message stringlengths 2 16.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 575 109k | cluster float64 16 16 | __index_level_0__ int64 1.15k 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke stands on a number line. He has L ears, and he will walk along the line continuously under the following conditions:
* He never visits a point with coordinate less than 0, or a point with coordinate greater than L.
* He starts walking at a point with integer coordinate, and also finishes walking at a point with integer coordinate.
* He only changes direction at a point with integer coordinate.
Each time when Snuke passes a point with coordinate i-0.5, where i is an integer, he put a stone in his i-th ear.
After Snuke finishes walking, Ringo will repeat the following operations in some order so that, for each i, Snuke's i-th ear contains A_i stones:
* Put a stone in one of Snuke's ears.
* Remove a stone from one of Snuke's ears.
Find the minimum number of operations required when Ringo can freely decide how Snuke walks.
Constraints
* 1 \leq L \leq 2\times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq L)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
L
A_1
:
A_L
Output
Print the minimum number of operations required when Ringo can freely decide how Snuke walks.
Examples
Input
4
1
0
2
3
Output
1
Input
8
2
0
0
2
1
3
4
1
Output
3
Input
7
314159265
358979323
846264338
327950288
419716939
937510582
0
Output
1
Submitted Solution:
```
L = int(input())
a_list = [int(input()) for _ in range(L)]
extra = 0
for a in a_list[::-1]:
if a == 0:
extra += 1
else:
break
prev_sum = 0
skip_cnt = 0
ans = 0
start = False
even_cnt = 0
for a in a_list:
if a == 0:
skip_cnt += 1
if skip_cnt >= prev_sum:
ans = 0
ans += prev_sum
start = False
else:
if start:
ans += 1
else:
if a % 2 == 0:
even_cnt += 1
prev_sum += a
start = True
ans -= extra
print(ans + 1 if even_cnt >= 2 else ans)
``` | instruction | 0 | 80,669 | 16 | 161,338 |
No | output | 1 | 80,669 | 16 | 161,339 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No | instruction | 0 | 81,474 | 16 | 162,948 |
"Correct Solution:
```
import sys
class UnionFind:
def __init__(self, n):
self.table = [-1] * n
def _root(self, x):
if self.table[x] < 0:
return x
else:
self.table[x] = self._root(self.table[x])
return self.table[x]
def find(self, x, y):
return self._root(x) == self._root(y)
def union(self, x, y):
r1 = self._root(x)
r2 = self._root(y)
if r1 == r2:
return
d1 = self.table[r1]
d2 = self.table[r2]
if d1 <= d2:
self.table[r2] = r1
self.table[r1] += d2
else:
self.table[r1] = r2
self.table[r2] += d1
def connected_count(self):
return sum(x < 0 for x in self.table)
n, m, q = list(map(int, input().split()))
uft = UnionFind(n)
hyper_paths = set()
for line in sys.stdin:
a, b, c = list(map(int, line.split()))
if c == 1:
hyper_paths.add((a, b))
continue
uft.union(a, b)
for a, b in hyper_paths:
if uft.find(a, b):
print('No')
exit()
cc = uft.connected_count()
min_m = n if len(hyper_paths) > 0 else n - 1
max_m = n - cc + cc * (cc - 1) // 2
print('Yes' if min_m <= m <= max_m else 'No')
``` | output | 1 | 81,474 | 16 | 162,949 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No | instruction | 0 | 81,475 | 16 | 162,950 |
"Correct Solution:
```
class UnionFind:
def __init__(self, n):
self.par = [-1 for i in range(n+1)]
self.rank = [0] * (n+1)
# 検索
def find(self, x):
if self.par[x] < 0:
return x
else:
self.par[x] = self.find(self.par[x])
return self.par[x]
# 併合
def union(self, x, y):
x = self.find(x)
y = self.find(y)
if not x==y: # 根が同じでない場合のみ併合する
if self.rank[x] < self.rank[y]:
self.par[y] += self.par[x] # 要素数を併合
self.par[x] = y # 根を付け替えている
else:
self.par[x] += self.par[y]
self.par[y] = x
if self.rank[x] == self.rank[y]:
self.rank[x] += 1
# 同じ集合に属するか判定
def same_check(self, x, y):
return self.find(x) == self.find(y)
def main():
import sys
input = sys.stdin.readline
N,M,Q = map(int,input().split())
KI = UnionFind(N-1)
CC = []
for i in range(Q):
A,B,C = map(int,input().split())
if C == 0:
KI.union(A,B)
else:
CC.append([A,B])
flag = 0
oya = {}
for i in range(N):
p = KI.find(i)
oya[p]=1
PPP = len(oya)
for i in CC:
A,B = i
if KI.same_check(A,B):
flag = 1
break
elif PPP<=2:
flag = 1
break
elif M == N-1:
flag = 1
break
if N-1+((PPP-2)*(PPP-1))//2 < M:
flag = 1
if flag == 0:
print("Yes")
else:
print("No")
main()
``` | output | 1 | 81,475 | 16 | 162,951 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No | instruction | 0 | 81,476 | 16 | 162,952 |
"Correct Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,copy,functools
import time,random
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
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 list(map(int, sys.stdin.readline().split()))
def LLI(): return [list(map(int, l.split())) for l in sys.stdin.readlines()]
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 pe(s): return print(str(s), file=sys.stderr)
def JA(a, sep): return sep.join(map(str, a))
def JAA(a, s, t): return s.join(t.join(map(str, b)) for b in a)
class UnionFind:
def __init__(self, size):
self.table = [-1 for _ in range(size)]
self.l = size
def find(self, x):
if self.table[x] < 0:
return x
else:
self.table[x] = self.find(self.table[x])
return self.table[x]
def union(self, x, y):
s1 = self.find(x)
s2 = self.find(y)
if s1 != s2:
if self.table[s1] <= self.table[s2]:
self.table[s1] += self.table[s2]
self.table[s2] = s1
else:
self.table[s2] += self.table[s1]
self.table[s1] = s2
self.l -= 1
return True
return False
def subsetall(self):
a = []
for i in range(len(self.table)):
if self.table[i] < 0:
a.append((i, -self.table[i]))
return a
def main():
n,m,q = LI()
aa = [LI() for _ in range(q)]
uf = UnionFind(n)
t = 0
cc = 0
for a,b,c in aa:
if c == 0:
if uf.union(a,b):
t += 1
else:
cc += 1
for a,b,c in aa:
if c == 0:
continue
if uf.find(a) == uf.find(b):
return 'No'
if m == n - 1:
if cc == 0:
return 'Yes'
return 'No'
if m <= n - uf.l + uf.l * (uf.l-1) // 2:
return 'Yes'
return 'No'
print(main())
``` | output | 1 | 81,476 | 16 | 162,953 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No | instruction | 0 | 81,477 | 16 | 162,954 |
"Correct Solution:
```
import sys
input=sys.stdin.readline
class UnionFind:
def __init__(self,n):
self.par=[i for i in range(n)]
self.rank=[0]*n
def find(self,x):
if self.par[x]==x:
return x
else:
self.par[x]=self.find(self.par[x])
return self.par[x]
def union(self,x,y):
x=self.find(x)
y=self.find(y)
if x==y:
return
if self.rank[x]<self.rank[y]:
self.par[x]=y
else:
self.par[y]=x
if self.rank[x]==self.rank[y]:
self.rank[x]+=1
def same_check(self,x,y):
return self.find(x)==self.find(y)
def main():
n,m,q=map(int,input().split())
E=[]
uf=UnionFind(n)
for _ in range(q):
a,b,c=map(int,input().split())
if c:
E.append((a,b))
else:
uf.union(a,b)
s=set()
for i in range(n):
s.add(uf.find(i))
k=len(s)
if E and (k<=2 or m==n-1):
print('No')
return
for a,b in E:
if uf.same_check(a,b):
print('No')
return
print('Yes' if m<=n+k*(k-3)//2 else 'No')
if __name__=='__main__':
main()
``` | output | 1 | 81,477 | 16 | 162,955 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No | instruction | 0 | 81,478 | 16 | 162,956 |
"Correct Solution:
```
class UnionFindNode:
def __init__(self, group_id, parent=None, value=None):
self.group_id_ = group_id
self.parent_ = parent
self.value = value
self.rank_ = 1
self.member_num_ = 1
def is_root(self):
return not self.parent_
def root(self):
parent = self
while not parent.is_root():
parent = parent.parent_
self.parent_ = parent
return parent
def find(self):
root = self.root()
return root.group_id_
def rank(self):
root = self.root()
return root.rank_
def unite(self, unite_node):
root = self.root()
unite_root = unite_node.root()
if root.group_id_ != unite_root.group_id_:
if root.rank() > unite_root.rank():
unite_root.parent_ = root
root.rank_ = max(root.rank_, unite_root.rank_ + 1)
root.member_num_ = root.member_num_ + unite_root.member_num_
else:
root.parent_ = unite_root
unite_root.rank_ = max(root.rank_ + 1, unite_root.rank_)
unite_root.member_num_ = root.member_num_ + unite_root.member_num_
if __name__ == "__main__":
N,M,Q=[int(i) for i in input().strip().split(" ")]
node_list = [UnionFindNode(i) for i in range(N)]
import sys
es = set()
for line in sys.stdin:
x,y,z=[int(i) for i in line.strip().split(" ")]
if z == 0:
node_list[x].unite(node_list[y])
else:
es.add((x,y))
if M == N-1:
if len(es):
print("No")
sys.exit()
for e in es:
if node_list[e[0]].root() == node_list[e[1]].root():
print("No")
sys.exit()
counter = 0
b = 0
for node in node_list:
if node.is_root():
counter += 1
b += node.root().member_num_ - 1
if M<=b+((counter)*(counter-1)//2):
print("Yes")
else:
print("No")
``` | output | 1 | 81,478 | 16 | 162,957 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No | instruction | 0 | 81,479 | 16 | 162,958 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
N, M, Q = map(int, input().split())
E = [list(map(int, input().split())) for i in range(Q)]
f = [i for i in range(N)]
def find(x):
if x != f[x]:
f[x] = find(f[x])
return f[x]
def union(x, y):
fx, fy = find(x), find(y)
if fx == fy: return False
f[fx] = fy
return True
E1 = []
for a, b, c in E:
if c == 0:
union(a, b)
else:
E1.append((a, b))
par = [find(x) for x in range(N)]
for a, b in E1:
if par[a] == par[b]:
print('No')
exit()
C = len(set(par))
if len(E1) == 0:
if N - 1 <= M <= (N - C) + C * (C - 1) // 2:
print("Yes")
else:
print("No")
else:
if N <= M <= (N - C) + C * (C - 1) // 2:
print("Yes")
else:
print("No")
``` | output | 1 | 81,479 | 16 | 162,959 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No | instruction | 0 | 81,480 | 16 | 162,960 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
N,M,Q=map(int,input().split())
E=[list(map(int,input().split())) for i in range(Q)]
# UnionFind
Group=[i for i in range(N)]# グループ分け.Group[i]=jのときiとjは同じグループ
def find(x):# find(a)=find(b)のとき同じグループ
while Group[x] != x:
x=Group[x]
return x
def Union(x,y): # xとyが同じグループになるよう更新
if find(x) != find(y):
Group[find(y)]=Group[find(x)]=min(find(y),find(x))
E1=[]
for a,b,x in E:
if x==0:
Union(a,b)
else:
E1.append((a,b))
Group=[find(i) for i in range(N)]
for a,b in E1:
if Group[a]==Group[b]:
print("No")
sys.exit()
C=len(set(Group))
if len(E1)==0:
if N-1<=M<=(N-C)+C*(C-1)//2:
print("Yes")
else:
print("No")
else:
if N<=M<=(N-C)+C*(C-1)//2:
print("Yes")
else:
print("No")
``` | output | 1 | 81,480 | 16 | 162,961 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No | instruction | 0 | 81,481 | 16 | 162,962 |
"Correct Solution:
```
class UnionFind:
def __init__(self, n):
self.par = [i for i in range(n+1)]
self.rank = [0] * (n+1)
# search
def find(self, x):
if self.par[x] == x:
return x
else:
self.par[x] = self.find(self.par[x])
return self.par[x]
# unite
def union(self, x, y):
x = self.find(x)
y = self.find(y)
if self.rank[x] < self.rank[y]:
self.par[x] = y
else:
self.par[y] = x
if self.rank[x] == self.rank[y]:
self.rank[x] += 1
# check
def same_check(self, x, y):
return self.find(x) == self.find(y)
def solve_d(n, m, q, a_list, b_list, c_list):
res = 'Yes'
uf = UnionFind(n - 1)
for i in range(q):
if c_list[i] == 0:
uf.union(a_list[i], b_list[i])
for i in range(q):
if c_list[i] == 1:
if uf.same_check(a_list[i], b_list[i]):
res = 'No'
par_list = [0] * n
for i in range(n):
par_list[i] = uf.find(i)
k = len(set(par_list))
# print(k, par_list)
if max(c_list) == 0:
min_m = n - 1
else:
min_m = n
if m < min_m:
res = 'No'
elif m > n + k * (k - 3) // 2:
res = 'No'
return res
def main():
n, m, q = map(int, input().split())
a_list = [0] * q
b_list = [0] * q
c_list = [0] * q
for i in range(q):
a, b, c = map(int, input().split())
a_list[i] = a
b_list[i] = b
c_list[i] = c
res = solve_d(n, m, q, a_list, b_list, c_list)
print(res)
if __name__ == "__main__":
main()
``` | output | 1 | 81,481 | 16 | 162,963 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No
Submitted Solution:
```
#!/usr/bin/env python3
n, m, q = [int(item) for item in input().split()]
class UnionFind:
def __init__(self, n):
self.par = [i for i in range(n)]
self.size = [1] * n
self.rank = [0] * n
def find(self, x):
if self.par[x] == x:
return x
else:
self.par[x] = self.find(self.par[x])
return self.par[x]
def same_check(self, x, y):
return self.find(x) == self.find(y)
def get_size(self, x):
return self.size[self.find(x)]
def union(self, x, y):
x = self.find(x)
y = self.find(y)
if self.rank[x] < self.rank[y]:
self.par[x] = y
else:
self.par[y] = x
if self.rank[x] == self.rank[y]:
self.rank[x] += 1
Forest = UnionFind(n)
circles = []
group_num = n
edge_num = 0
seen = set()
for i in range(q):
a, b, c = [int(item) for item in input().split()]
if a > b:
a, b = b, a
if (a, b, c) in seen:
continue
if c == 0:
# loop with simple path
if not Forest.same_check(a, b):
Forest.union(a, b)
group_num -= 1
edge_num += 1
else:
circles.append((a, b, c))
seen.add((a, b, c))
for a, b, c in circles:
# multipath in tree
if Forest.same_check(a, b):
print("No")
exit()
# if group_num == 2:
# print("No")
# exit()
if len(circles) > 0:
edge_min = edge_num + group_num
edge_max = edge_num + group_num * (group_num - 1) // 2
else:
edge_min = edge_num + group_num - 1
edge_max = edge_num + group_num * (group_num - 1) // 2
if edge_min <= m <= edge_max:
print("Yes")
else:
print("No")
``` | instruction | 0 | 81,482 | 16 | 162,964 |
Yes | output | 1 | 81,482 | 16 | 162,965 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No
Submitted Solution:
```
import sys
input=sys.stdin.readline
def find_parent(x):
y=parent[x]
if y<0:
return x
parent[x]=find_parent(y)
return parent[x]
def connect(a,b):
c=find_parent(a)
d=find_parent(b)
if c==d:
return
if parent[c]<parent[d]:
parent[c]+=parent[d]
parent[d]=c
else:
parent[d]+=parent[c]
parent[c]=d
return
N,M,Q=map(int,input().split())
data=[[],[]]
for i in range(Q):
a,b,c=map(int,input().split())
data[c].append((a,b))
parent=[-1]*N
for a,b in data[0]:
connect(a,b)
cnt=0
for u in parent:
if u<0:
cnt+=1
for a,b in data[1]:
if find_parent(a)==find_parent(b):
print("No")
sys.exit()
if M==N-1:
if not data[1]:
print("Yes")
else:
print("No")
else:
M-=N
if M<=cnt*(cnt-1)//2-cnt:
print("Yes")
else:
print("No")
``` | instruction | 0 | 81,483 | 16 | 162,966 |
Yes | output | 1 | 81,483 | 16 | 162,967 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No
Submitted Solution:
```
#!/usr/bin/env python3
n, m, q = [int(item) for item in input().split()]
class UnionFind:
def __init__(self, n):
self.par = [i for i in range(n)]
self.size = [1] * n
self.rank = [0] * n
def find(self, x):
if self.par[x] == x:
return x
else:
self.par[x] = self.find(self.par[x])
return self.par[x]
def same_check(self, x, y):
return self.find(x) == self.find(y)
def get_size(self, x):
return self.size[self.find(x)]
def union(self, x, y):
x = self.find(x)
y = self.find(y)
if self.rank[x] < self.rank[y]:
self.par[x] = y
else:
self.par[y] = x
if self.rank[x] == self.rank[y]:
self.rank[x] += 1
Forest = UnionFind(n)
circles = []
group_num = n
edge_num = 0
seen = set()
for i in range(q):
a, b, c = [int(item) for item in input().split()]
if a > b:
a, b = b, a
if (a, b, c) in seen:
continue
if c == 0:
# loop with simple path
if not Forest.same_check(a, b):
Forest.union(a, b)
group_num -= 1
edge_num += 1
else:
circles.append((a, b, c))
seen.add((a, b, c))
for a, b, c in circles:
# multipath in tree
if Forest.same_check(a, b):
print("No")
exit()
if group_num == 2:
print("No")
exit()
if len(circles) > 0:
edge_min = edge_num + group_num
edge_max = edge_num + group_num * (group_num - 1) // 2
else:
edge_min = edge_num + group_num - 1
edge_max = edge_num + group_num * (group_num - 1) // 2
if edge_min <= m <= edge_max:
print("Yes")
else:
print("No")
``` | instruction | 0 | 81,484 | 16 | 162,968 |
Yes | output | 1 | 81,484 | 16 | 162,969 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No
Submitted Solution:
```
s = input().split(" ")
n = int(s[0])
m = int(s[1])
q = int(s[2])
path_list =[]
rank = [0 for i in range(n)]
multi = []
for i in range(q):
sp = input().split(" ")
path = [int(pstr) for pstr in sp]
path_list.append(path)
par = [i for i in range(n)]
#union-find
#xの木の根を得る
def root_find(x):
if par[x] != x:
par[x] = root_find(par[x])
return par[x]
else:
return x
#併合する
def unite(x,y):
rx = root_find(x)
ry = root_find(y)
if rx != ry:
if rank[x] > rank[y]:
par[y] = rx
elif rank[x] == rank[y]:
par[y] = rx
rank[x] += 1
else:
par[x] = ry
for i in range(q):
a = path_list[i][0]
b = path_list[i][1]
c = path_list[i][2]
if c == 0 :
pa = root_find(a)
pb = root_find(b)
if pa != pb:
unite(pa,pb)
else:
multi.append((a,b))
"""
だめなじょうけん
・a,bが木であるはずなのに閉路がある
・ありうる辺の上限よりもMが大きい、もしくは辺の下限N-1よりもMが小さい
"""
for a,b in multi:
if root_find(a) == root_find(b):
print("No")
exit(0)
k = 0
for i in range(n):
if root_find(i) == i:
k += 1
if len(multi) > 0:
min_edge = n
else:
min_edge = n - 1
max_edge = n + k * (k - 3) // 2
if min_edge <= m <= max_edge:
print("Yes")
else:
print("No")
``` | instruction | 0 | 81,485 | 16 | 162,970 |
Yes | output | 1 | 81,485 | 16 | 162,971 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No
Submitted Solution:
```
#! /usr/bin/env python3
### @file up.py
### @brief
### @author Yusuke Matsunaga (松永 裕介)
###
### Copyright (C) 2019 Yusuke Matsunaga
### All rights reserved.
n_str, m_str, q_str = input().split()
n = int(n_str)
m = int(m_str)
q = int(q_str)
# single path と multi path のペアを作る．
single_pair = []
multi_pair = []
for i in range(q) :
a_str, b_str, c_str = input().split()
a = int(a_str)
b = int(b_str)
c = int(c_str)
assert 0 <= a < n
assert 0 <= b < n
assert c == 0 or c == 1
# 正規化しておく
if b < a :
tmp = a
a = b
b = tmp
if c :
# multi path
multi_pair.append( (a, b) )
else :
# single path
single_pair.append( (a, b) )
# 特別なケース
if m == n - 1 and len(multi_pair) > 0 :
# M = N - 1 は木構造しかありえない．
print('No')
exit(0)
# single path のグループを作る．
adj_list = [ [] for i in range(n) ]
for a, b in single_pair :
adj_list[a].append(b)
adj_list[b].append(a)
group_id = [ -1 for i in range(n) ]
def dfs(i, gid) :
if group_id[i] != -1 :
# 処理済み
#assert group_id[i] == gid
return
group_id[i] = gid
for j in adj_list[i] :
pass
# dfs(j, gid)
gid = 0
for i in range(n) :
if group_id[i] == -1 :
group_id[i] = gid
for j in adj_list[i] :
dfs(j, gid)
gid += 1
exit(0)
``` | instruction | 0 | 81,486 | 16 | 162,972 |
No | output | 1 | 81,486 | 16 | 162,973 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No
Submitted Solution:
```
N, M, Q = map(int, input().split())
x = N * 123 + M * 34 + Q * 11
for _ in range(Q):
a, b, c = map(int, input().split())
x = (x * 7 + a * 123 + b * 34 + c * 11) % (10**9+7)
if x % 20 == 1 or x % 20 == 2 or x % 20 == 4 or x % 20 == 7 or x % 20 == 9 or x % 20 == 13:
print("Yes")
elif x % 20 == 5 or x % 20 == 14 or x % 20 == 15 or x % 20 == 17 or x % 20 == 18 or x % 19 == 1 or x % 20 == 19 or x % 19 == 0 or x % 19 == 2:
print("No")
elif x % 12 == 1:
print(1//0)
else:
print(1//0)
``` | instruction | 0 | 81,487 | 16 | 162,974 |
No | output | 1 | 81,487 | 16 | 162,975 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No
Submitted Solution:
```
N, M, Q = map(int, input().split())
x = N * 123 + M * 34 + Q * 11
for _ in range(Q):
a, b, c = map(int, input().split())
x = (x * 7 + a * 123 + b * 34 + c * 11) % (10**9+7)
if x % 20 == 0:
print("Yes")
else:
print("3")
``` | instruction | 0 | 81,488 | 16 | 162,976 |
No | output | 1 | 81,488 | 16 | 162,977 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.
One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:
* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.
Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.
Constraints
* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}
Output
If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.
Examples
Input
5 5 3
0 1 0
1 2 1
2 3 0
Output
Yes
Input
4 4 3
0 1 0
1 2 1
2 3 0
Output
No
Input
10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0
Output
No
Submitted Solution:
```
N, M, Q = map(int, input().split())
x = N * 123 + M * 34 + Q * 11
for _ in range(Q):
a, b, c = map(int, input().split())
x = (x * 7 + a * 123 + b * 34 + c * 11) % (10**9+7)
if x % 20 == 1 or x % 20 == 2 or x % 20 == 4 or x % 20 == 7 or x % 20 == 9 or x % 20 == 13:
print("Yes")
elif x % 20 == 5 or x % 20 == 14 or x % 20 == 15:
print("No")
elif x % 19 == 0:
print(1//0)
elif x % 19 == 1:
while 1:
pass
else:
print("3")
``` | instruction | 0 | 81,489 | 16 | 162,978 |
No | output | 1 | 81,489 | 16 | 162,979 |
Provide a correct Python 3 solution for this coding contest problem.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE | instruction | 0 | 81,554 | 16 | 163,108 |
"Correct Solution:
```
from fractions import gcd
n, k = map(int, input().split())
a = list(map(int, input().split()))
n = a[0]
max_num = max(a)
for num in a[1:]:
n = gcd(n, num)
if k % n == 0 and k <= max_num:
print("POSSIBLE")
else:
print("IMPOSSIBLE")
``` | output | 1 | 81,554 | 16 | 163,109 |
Provide a correct Python 3 solution for this coding contest problem.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE | instruction | 0 | 81,555 | 16 | 163,110 |
"Correct Solution:
```
from fractions import gcd
N,K=map(int,input().split())
A=list(map(int,input().split()))
maxi=max(A)
if K>maxi:
ans="IMPOSSIBLE"
else:
t=A[0]
for i in range(1,N):
t = gcd(t,A[i])
if K%t==0:
ans="POSSIBLE"
else:
ans="IMPOSSIBLE"
print(ans)
``` | output | 1 | 81,555 | 16 | 163,111 |
Provide a correct Python 3 solution for this coding contest problem.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE | instruction | 0 | 81,556 | 16 | 163,112 |
"Correct Solution:
```
from fractions import gcd
n, k = map(int, input().split())
a = sorted(list(map(int, input().split())))
if max(a) < k:
print("IMPOSSIBLE")
exit()
x = a[0]
for i in range(1,n):
x = gcd(x, a[i])
print("IMPOSSIBLE" if k % x else "POSSIBLE")
``` | output | 1 | 81,556 | 16 | 163,113 |
Provide a correct Python 3 solution for this coding contest problem.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE | instruction | 0 | 81,557 | 16 | 163,114 |
"Correct Solution:
```
import fractions
n,k = map(int,input().split())
a = sorted(list(map(int,input().split())))
a_max = max(a)
a_gcd = a[0]
for i in range(n):
a_gcd = fractions.gcd(a_gcd,a[i])
if k <= a_max and k % a_gcd == 0:
print("POSSIBLE")
else:
print("IMPOSSIBLE")
``` | output | 1 | 81,557 | 16 | 163,115 |
Provide a correct Python 3 solution for this coding contest problem.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE | instruction | 0 | 81,558 | 16 | 163,116 |
"Correct Solution:
```
from math import gcd
n,k = map(int,input().split())
A = list(map(int,input().split()))
g = A[0]
m = max(A)
for x in A:
g = gcd(g,x)
print("POSSIBLE" if k%g == 0 and m >= k else "IMPOSSIBLE")
``` | output | 1 | 81,558 | 16 | 163,117 |
Provide a correct Python 3 solution for this coding contest problem.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE | instruction | 0 | 81,559 | 16 | 163,118 |
"Correct Solution:
```
from fractions import gcd
N, K = map(int, input().split())
A = list(map(int,input().split()))
g = A[0]
for i in range(1, N):
g = gcd(g, A[i])
if K > max(A):
print("IMPOSSIBLE")
elif K % g != 0:
print("IMPOSSIBLE")
else:
print("POSSIBLE")
``` | output | 1 | 81,559 | 16 | 163,119 |
Provide a correct Python 3 solution for this coding contest problem.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE | instruction | 0 | 81,560 | 16 | 163,120 |
"Correct Solution:
```
import fractions
n, k = map(int, input().split())
a = list(map(int, input().split()))
if max(a)<k:
print("IMPOSSIBLE")
exit()
g = a[0]
for i in range(1, n):
g = fractions.gcd(g, a[i])
if k % g == 0:
print("POSSIBLE")
else:
print("IMPOSSIBLE")
``` | output | 1 | 81,560 | 16 | 163,121 |
Provide a correct Python 3 solution for this coding contest problem.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE | instruction | 0 | 81,561 | 16 | 163,122 |
"Correct Solution:
```
import fractions as fr
from functools import reduce
def gcd(a):
return reduce(fr.gcd, a)
n, k = map(int, input().split())
a = list(map(int, input().split()))
g = gcd(a)
print("POSSIBLE" if (k in a) or (max(a) >= k and (g == 1 or k%g == 0)) else "IMPOSSIBLE")
``` | output | 1 | 81,561 | 16 | 163,123 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE
Submitted Solution:
```
from fractions import gcd
from functools import reduce
N, K = map(int, input().split())
A = list(map(int, input().split()))
g = reduce(gcd, A)
print('IMPOSSIBLE' if K > max(A) or K % g else 'POSSIBLE')
``` | instruction | 0 | 81,562 | 16 | 163,124 |
Yes | output | 1 | 81,562 | 16 | 163,125 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE
Submitted Solution:
```
def gcd(a, b):
if b == 0: return a
return gcd(b, a % b)
n, k = map(int, input().split())
arr = list(map(int, input().split()))
g = arr[0]
for e in arr[1:]:
g = gcd(g, e)
if k <= max(arr) and k//g*g == k:
print("POSSIBLE")
else:
print("IMPOSSIBLE")
``` | instruction | 0 | 81,563 | 16 | 163,126 |
Yes | output | 1 | 81,563 | 16 | 163,127 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE
Submitted Solution:
```
def gcd(x, y):
while y != 0:
x, y = y, x % y
return x
n, k = map(int, input().split(), )
a = [ int(x) for x in input().split() ]
g = 0
for aa in a:
g = gcd(g, aa)
print("POSSIBLE" if k <= max(a) and k%g == 0 else "IMPOSSIBLE")
``` | instruction | 0 | 81,564 | 16 | 163,128 |
Yes | output | 1 | 81,564 | 16 | 163,129 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE
Submitted Solution:
```
N, K=map(int, input().split())
A=list(sorted(list(map(int, input().split())), reverse=True))
def gcd(a,b):
while b:
a,b=b,a%b
return a
g=A[0]
for i in range(1,len(A)):
g=gcd(g,A[i])
print("POSSIBLE" if K%g==0 and K<=max(A) else "IMPOSSIBLE")
``` | instruction | 0 | 81,565 | 16 | 163,130 |
Yes | output | 1 | 81,565 | 16 | 163,131 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE
Submitted Solution:
```
n, k = map(int, input().split())
a = list(map(int, input().split()))
a.sort()
if a[-1] < k:
print('IMPOSSIBLE')
elif k in a:
print('POSSIBLE')
else:
b = []
while len(a) != len(b):
b = a.copy()
lea = a[0]
for i in range(n-1):
a.append(a[i+1]-a[i])
a = list(set(a))
if k % a[0] == 0:
print('POSSIBLE')
else: print('IMPOSSIBLE')
``` | instruction | 0 | 81,566 | 16 | 163,132 |
No | output | 1 | 81,566 | 16 | 163,133 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE
Submitted Solution:
```
# A - Getting Difference
import math
from functools import reduce
N, K = map(int, input().split())
A = list(map(int, input().split()))
gcd = reduce(math.gcd, A)
if max(A)>=K and K%gcd==0:
print('POSSIBLE')
else:
print('IMPOSSIBLE')
``` | instruction | 0 | 81,567 | 16 | 163,134 |
No | output | 1 | 81,567 | 16 | 163,135 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE
Submitted Solution:
```
N,K = map(int,input().split())
A = list(map(int,input().split()))
ans = 'IMPOSSIBLE'
if max(A) >= K:
from math import gcd
from functools import reduce
g = reduce(gcd,A)
if K % g == 0: ans = 'POSSIBLE'
print(ans)
``` | instruction | 0 | 81,568 | 16 | 163,136 |
No | output | 1 | 81,568 | 16 | 163,137 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
* Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9
* 1 \leq K \leq 10^9
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1 A_2 ... A_N
Output
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print `POSSIBLE`; if it is not possible, print `IMPOSSIBLE`.
Examples
Input
3 7
9 3 4
Output
POSSIBLE
Input
3 5
6 9 3
Output
IMPOSSIBLE
Input
4 11
11 3 7 15
Output
POSSIBLE
Input
5 12
10 2 8 6 4
Output
IMPOSSIBLE
Submitted Solution:
```
import fractions
from functools import reduce
def lcm_base(x, y):
return (x * y) // fractions.gcd(x, y)
def lcm_list(numbers):
return reduce(lcm_base, numbers, 1)
def solve():
n,k= (int(i) for i in input().split())
a = list(int(i) for i in input().split())
ans = 'IMPOSSIBLE'
if max(a) < k :
return ans
elif k in a:
ans = 'POSSIBLE'
return ans
else:
gcd = lcm_list(a)
if gcd == 1 or k%gcd == 0 :ans ='POSSIBLE'
return ans
return ans
if __name__ == '__main__':
print(solve())
``` | instruction | 0 | 81,569 | 16 | 163,138 |
No | output | 1 | 81,569 | 16 | 163,139 |
Provide a correct Python 3 solution for this coding contest problem.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209 | instruction | 0 | 82,443 | 16 | 164,886 |
"Correct Solution:
```
from collections import deque;h,w=map(int,input().split());m=[input()for _ in[0]*h];v=[[-1]*w for _ in[0]*h];q=deque([[0,0]]);v[0][0]=0;c=sum(t.count('#')for t in m)
while q:
y,x=q.popleft()
for i,j in([1,0],[-1,0],[0,1],[0,-1]):
t,u=y+i,x+j
if t+1and t<h and u+1and u<w and m[t][u]=='.'and v[t][u]<0:v[t][u]=v[y][x]+1;q.append([t,u])
print(-1*(v[h-1][w-1]<0)or h*w-c-v[h-1][w-1]-1)
``` | output | 1 | 82,443 | 16 | 164,887 |
Provide a correct Python 3 solution for this coding contest problem.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209 | instruction | 0 | 82,444 | 16 | 164,888 |
"Correct Solution:
```
h, w = map(int, input().split())
s = [[0 if c == '#' else 1 for c in input()] for _ in range(h)]
directions = [(0, -1), (-1, 0), (0, 1), (1, 0)]
dist = [[-1 for _ in range(w)] for _ in range(h)]
dist[0][0] = 0
q = [(0, 0)]
for y, x in q:
for dy, dx in directions:
ny, nx = y + dy, x + dx
if (ny < 0 or h <= ny) or (nx < 0 or w <= nx):
continue
if not s[ny][nx]:
continue
if dist[ny][nx] >= 0:
continue
dist[ny][nx] = dist[y][x] + 1
q.append((ny, nx))
if dist[-1][-1] < 0:
print(-1)
else:
print(sum(sum(si) for si in s) - dist[-1][-1] - 1)
``` | output | 1 | 82,444 | 16 | 164,889 |
Provide a correct Python 3 solution for this coding contest problem.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209 | instruction | 0 | 82,445 | 16 | 164,890 |
"Correct Solution:
```
from collections import deque
H,W = map(int,input().split())
s = list(input() for i in range(H))
board = [[1]*(W+2) for i in range(H+2)]
white = 0
for i in range(H):
for j in range(W):
if s[i][j] == '.':
white += 1
board[i+1][j+1] = 0
queue = deque([[1,1]])
v = [[1,0],[-1,0],[0,-1],[0,1]]
while queue != deque([]):
x,y = queue.popleft()
for a,b in v:
if board[x+a][y+b] == 0:
board[x+a][y+b] = board[x][y]+1
queue.append([x+a,y+b])
if board[H][W] != 0:
print(white-board[H][W]-1)
else:
print(-1)
``` | output | 1 | 82,445 | 16 | 164,891 |
Provide a correct Python 3 solution for this coding contest problem.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209 | instruction | 0 | 82,446 | 16 | 164,892 |
"Correct Solution:
```
H, W = map(int, input().split())
l = [list(input()) for _ in range(H)]
from collections import deque
q = deque([(0, 0)])
d = [(1, 0), (-1, 0), (0, 1), (0, -1)]
l[0][0] = 0
while q:
y, x = q.popleft()
for dy, dx in d:
if 0 <= y+dy < H and 0 <= x+dx < W and l[y+dy][x+dx] == '.':
l[y+dy][x+dx] = l[y][x] + 1
q.append((y+dy, x+dx))
try:
g = l[H-1][W-1]
total = 0
for _l in l:
for i in _l:
if i != '#':
total += 1
print(total - g - 1)
except:
print(-1)
``` | output | 1 | 82,446 | 16 | 164,893 |
Provide a correct Python 3 solution for this coding contest problem.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209 | instruction | 0 | 82,447 | 16 | 164,894 |
"Correct Solution:
```
from collections import deque
h, w = map(int, input().split())
maze = {(i,j):c for i in range(h) for j, c in enumerate(input())}
blacks = sum(c == '#' for c in maze.values())
def bfs(i, j):
dq = deque()
dq.appendleft((1, (i, j)))
while dq:
steps, (i, j) = dq.pop()
if (i, j) == (h-1, w-1):
return steps
if maze.get((i, j), '#') == '#':
continue
maze[(i, j)] = '#'
dirs = ((-1, 0), (1, 0), (0, 1), (0, -1))
dq.extendleft((steps+1, (i+di, j+dj)) for di, dj in dirs)
res = bfs(0, 0)
print(-1 if res is None else h*w - res - blacks)
``` | output | 1 | 82,447 | 16 | 164,895 |
Provide a correct Python 3 solution for this coding contest problem.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209 | instruction | 0 | 82,448 | 16 | 164,896 |
"Correct Solution:
```
h,w=map(int,input().split())
l=[[1]*(w+2)]+[[1]+[1 if i=="#" else 0 for i in input()]+[1] for i in range(h)]+[[1]*(w+2)]
c=[[0]*(w+2) for i in range(h+2)]
q=[(1,1)]
e=[(0,1),(0,-1),(1,0),(-1,0)]
kyori=1
while len(q)>0 and c[h][w]==0:
tl=q
q=[]
for x,y in tl:
for X,Y in e:
if(l[y+Y][x+X]==0 and c[y+Y][x+X]==0):
q.append((x+X,y+Y))
c[y+Y][x+X]=1
kyori+=1
if c[h][w]==0:
print(-1)
else:
print(sum([i.count(0) for i in l])-kyori)
``` | output | 1 | 82,448 | 16 | 164,897 |
Provide a correct Python 3 solution for this coding contest problem.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209 | instruction | 0 | 82,449 | 16 | 164,898 |
"Correct Solution:
```
H, W = map(int, input().split())
G = [list(input()) for _ in range(H)]
que = [[0,0]]
dist = [[-1]*W for _ in range(H)]
direction = [[0,1], [0,-1], [1,0], [-1,0]]
dist[0][0] = 0
while que:
h, w = que.pop(0)
for dh, dw in direction:
if h+dh <0 or h+dh >= H or w+dw <0 or w+dw >= W:
continue
if G[h+dh][w+dw] == '#':
continue
if dist[h+dh][w+dw] != -1:
continue
dist[h+dh][w+dw] = dist[h][w] +1
que.append([h+dh, w+dw])
if dist[H-1][W-1] == -1:
print(-1)
else:
num = 0
for i in range(H):
num += G[i].count('#')
print(H*W-num-dist[H-1][W-1]-1)
``` | output | 1 | 82,449 | 16 | 164,899 |
Provide a correct Python 3 solution for this coding contest problem.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209 | instruction | 0 | 82,450 | 16 | 164,900 |
"Correct Solution:
```
# /usr/bin/python
# -*- coding: utf-8 -*-
#
import sys
H,W = map(int, input().split())
num_w = -1
srch = []
for i in range(H):
h = list(str(sys.stdin.readline().rstrip()))
for j in range(W):
if h[j] == ".":
srch.append([i+1,j+1])
num_w += 1
Cn = [[sys.maxsize for j in range(W+2)] for i in range(H+2)]
Cn[1][1] = 0
for _ in range(num_w):
for i,j in srch[1:]:
Cn[i][j] = min(Cn[i-1][j],Cn[i][j-1],Cn[i+1][j],Cn[i][j+1])+1
if Cn[H][W] < sys.maxsize:
print(num_w - Cn[H][W])
else:
print(-1)
``` | output | 1 | 82,450 | 16 | 164,901 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209
Submitted Solution:
```
from collections import deque
H, W = [int(i) for i in input().split()]
S = [list(input()) for _ in range(H)]
white = sum(s.count(".") for s in S)
Q = deque([(0, 0, 1)])
while Q:
h, w, count = Q.popleft()
if (h, w) == (H - 1, W - 1):
print(white - count)
quit()
for nh, nw in [(h, w + 1), (h, w - 1), (h + 1, w), (h - 1, w)]:
if not (0 <= nh < H and 0 <= nw < W):
continue
if S[nh][nw] == ".":
S[nh][nw] = "" # visited
Q.append((nh, nw, count + 1))
print(-1)
``` | instruction | 0 | 82,451 | 16 | 164,902 |
Yes | output | 1 | 82,451 | 16 | 164,903 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209
Submitted Solution:
```
import queue
H, W = list(map(int, input().split()))
s = [list(input()) + ['#'] for i in range(H)] + [['#' for i in range(W+1)]]
white = sum([s[i].count('.') for i in range(H)])
q = queue.Queue()
s[0][0] = 1
q.put((0,0))
while not q.empty():
i, j = q.get()
for x, y in [(i+1,j), (i-1,j), (i,j+1), (i,j-1)]:
if s[x][y] == '.':
s[x][y] = s[i][j]+1
q.put((x, y))
if s[H-1][W-1] in ['.', '#']:
print(-1)
else:
print(white-s[H-1][W-1])
``` | instruction | 0 | 82,452 | 16 | 164,904 |
Yes | output | 1 | 82,452 | 16 | 164,905 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209
Submitted Solution:
```
from collections import deque
dis = [[1, 0], [-1, 0], [0, 1], [0, -1]]
H, W = map(int, input().split())
A = []
count = 0
for i in range(H):
a = input()
A.append(a)
count += a.count(".")
B = [[0 for j in range(W)] for i in range(H)]
D = deque([[0, 0]])
B[0][0] = 1
while len(D) > 0:
d = D.popleft()
for k in range(4):
p = d[0] + dis[k][0]
q = d[1] + dis[k][1]
if 0 <= p < H and 0 <= q < W and A[p][q] == "." and B[p][q] == 0:
B[p][q] = B[d[0]][d[1]] + 1
D.append([p, q])
if B[H-1][W-1] == 0:
print(-1)
else:
print(count - B[H-1][W-1])
``` | instruction | 0 | 82,453 | 16 | 164,906 |
Yes | output | 1 | 82,453 | 16 | 164,907 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209
Submitted Solution:
```
H,W=map(int, input().split())
S = tuple(input().rstrip() for _ in range(H))
a=0
d=[(1,0),(-1,0),(0,1),(0,-1)]
lity=[[0 for i in range(W)] for j in range(H)]
lity[0][0]=1
def roop()->None:
p=[(0,0)]
while p:
x,y=p.pop(0)
for dx,dy in d:
if 0<=x+dx<H and 0<=y+dy<W and S[x+dx][y+dy]=='.' and lity[x+dx][y+dy]==0:
p.append((x+dx,y+dy))
lity[x+dx][y+dy]=lity[x][y]+1
roop()
white=sum(t.count(".") for t in S)
x=lity[-1][-1]
ans = white - x
if 0<x:
print(ans)
else:
print(-1)
``` | instruction | 0 | 82,454 | 16 | 164,908 |
Yes | output | 1 | 82,454 | 16 | 164,909 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209
Submitted Solution:
```
# https://atcoder.jp/contests/abc088/tasks/abc088_d
H, W = map(int, input().split())
s = [input() for _ in range(H)]
d = [[-1 for _ in range(W)] for _ in range(W)]
# 0,0 to h-1, w-1
d[0][0] = 0
queue = []
queue.append((0, 0))
while len(queue) > 0:
p = queue.pop(0)
y, x = p[0], p[1]
dx4 = [0, 0, 1, -1]
dy4 = [1, -1, 0, 0]
for dx, dy in zip(dx4, dy4):
next_y = y + dy
next_x = x + dx
if 0 <= next_y < H and 0 <= next_x < W and s[next_y][next_x] != "#" and d[next_y][next_x] == -1:
d[next_y][next_x] = d[y][x] + 1
queue.append((next_y, next_x))
count = 0
for l in s:
count += l.count(".")
print(count - d[H-1][W-1] - 1)
# [print(l) for l in s]
# [print(l) for l in d]
``` | instruction | 0 | 82,455 | 16 | 164,910 |
No | output | 1 | 82,455 | 16 | 164,911 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209
Submitted Solution:
```
from collections import deque
h,w=map(lambda x: int(x), input().split())
s=[[] for _ in range(h)]
black=0
for i in range(h):
s[i]=input()
black+=s[i].count('#')
dist=[[-1 for _ in range(w)] for _ in range(h)]
que = deque([(0, 0)])
dist[0][0]=0
while que:
y, x=que.popleft()
for y1, x1 in [(y-1, x), (y+1, x), (y, x-1), (y, x+1)]:
if y1<0 or y1>h-1 or x1<0 or x1>w-1:
continue
if s[y1][x1]=='#':
continue
if dist[y1][x1]!=-1:
continue
dist[y1][x1]=dist[y][x]+1
que.append((y1,x1))
print(h*w-black-dist[h-1][w-1]-1)
``` | instruction | 0 | 82,456 | 16 | 164,912 |
No | output | 1 | 82,456 | 16 | 164,913 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209
Submitted Solution:
```
#すでに調べているか確認
def check(i, j, check, s):
if s[i][j] == "#":
return 0
else:
for a in range(len(check)):
if check[a][0] == i and check[a][1] == j:
return 0
else:
return 1
H, W = map(int, input().split())
s = [0] * W
t = [[0 for i in range(W)] for j in range(H)]
for i in range(H):
s[i] = list(input())
#各マス目の大きさが入っている
t[0][0] = 1
#キュー
queue = [[0,0]]
#調べたマスのリスト
checklist = []
z = 1
while(1):
if not queue:
z = 0
break
#キューから取り出す
i = queue[0][0]
j = queue[0][1]
del queue[0]
#ゴールか判断する
if i == H-1 and j == W-1:
break
checklist.append([i, j])
if i > 0:
if check(i-1, j, checklist, s) == 1:
queue.append([i-1, j])
t[i-1][j] = t[i][j] + 1
if j > 0:
if check(i, j-1, checklist, s) == 1:
queue.append([i, j-1])
t[i][j-1] = t[i][j] + 1
if i < H - 1:
if check(i+1, j, checklist, s) == 1:
queue.append([i+1, j])
t[i+1][j] = t[i][j] + 1
if j < W - 1:
if check(i, j+1, checklist, s) == 1:
queue.append([i, j+1])
t[i][j+1] = t[i][j] + 1
point = 0
if z = 1:
for i in range(W):
for j in range(H):
if s[i][j] == '.':
point = point + 1
print(point - t[H-1][W-1])
else:
print(-1)
``` | instruction | 0 | 82,457 | 16 | 164,914 |
No | output | 1 | 82,457 | 16 | 164,915 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Constraints
* H is an integer between 2 and 50 (inclusive).
* W is an integer between 2 and 50 (inclusive).
* s_{i, j} is `.` or `#` (1 \leq i \leq H, 1 \leq j \leq W).
* s_{1, 1} and s_{H, W} are `.`.
Input
Input is given from Standard Input in the following format:
H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}
Output
Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.
Examples
Input
3 3
..#
#..
...
Output
2
Input
3 3
..#
..
...
Output
2
Input
10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................
Output
209
Submitted Solution:
```
def grid_repainting(H: int, W: int, S: int) -> int:
# ルート探索用の行列。
# R[h][w] は (0, 0) -> (h, w) の最短距離になる。
INF = float('inf')
R = [[INF] * W for _ in range(H)]
R[0][0] = 1
black_num = 0
for h in range(H):
for w in range(W):
if S[h][w] == '#':
# 黒いマス目は無視
black_num += 1
continue
if w > 0:
R[h][w] = min(R[h][w], R[h][w - 1] + 1)
if h > 0:
R[h][w] = min(R[h][w], R[h - 1][w] + 1)
if R[H - 1][W - 1] is INF:
return - 1
white_num = H * W - black_num
# R[H-1][W-1] は (0, 0) -> (H-1, W-1) に至るために必要な
# 最小のマス数になっている。これ以外の全部の白ますは黒マスに変
# えていいので、それが最大スコア。
return white_num - R[H-1][W-1]
if __name__ == "__main__":
H = 0
H, W = map(int, input().split())
S = [input() for _ in range(H)]
ans = grid_repainting(H, W, S)
print(ans)
``` | instruction | 0 | 82,458 | 16 | 164,916 |
No | output | 1 | 82,458 | 16 | 164,917 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares in a row, numbered 1 through N from left to right. Snuke and Rng are playing a board game using these squares, described below:
1. First, Snuke writes an integer into each square.
2. Each of the two players possesses one piece. Snuke places his piece onto square 1, and Rng places his onto square 2.
3. The player whose piece is to the left of the opponent's, moves his piece. The destination must be a square to the right of the square where the piece is currently placed, and must not be a square where the opponent's piece is placed.
4. Repeat step 3. When the pieces cannot be moved any more, the game ends.
5. The score of each player is calculated as the sum of the integers written in the squares where the player has placed his piece before the end of the game.
Snuke has already written an integer A_i into square i (1≦i≦N-1), but not into square N yet. He has decided to calculate for each of M integers X_1,X_2,...,X_M, if he writes it into square N and the game is played, what the value "(Snuke's score) - (Rng's score)" will be. Here, it is assumed that each player moves his piece to maximize the value "(the player's score) - (the opponent's score)".
Constraints
* 3≦N≦200,000
* 0≦A_i≦10^6
* The sum of all A_i is at most 10^6.
* 1≦M≦200,000
* 0≦X_i≦10^9
Input
The input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{N-1}
M
X_1
X_2
:
X_M
Output
For each of the M integers X_1, ..., X_M, print the value "(Snuke's score) - (Rng's score)" if it is written into square N, one per line.
Examples
Input
5
2 7 1 8
1
2
Output
0
Input
9
2 0 1 6 1 1 2 6
5
2016
1
1
2
6
Output
2001
6
6
7
7
Submitted Solution:
```
from sys import exit, setrecursionlimit
from functools import reduce
from itertools import *
from collections import defaultdict
from bisect import bisect
def read():
return int(input())
def reads():
return [int(x) for x in input().split()]
setrecursionlimit(1000000)
INF = 10**8
N = read()
A = reads()
assert(read() == 1)
A.append(read())
psum = [0] * (N+1)
for i in range(N):
psum[i+1] = psum[i] + A[i]
def isum(i, j):
return psum[j] - psum[i]
s = [0] * N
s[N-2] = A[N-2] - A[N-1]
for i in range(N-3, -1, -1):
s[i] = A[i] - min(isum(i+1,j) + s[j] for j in range(i+1,N-1))
print(s[0])
# def solve(p, i):
# s = (p, i)
# if s in d:
# return d[s]
#
# if p == "S":
# res = 0
# for j in range(i):
# res = max(res, solve("R",j) - A[i] + sum(j+2,i+1))
# else:
# res = INF
# for j in range(i):
# res = min(res, solve("S",j) + A[i] - sum(j+2,i+1))
#
# d[s] = res
# return res
# result = max(solve("S",N-2), solve("R",N-2))
# print(result)
# print(d)
``` | instruction | 0 | 82,479 | 16 | 164,958 |
No | output | 1 | 82,479 | 16 | 164,959 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.