of $a_i ( i = 0, 1, ..., n-1 )$ are 0. Constraints * $1 ≤ n ≤ 100000$ * $1 ≤ q ≤ 100000$ * $0 ≤ s ≤ t < n$ * $-1000 ≤ x ≤ 1000$ Input $n$ $q$ $query_1$ $query_2$ : $query_q$ In the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$th query $query_i$ is given in the following format: 0 $s$ $t$ $x$ or 1 $s$ $t$ The first digit represents the type of the query. '0' denotes $add(s, t, x)$ and '1' denotes $find(s, t)$. Output For each $find$ query, print the minimum value. Example Input 6 7 0 1 3 1 0 2 4 -2 1 0 5 1 0 1 0 3 5 3 1 3 4 1 0 5 Output -2 0 1 -1
instruction
0
40,409
5
80,818
"Correct Solution: ``` import sys input = sys.stdin.readline N,Q=map(int,input().split()) seg_el=1<<(N.bit_length()) # Segment treeの台の要素数 SEG=[0]*(2*seg_el) # 1-indexedなので、要素数2*seg_el.Segment treeの初期値で初期化 LAZY=[0]*(2*seg_el) # 1-indexedなので、要素数2*seg_el.Segment treeの初期値で初期化 def indexes(L,R): # 遅延伝搬すべきノードのリストを返す. (つまり, updateやgetvaluesで見るノードより上にあるノードたち) INDLIST=[] R-=1 L>>=1 R>>=1 while L!=R: if L>R: INDLIST.append(L) L>>=1 else: INDLIST.append(R) R>>=1 while L!=0: INDLIST.append(L) L>>=1 return INDLIST def adds(l,r,x): # 区間[l,r)を +x 更新 L=l+seg_el R=r+seg_el L//=(L & (-L)) R//=(R & (-R)) UPIND=indexes(L,R) while L!=R: if L > R: SEG[L]+=x LAZY[L]+=x L+=1 L//=(L & (-L)) else: R-=1 SEG[R]+=x LAZY[R]+=x R//=(R & (-R)) for ind in UPIND: SEG[ind]=min(SEG[ind<<1],SEG[1+(ind<<1)])+LAZY[ind] def getvalues(l,r): # 区間[l,r)に関するminを調べる L=l+seg_el R=r+seg_el L//=(L & (-L)) R//=(R & (-R)) UPIND=indexes(L,R) for ind in UPIND[::-1]: # 遅延伝搬 if LAZY[ind]!=0: plus_lazy=LAZY[ind] SEG[ind<<1]+=plus_lazy SEG[1+(ind<<1)]+=plus_lazy LAZY[ind<<1]+=plus_lazy LAZY[1+(ind<<1)]+=plus_lazy LAZY[ind]=0 ANS=1<<31 while L!=R: if L > R: ANS=min(ANS , SEG[L]) L+=1 L//=(L & (-L)) else: R-=1 ANS=min(ANS , SEG[R]) R//=(R & (-R)) return ANS ANS=[] for _ in range(Q): query=list(map(int,input().split())) if query[0]==0: adds(query[1],query[2]+1,query[3]) else: ANS.append(getvalues(query[1],query[2]+1)) print("\n".join([str(ans) for ans in ANS])) ```
output
1
40,409
5
80,819
Provide a correct Python 3 solution for this coding contest problem. Write a program which manipulates a sequence $A$ = {$a_0, a_1, ..., a_{n-1}$} with the following operations: * $add(s, t, x)$ : add $x$ to $a_s, a_{s+1}, ..., a_t$. * $find(s, t)$ : report the minimum value in $a_s, a_{s+1}, ..., a_t$. Note that the initial values of $a_i ( i = 0, 1, ..., n-1 )$ are 0. Constraints * $1 ≤ n ≤ 100000$ * $1 ≤ q ≤ 100000$ * $0 ≤ s ≤ t < n$ * $-1000 ≤ x ≤ 1000$ Input $n$ $q$ $query_1$ $query_2$ : $query_q$ In the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$th query $query_i$ is given in the following format: 0 $s$ $t$ $x$ or 1 $s$ $t$ The first digit represents the type of the query. '0' denotes $add(s, t, x)$ and '1' denotes $find(s, t)$. Output For each $find$ query, print the minimum value. Example Input 6 7 0 1 3 1 0 2 4 -2 1 0 5 1 0 1 0 3 5 3 1 3 4 1 0 5 Output -2 0 1 -1
instruction
0
40,410
5
80,820
"Correct Solution: ``` # https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/all/DSL_2_H class SegmentTreeForRMQandRAQ: # range minimum query and range add query def __init__(self, ls: list, segfunc=min, identity_element=2**31, lazy_ide=0): ''' セグ木 一次元のリストlsを受け取り初期化する。O(len(ls)) 区間のルールはsegfuncによって定義される identity elementは単位元。e.g., 最小値を求めたい→inf, 和→0, 積→1, gcd→0 [単位元](https://ja.wikipedia.org/wiki/%E5%8D%98%E4%BD%8D%E5%85%83) ''' self.ide = identity_element self.lide = lazy_ide # lazy用単位元 self.func = segfunc n = len(ls) self.num = 2 ** (n - 1).bit_length() # n以上の最小の2のべき乗 self.tree = [self.ide] * (2 * self.num) # 関係ない値を-1においてアクセスを許すと都合が良い self.lazy = [self.lide] * (2 * self.num) # 遅延配列 for i, l in enumerate(ls): # 木の葉に代入 self.tree[i + self.num - 1] = l for i in range(self.num - 2, -1, -1): # 子を束ねて親を更新 self.tree[i] = segfunc(self.tree[2 * i + 1], self.tree[2 * i + 2]) def _gidx(self, l, r): ''' lazy propagation用idx生成器 木の下から生成される。1based-indexなので注意.(使うときは-1するとか) もとの配列において[l,r)を指定したときに更新すべきidxをyieldする treesizeは多くの場合self.num ''' L, R = l + self.num, r + self.num lm = (L // (L & -L)) >> 1 # これで成り立つの天才か? rm = (R // (R & -R)) >> 1 while L < R: if R <= rm: yield R if L <= lm: yield L L >>= 1 R >>= 1 while L: # Rでもいいけどね yield L L >>= 1 def _lazyprop(self, *ids): ''' 遅延評価用の関数 - self.tree[i] に self.lazy[i]の値を伝播させて遅延更新する - 子ノードにself.lazyの値を伝播させる **ここは問題ごとに書き換える必要がある** - self.lazy[i]をリセットする ''' for i in reversed(ids): i -= 1 # 0basedindexに修正 v = self.lazy[i] if v == self.lide: continue # 単位元ならする必要のNASA # どうやって遅延更新するかは問題によってことなる # 今回なら範囲(最小値を持つ)に加算なので、そのままvを加算すればよい self.tree[2 * i + 1] += v self.tree[2 * i + 2] += v self.lazy[2 * i + 1] += v self.lazy[2 * i + 2] += v self.lazy[i] = self.lide # 遅延配列を空に戻す def update(self, l, r, x): ''' [l,r)番目の要素をxに変更する(木の中間ノードも更新する) O(logN) ''' # 1, 根から区間内においてlazyの値を伝播しておく(self.treeの値が有効になる) ids = tuple(self._gidx(l, r)) # self._lazyprop(*ids) # 足し算はlazyに対し込んでも良いのでupdate時にpropしなくても良い # 2, 区間に対してtree,lazyの値を更新 (treeは根方向に更新するため、lazyはpropで葉方向に更新するため) if r <= l: return ValueError('invalid index (l,rがありえないよ)') l += self.num r += self.num while l < r: # ** 問題によって値のセットの仕方も変えるべし** if r & 1: r -= 1 self.tree[r - 1] += x self.lazy[r - 1] += x if l & 1: self.tree[l - 1] += x self.lazy[l - 1] += x l += 1 l >>= 1 r >>= 1 # 3, 伝播させた区間について下からdataの値を伝播する for i in ids: i -= 1 # to 0based self.tree[i] = self.func( # ここでlazyの値を考慮しなければ行けない self.tree[2 * i + 1], self.tree[2 * i + 2]) + self.lazy[i] def query(self, l, r): ''' 区間[l,r)に対するクエリをO(logN)で処理する。例えばその区間の最小値、最大値、gcdなど ''' if r <= l: return ValueError('invalid index (l,rがありえないよ)') # 1, 根からにlazyの値を伝播させる self._lazyprop(*self._gidx(l, r)) # 2, 区間[l,r)の最小値を求める l += self.num r += self.num res = self.ide while l < r: # 右から寄りながら結果を結合していくイメージ if r & 1: r -= 1 res = self.func(res, self.tree[r - 1]) if l & 1: res = self.func(res, self.tree[l - 1]) l += 1 l >>= 1 r >>= 1 # 親の一つ左に移動 return res n, q = map(int, input().split()) ls = [0] * n seg = SegmentTreeForRMQandRAQ(ls) for _ in range(q): cmd, *tmp = map(int, input().split()) if cmd == 0: s, t, x = tmp seg.update(s, t + 1, x) else: s, t = tmp print(seg.query(s, t + 1)) ```
output
1
40,410
5
80,821
Provide a correct Python 3 solution for this coding contest problem. Write a program which manipulates a sequence $A$ = {$a_0, a_1, ..., a_{n-1}$} with the following operations: * $add(s, t, x)$ : add $x$ to $a_s, a_{s+1}, ..., a_t$. * $find(s, t)$ : report the minimum value in $a_s, a_{s+1}, ..., a_t$. Note that the initial values of $a_i ( i = 0, 1, ..., n-1 )$ are 0. Constraints * $1 ≤ n ≤ 100000$ * $1 ≤ q ≤ 100000$ * $0 ≤ s ≤ t < n$ * $-1000 ≤ x ≤ 1000$ Input $n$ $q$ $query_1$ $query_2$ : $query_q$ In the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$th query $query_i$ is given in the following format: 0 $s$ $t$ $x$ or 1 $s$ $t$ The first digit represents the type of the query. '0' denotes $add(s, t, x)$ and '1' denotes $find(s, t)$. Output For each $find$ query, print the minimum value. Example Input 6 7 0 1 3 1 0 2 4 -2 1 0 5 1 0 1 0 3 5 3 1 3 4 1 0 5 Output -2 0 1 -1
instruction
0
40,411
5
80,822
"Correct Solution: ``` # -*- coding: utf-8 -*- import sys input = sys.stdin.readline 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 list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)] def ceil(x, y=1): return int(-(-x // y)) def INT(): return int(input()) def MAP(): return map(int, input().split()) def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)] def Yes(): print('Yes') def No(): print('No') def YES(): print('YES') def NO(): print('NO') sys.setrecursionlimit(10 ** 9) INF = 2 ** 31 - 1 MOD = 10 ** 9 + 7 class StarrySkyTree: """ Starry Sky Tree """ def __init__(self, N, func, intv): self.intv = intv self.func = func LV = (N-1).bit_length() self.N0 = 2**LV self.data = [0]*(2*self.N0) self.lazy = [0]*(2*self.N0) # 伝搬される区間のインデックス(1-indexed)を全て列挙するgenerator def gindex(self, l, r): L = l + self.N0; R = r + self.N0 lm = (L // (L & -L)) >> 1 rm = (R // (R & -R)) >> 1 while L < R: if R <= rm: yield R if L <= lm: yield L L >>= 1; R >>= 1 while L: yield L L >>= 1 # 遅延評価の伝搬処理 def propagates(self, *ids): # 1-indexedで単調増加のインデックスリスト for i in reversed(ids): v = self.lazy[i-1] if not v: continue self.lazy[2*i-1] += v; self.lazy[2*i] += v self.data[2*i-1] += v; self.data[2*i] += v self.lazy[i-1] = 0 def update(self, l, r, x): """ 区間[l,r)の値にxを加算 """ # 1. lazyの値は伝搬させない # 2. 区間[l,r)のdata, lazyの値を更新 L = self.N0 + l; R = self.N0 + r while L < R: if R & 1: R -= 1 self.lazy[R-1] += x; self.data[R-1] += x if L & 1: self.lazy[L-1] += x; self.data[L-1] += x L += 1 L >>= 1; R >>= 1 # 3. 更新される区間を部分的に含んだ区間のdataの値を更新 (lazyの値を考慮) for i in self.gindex(l, r): self.data[i-1] = self.func(self.data[2*i-1], self.data[2*i]) + self.lazy[i-1] def query(self, l, r): """ 区間[l,r)の最小値を取得 """ # 1. トップダウンにlazyの値を伝搬 self.propagates(*self.gindex(l, r)) L = self.N0 + l; R = self.N0 + r # 2. 区間[l, r)の最小値を求める s = self.intv while L < R: if R & 1: R -= 1 s = self.func(s, self.data[R-1]) if L & 1: s = self.func(s, self.data[L-1]) L += 1 L >>= 1; R >>= 1 return s N, Q = MAP() sst = StarrySkyTree(N+1, min, INF) ans = [] for i in range(Q): cmd, *arg = MAP() if cmd == 0: s, t, x = arg sst.update(s, t+1, x) else: s, t = arg ans.append(str(sst.query(s, t+1))) print('\n'.join(ans)) ```
output
1
40,411
5
80,823
Provide a correct Python 3 solution for this coding contest problem. Write a program which manipulates a sequence $A$ = {$a_0, a_1, ..., a_{n-1}$} with the following operations: * $add(s, t, x)$ : add $x$ to $a_s, a_{s+1}, ..., a_t$. * $find(s, t)$ : report the minimum value in $a_s, a_{s+1}, ..., a_t$. Note that the initial values of $a_i ( i = 0, 1, ..., n-1 )$ are 0. Constraints * $1 ≤ n ≤ 100000$ * $1 ≤ q ≤ 100000$ * $0 ≤ s ≤ t < n$ * $-1000 ≤ x ≤ 1000$ Input $n$ $q$ $query_1$ $query_2$ : $query_q$ In the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$th query $query_i$ is given in the following format: 0 $s$ $t$ $x$ or 1 $s$ $t$ The first digit represents the type of the query. '0' denotes $add(s, t, x)$ and '1' denotes $find(s, t)$. Output For each $find$ query, print the minimum value. Example Input 6 7 0 1 3 1 0 2 4 -2 1 0 5 1 0 1 0 3 5 3 1 3 4 1 0 5 Output -2 0 1 -1
instruction
0
40,412
5
80,824
"Correct Solution: ``` #!/usr/bin/env python3 # DSL_2_H: RMQ and RAQ # Range Minimum Query and Range Add Query # Lazy propagate segment tree from array import array import sys class SegmentTree: MAXV = 1000 * 10**5 + 1 def __init__(self, n): size = 1 while size < n: size *= 2 self.size = 2*size - 1 self.data = array('i', [0] * self.size) self.lazy = array('i', [0] * self.size) def add(self, lo, hi, v): def _add(r, i, j, lz): left, right = r*2 + 1, r*2 + 2 if lazy[r]: lz += lazy[r] lazy[r] = 0 if lo <= i and j <= hi: lz += v if lz: data[r] += lz if i < j: lazy[left] += lz lazy[right] += lz else: mid = (i + j) // 2 if mid >= lo: lv = _add(left, i, mid, lz) else: lazy[left] += lz lv = data[left] + lazy[left] if mid < hi: rv = _add(right, mid+1, j, lz) else: lazy[right] += lz rv = data[right] + lazy[right] if lv < rv: data[r] = lv else: data[r] = rv return data[r] lazy = self.lazy data = self.data _add(0, 0, self.size//2, 0) def min(self, lo, hi): def _min(r, i, j, lz): left, right = r*2 + 1, r*2 + 2 if lazy[r]: lz += lazy[r] lazy[r] = 0 if lz: data[r] += lz if lo <= i and j <= hi: if lz and i < j: lazy[left] += lz lazy[right] += lz return data[r] else: mid = (i + j) // 2 if mid >= lo: lv = _min(left, i, mid, lz) else: lazy[left] += lz lv = self.MAXV if mid < hi: rv = _min(right, mid+1, j, lz) else: lazy[right] += lz rv = self.MAXV if lv < rv: return lv else: return rv lazy = self.lazy data = self.data return _min(0, 0, self.size//2, 0) def run(): n, q = [int(i) for i in input().split()] tree = SegmentTree(n) ret = [] for line in sys.stdin: com, *args = line.split() if com == '0': s, t, x = map(int, args) tree.add(s, t, x) elif com == '1': s, t = map(int, args) ret.append(tree.min(s, t)) sys.stdout.write("\n".join([str(i) for i in ret])) sys.stdout.write("\n") if __name__ == '__main__': run() ```
output
1
40,412
5
80,825
Provide a correct Python 3 solution for this coding contest problem. Write a program which manipulates a sequence $A$ = {$a_0, a_1, ..., a_{n-1}$} with the following operations: * $add(s, t, x)$ : add $x$ to $a_s, a_{s+1}, ..., a_t$. * $find(s, t)$ : report the minimum value in $a_s, a_{s+1}, ..., a_t$. Note that the initial values of $a_i ( i = 0, 1, ..., n-1 )$ are 0. Constraints * $1 ≤ n ≤ 100000$ * $1 ≤ q ≤ 100000$ * $0 ≤ s ≤ t < n$ * $-1000 ≤ x ≤ 1000$ Input $n$ $q$ $query_1$ $query_2$ : $query_q$ In the first line, $n$ (the number of elements in $A$) and $q$ (the number of queries) are given. Then, $i$th query $query_i$ is given in the following format: 0 $s$ $t$ $x$ or 1 $s$ $t$ The first digit represents the type of the query. '0' denotes $add(s, t, x)$ and '1' denotes $find(s, t)$. Output For each $find$ query, print the minimum value. Example Input 6 7 0 1 3 1 0 2 4 -2 1 0 5 1 0 1 0 3 5 3 1 3 4 1 0 5 Output -2 0 1 -1
instruction
0
40,413
5
80,826
"Correct Solution: ``` import sys class Lazysegtree: #RAQ def __init__(self, A, intv, initialize = True, segf = min): #区間は 1-indexed で管理 self.N = len(A) self.N0 = 2**(self.N-1).bit_length() self.intv = intv self.segf = segf self.lazy = [0]*(2*self.N0) if initialize: self.data = [intv]*self.N0 + A + [intv]*(self.N0 - self.N) for i in range(self.N0-1, 0, -1): self.data[i] = self.segf(self.data[2*i], self.data[2*i+1]) else: self.data = [intv]*(2*self.N0) def _ascend(self, k): k = k >> 1 c = k.bit_length() for j in range(c): idx = k >> j self.data[idx] = self.segf(self.data[2*idx], self.data[2*idx+1]) \ + self.lazy[idx] def _descend(self, k): k = k >> 1 idx = 1 c = k.bit_length() for j in range(1, c+1): idx = k >> (c - j) ax = self.lazy[idx] if not ax: continue self.lazy[idx] = 0 self.data[2*idx] += ax self.data[2*idx+1] += ax self.lazy[2*idx] += ax self.lazy[2*idx+1] += ax def query(self, l, r): L = l+self.N0 R = r+self.N0 Li = L//(L & -L) Ri = R//(R & -R) self._descend(Li) self._descend(Ri - 1) s = self.intv while L < R: if R & 1: R -= 1 s = self.segf(s, self.data[R]) if L & 1: s = self.segf(s, self.data[L]) L += 1 L >>= 1 R >>= 1 return s def update(self, l, r, x): L = l+self.N0 R = r+self.N0 Li = L//(L & -L) Ri = R//(R & -R) while L < R : if R & 1: R -= 1 self.data[R] += x self.lazy[R] += x if L & 1: self.data[L] += x self.lazy[L] += x L += 1 L >>= 1 R >>= 1 self._ascend(Li) self._ascend(Ri-1) N, Q = map(int, input().split()) T = Lazysegtree([0]*N, 2<<31) Ans = [] for jq in range(Q): t, *q = map(int, sys.stdin.readline().split()) q[1] += 1 if t: Ans.append(T.query(*q)) else: T.update(*q) print('\n'.join(map(str, Ans))) ```
output
1
40,413
5
80,827