message stringlengths 2 44.5k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 42 109k | cluster float64 5 5 | __index_level_0__ int64 84 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given an array a of length n, find another array, b, of length n such that:
* for each i (1 ≤ i ≤ n) MEX(\\{b_1, b_2, …, b_i\})=a_i.
The MEX of a set of integers is the smallest non-negative integer that doesn't belong to this set.
If such array doesn't exist, determine this.
Input
The first line contains an integer n (1 ≤ n ≤ 10^5) — the length of the array a.
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ i) — the elements of the array a. It's guaranteed that a_i ≤ a_{i+1} for 1≤ i < n.
Output
If there's no such array, print a single line containing -1.
Otherwise, print a single line containing n integers b_1, b_2, …, b_n (0 ≤ b_i ≤ 10^6)
If there are multiple answers, print any.
Examples
Input
3
1 2 3
Output
0 1 2
Input
4
0 0 0 2
Output
1 3 4 0
Input
3
1 1 3
Output
0 2 1
Note
In the second test case, other answers like [1,1,1,0], for example, are valid.
Submitted Solution:
```
import sys
def minp():
return sys.stdin.readline().strip()
def mint():
return int(minp())
def mints():
return map(int, minp().split())
def check(a, b):
n = len(a)
bb = [False]*(n+1)
c = [0]*n
j = 0
z = 0
for i in a:
if i <= n:
bb[i] = True
while bb[j]:
j += 1
if b[z] != j:
return False
z += 1
return True
def solve():
n = mint()
a = list(mints())
b = [None]*n
c = [False]*(n+1)
for i in range(1,n):
if a[i] != a[i-1]:
b[i] = a[i-1]
if a[i-1] <= n:
c[a[i-1]] = True
if a[-1] <= n:
c[a[-1]] = True
if a[0] != 0:
b[0] = 0
c[0] = True
#print(b)
#print(c)
j = 0
for i in range(n):
if b[i] is None:
while c[j]:
j += 1
b[i] = j
c[j] = True
#print(b)
#print(check(b,a))
if check(b,a):
print(' '.join(map(str,b)))
else:
print(-1)
#for i in range(mint()):
solve()
``` | instruction | 0 | 6,757 | 5 | 13,514 |
Yes | output | 1 | 6,757 | 5 | 13,515 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given an array a of length n, find another array, b, of length n such that:
* for each i (1 ≤ i ≤ n) MEX(\\{b_1, b_2, …, b_i\})=a_i.
The MEX of a set of integers is the smallest non-negative integer that doesn't belong to this set.
If such array doesn't exist, determine this.
Input
The first line contains an integer n (1 ≤ n ≤ 10^5) — the length of the array a.
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ i) — the elements of the array a. It's guaranteed that a_i ≤ a_{i+1} for 1≤ i < n.
Output
If there's no such array, print a single line containing -1.
Otherwise, print a single line containing n integers b_1, b_2, …, b_n (0 ≤ b_i ≤ 10^6)
If there are multiple answers, print any.
Examples
Input
3
1 2 3
Output
0 1 2
Input
4
0 0 0 2
Output
1 3 4 0
Input
3
1 1 3
Output
0 2 1
Note
In the second test case, other answers like [1,1,1,0], for example, are valid.
Submitted Solution:
```
n=int(input())
s=input().split()
flag=0
for j in range(n):
s[j]=int(s[j])
if s[j]>j+1:
flag=1
if flag==1:
print(-1)
else:
if s[0]==1:
for j in range (n-1):
if s[j+1]-s[j]>1:
flag=1
break
if flag==1:
print(-1)
else:
for j in range (n):
print(s[j]-1,end="")
else:
for j in range (n):
if s[j]>=3:
rr=j
else:
rr=0
if rr:
for j in range (rr,n-1):
if s[j+1]-s[j]>1:
flag=1
break
for j in range (n):
if s[j]==1:
flag=1
if flag==1:
print(-1)
else:
for j in range (n):
if s[j]==0:
print("1 ",end="")
elif s[j]==2:
print("0 ",end="")
else:
print(s[j]-1,end="")
``` | instruction | 0 | 6,758 | 5 | 13,516 |
No | output | 1 | 6,758 | 5 | 13,517 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given an array a of length n, find another array, b, of length n such that:
* for each i (1 ≤ i ≤ n) MEX(\\{b_1, b_2, …, b_i\})=a_i.
The MEX of a set of integers is the smallest non-negative integer that doesn't belong to this set.
If such array doesn't exist, determine this.
Input
The first line contains an integer n (1 ≤ n ≤ 10^5) — the length of the array a.
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ i) — the elements of the array a. It's guaranteed that a_i ≤ a_{i+1} for 1≤ i < n.
Output
If there's no such array, print a single line containing -1.
Otherwise, print a single line containing n integers b_1, b_2, …, b_n (0 ≤ b_i ≤ 10^6)
If there are multiple answers, print any.
Examples
Input
3
1 2 3
Output
0 1 2
Input
4
0 0 0 2
Output
1 3 4 0
Input
3
1 1 3
Output
0 2 1
Note
In the second test case, other answers like [1,1,1,0], for example, are valid.
Submitted Solution:
```
################om namh shivay##################37
###############(BHOLE KI FAUJ KREGI MAUJ)############37
from sys import stdin,stdout
import math,queue,heapq
fastinput=stdin.readline
fastout=stdout.write
t=1
while t:
t-=1
n=int(fastinput())
#n,m=map(int,fastinput().split())
#a=[0]+list(map(int,fastinput().split()))
b=list(map(int,fastinput().split()))
#matrix=[list(map(int,fastinput().split())) for _ in range(n)]
dubplicate=[]
ans=[]
j=1
if b[0]==0:
ans.append(1)
elif b[0]==1:
ans.append(0)
else:
print(-1)
exit()
flag=False
for i in range(1,n):
if b[i]==b[i-1]:
ans.append(ans[-1])
dubplicate.append(i)
else:
if (b[i]-b[i-1]-2)<=len(dubplicate):
ans.append(b[i-1])
x=b[i]-b[i-1]-1
j=1
while dubplicate and x>=j:
ans[dubplicate.pop()]=b[i-1]+j
j+=1
else:
flag=True
break
if flag:
print(-1)
else:
print(*ans)
``` | instruction | 0 | 6,759 | 5 | 13,518 |
No | output | 1 | 6,759 | 5 | 13,519 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given an array a of length n, find another array, b, of length n such that:
* for each i (1 ≤ i ≤ n) MEX(\\{b_1, b_2, …, b_i\})=a_i.
The MEX of a set of integers is the smallest non-negative integer that doesn't belong to this set.
If such array doesn't exist, determine this.
Input
The first line contains an integer n (1 ≤ n ≤ 10^5) — the length of the array a.
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ i) — the elements of the array a. It's guaranteed that a_i ≤ a_{i+1} for 1≤ i < n.
Output
If there's no such array, print a single line containing -1.
Otherwise, print a single line containing n integers b_1, b_2, …, b_n (0 ≤ b_i ≤ 10^6)
If there are multiple answers, print any.
Examples
Input
3
1 2 3
Output
0 1 2
Input
4
0 0 0 2
Output
1 3 4 0
Input
3
1 1 3
Output
0 2 1
Note
In the second test case, other answers like [1,1,1,0], for example, are valid.
Submitted Solution:
```
n = int(input())
l = list(map(int,input().split()))
for i in range(n):
print(l[i]+1,end=' ')
``` | instruction | 0 | 6,760 | 5 | 13,520 |
No | output | 1 | 6,760 | 5 | 13,521 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7 | instruction | 0 | 7,282 | 5 | 14,564 |
"Correct Solution:
```
import sys
input = sys.stdin.readline
N,K=map(int,input().split())
A=[int(input()) for i in range(N)]
def seg_function(x,y): # Segment treeで扱うfunction
return max(x,y)
seg_el=1<<((300000).bit_length()) # Segment treeの台の要素数
SEG=[0]*(2*seg_el) # 1-indexedなので、要素数2*seg_el.Segment treeの初期値で初期化
def update(n,x,seg_el): # A[n]をxに更新
i=n+seg_el
SEG[i]=max(SEG[i],x)
i>>=1 # 子ノードへ
while i!=0:
SEG[i]=seg_function(SEG[i*2],SEG[i*2+1])
i>>=1
def getvalues(l,r): # 区間[l,r)に関するseg_functionを調べる
L=l+seg_el
R=r+seg_el
ANS=0
while L<R:
if L & 1:
ANS=seg_function(ANS , SEG[L])
L+=1
if R & 1:
R-=1
ANS=seg_function(ANS , SEG[R])
L>>=1
R>>=1
return ANS
for a in A:
MAX=getvalues(max(0,a-K),min(300001,a+K+1))
update(a,MAX+1,seg_el)
print(SEG[1])
``` | output | 1 | 7,282 | 5 | 14,565 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7 | instruction | 0 | 7,283 | 5 | 14,566 |
"Correct Solution:
```
import sys
read = sys.stdin.read
readline = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 8)
INF = float('inf')
MOD = 10 ** 9 + 7
class SegTree:
def __init__(self, init_val, segfunc, ide_ele):
n = len(init_val)
self.segfunc = segfunc
self.ide_ele = ide_ele
self.num = 1 << (n - 1).bit_length()
self.tree = [ide_ele] * 2 * self.num
for i in range(n):
self.tree[self.num + i] = init_val[i]
for i in range(self.num - 1, 0, -1):
self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])
def update(self, k, x):
k += self.num
self.tree[k] = x
while k > 1:
self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
k >>= 1
def query(self, l, r):
res = self.ide_ele
l += self.num
r += self.num
while l < r:
if l & 1:
res = self.segfunc(res, self.tree[l])
l += 1
if r & 1:
res = self.segfunc(res, self.tree[r - 1])
l >>= 1
r >>= 1
return res
def segfunc(x, y):
return max(x, y)
def main():
N, K = map(int, readline().split())
A = list(int(readline()) for _ in range(N))
Amax = max(A)
dp = [0] * (Amax + 1)
ide_ele = -float('inf')
segtree = SegTree(dp, segfunc, ide_ele)
for a in A:
l = max(0, a - K)
r = min(Amax, a + K)
L = segtree.query(l, r + 1)
segtree.update(a, L + 1)
ans = segtree.query(0, Amax + 1)
print(ans)
if __name__ == '__main__':
main()
``` | output | 1 | 7,283 | 5 | 14,567 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7 | instruction | 0 | 7,284 | 5 | 14,568 |
"Correct Solution:
```
class Segment_Tree():
"""
このプログラム内は1-index
"""
def __init__(self,L,calc,unit):
"""calcを演算とするリストLのSegment Treeを作成
calc:演算(2変数関数,モノイド)
unit:モノイドcalcの単位元 (xe=ex=xを満たすe)
"""
self.calc=calc
self.unit=unit
N=len(L)
d=max(1,(N-1).bit_length())
k=1<<d
self.data=[unit]*k+L+[unit]*(k-len(L))
self.N=k
self.depth=d
for i in range(k-1,0,-1):
self.data[i]=calc(self.data[i<<1],self.data[i<<1|1])
def get(self,k,index=1):
"""第k要素を取得
"""
assert 0<=k-index<self.N,"添字が範囲外"
return self.data[k-index+self.N]
def update(self,k,x,index=1):
"""第k要素をxに変え,更新を行う.
k:数列の要素
x:更新後の値
"""
assert 0<=k-index<self.N,"添字が範囲外"
m=(k-index)+self.N
self.data[m]=x
while m>1:
m>>=1
self.data[m]=self.calc(self.data[m<<1],self.data[m<<1|1])
def product(self,From,To,index=1,left_closed=True,right_closed=True):
L=(From-index)+self.N+(not left_closed)
R=(To-index)+self.N+(right_closed)
vL=self.unit
vR=self.unit
while L<R:
if L&1:
vL=self.calc(vL,self.data[L])
L+=1
if R&1:
R-=1
vR=self.calc(self.data[R],vR)
L>>=1
R>>=1
return self.calc(vL,vR)
def all_prod(self):
return self.data[1]
#================================================
N,K=map(int,input().split())
A=[0]*N
for i in range(N):
A[i]=int(input())
T=max(A)
S=Segment_Tree([0]*(T+1),max,0)
DP=[0]*N
for i in range(N-1,-1,-1):
X=S.product(max(0,A[i]-K),min(T,A[i]+K),0)
DP[i]=X+1
S.update(A[i],X+1,0)
print(max(DP))
``` | output | 1 | 7,284 | 5 | 14,569 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7 | instruction | 0 | 7,285 | 5 | 14,570 |
"Correct Solution:
```
class SegTree:
X_unit = 0
X_f = max
def __init__(self, N):
self.N = N
self.X = [self.X_unit] * (N + N)
def build(self, seq):
for i, x in enumerate(seq, self.N):
self.X[i] = x
for i in range(self.N - 1, 0, -1):
self.X[i] = self.X_f(self.X[i << 1], self.X[i << 1 | 1])
def set_val(self, i, x):
i += self.N
self.X[i] = x
while i > 1:
i >>= 1
self.X[i] = self.X_f(self.X[i << 1], self.X[i << 1 | 1])
def fold(self, L, R):
L += self.N
R += self.N
vL = self.X_unit
vR = self.X_unit
while L < R:
if L & 1:
vL = self.X_f(vL, self.X[L])
L += 1
if R & 1:
R -= 1
vR = self.X_f(self.X[R], vR)
L >>= 1
R >>= 1
return self.X_f(vL, vR)
n,k = map(int,input().split())
seg = SegTree(300001)
# a = [0]*n
# seg.build(a)
for i in range(n):
a = int(input())
seg.set_val(a,seg.fold(max(0,a-k),min(300001,a+k+1)) + 1)
print(seg.fold(0,300001))
``` | output | 1 | 7,285 | 5 | 14,571 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7 | instruction | 0 | 7,286 | 5 | 14,572 |
"Correct Solution:
```
class SegmentTree:
def __init__(self, data, default=0, func=max):
self._default = default
self._func = func
self._len = len(data)
self._size = _size = 1 << (self._len - 1).bit_length()
self.data = [default] * (2 * _size)
self.data[_size:_size + self._len] = data
for i in reversed(range(_size)):
self.data[i] = func(self.data[i + i], self.data[i + i + 1])
def __delitem__(self, idx):
self[idx] = self._default
def __getitem__(self, idx):
return self.data[idx + self._size]
def __setitem__(self, idx, value):
idx += self._size
self.data[idx] = value
idx >>= 1
while idx:
self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
idx >>= 1
def __len__(self):
return self._len
def query(self, start, stop):
start += self._size
stop += self._size
res_left = res_right = self._default
while start < stop:
if start & 1:
res_left = self._func(res_left, self.data[start])
start += 1
if stop & 1:
stop -= 1
res_right = self._func(self.data[stop], res_right)
start >>= 1
stop >>= 1
return self._func(res_left, res_right)
def __repr__(self):
return "SegmentTree({0})".format(self.data)
import sys
input=sys.stdin.readline
n,k=map(int,input().split())
M=1048576
s=SegmentTree([0]*M)
for i in range(n):
a=int(input())
s[a]=1+s.query(max(a-k,0),a+k+1)
print(s.query(0,M))
``` | output | 1 | 7,286 | 5 | 14,573 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7 | instruction | 0 | 7,287 | 5 | 14,574 |
"Correct Solution:
```
class SegmentTree:
_op = None
_e = None
_size = None
_offset = None
_data = None
def __init__(self, size, op, e):
self._op = op
self._e = e
self._size = size
t = 1
while t < size:
t *= 2
self._offset = t - 1
self._data = [0] * (t * 2 - 1)
def build(self, iterable):
op = self._op
data = self._data
data[self._offset:self._offset + self._size] = iterable
for i in range(self._offset - 1, -1, -1):
data[i] = op(data[i * 2 + 1], data[i * 2 + 2])
def update(self, index, value):
op = self._op
data = self._data
i = self._offset + index
data[i] = value
while i >= 1:
i = (i - 1) // 2
data[i] = op(data[i * 2 + 1], data[i * 2 + 2])
def query(self, start, stop):
def iter_segments(data, l, r):
while l < r:
if l & 1 == 0:
yield data[l]
if r & 1 == 0:
yield data[r - 1]
l = l // 2
r = (r - 1) // 2
op = self._op
it = iter_segments(self._data, start + self._offset,
stop + self._offset)
result = self._e
for v in it:
result = op(result, v)
return result
N, K, *A = map(int, open(0).read().split())
st = SegmentTree(300000 + 1, max, 0)
for a in A:
st.update(a, st.query(max(a - K, 0), min(a + K + 1, 300000 + 1)) + 1)
print(st.query(0, 300000 + 1))
``` | output | 1 | 7,287 | 5 | 14,575 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7 | instruction | 0 | 7,288 | 5 | 14,576 |
"Correct Solution:
```
class Segtree():
def __init__(self, n):
self.num = 1 << (n - 1).bit_length()
self.tree = [0] * 2 * self.num
for i in range(self.num - 1, 0, -1):
self.tree[i] = max(self.tree[2 * i], self.tree[2 * i + 1])
def update(self, k, x):
k += self.num
self.tree[k] = x
while k > 1:
self.tree[k >> 1] = max(self.tree[k], self.tree[k ^ 1])
k >>= 1
def query(self, l, r):
res = 0
l, r = l + self.num, r + self.num
while l < r:
if l & 1:
res = max(res, self.tree[l])
l += 1
if r & 1:
res = max(res, self.tree[r - 1])
l, r = l >> 1, r >> 1
return res
n, k = map(int, input().split())
a = [int(input()) for _ in range(n)]
a_max = max(a) + 1
seg_dp = Segtree(a_max)
for ai in a:
tmp = seg_dp.query(max(ai - k, 0), min(ai + k + 1, a_max))
seg_dp.update(ai, tmp + 1)
print(max(seg_dp.tree))
``` | output | 1 | 7,288 | 5 | 14,577 |
Provide a correct Python 3 solution for this coding contest problem.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7 | instruction | 0 | 7,289 | 5 | 14,578 |
"Correct Solution:
```
class SegTree: # モノイドに対して適用可能、Nが2冪でなくても良い
def __init__(self,N,seg_func,unit):
self.N = 1 << (N-1).bit_length()
self.func = seg_func
self.unit = unit
self.tree = [self.unit]*(2*self.N)
def build(self,init_value): # 初期値を[N,2N)に格納
for i in range(len(init_value)):
self.tree[i+self.N] = init_value[i]
for i in range(self.N-1,0,-1):
self.tree[i] = self.func(self.tree[i << 1],self.tree[i << 1 | 1])
def set_val(self,i,x): # i番目(0-index)の値をxに変更
i += self.N
self.tree[i] = x
i >>= 1
while i:
self.tree[i] = self.func(self.tree[i << 1],self.tree[i << 1 | 1])
i >>= 1
def fold(self,L,R): # [L,R)の区間取得
L += self.N
R += self.N
vL = self.unit
vR = self.unit
while L < R:
if L & 1:
vL = self.func(vL,self.tree[L])
L += 1
if R & 1:
R -= 1
vR = self.func(self.tree[R],vR)
L >>= 1
R >>= 1
return self.func(vL,vR)
import sys
sys.setrecursionlimit(10**7)
def I(): return int(sys.stdin.readline().rstrip())
def MI(): return map(int,sys.stdin.readline().rstrip().split())
N,K = MI()
ST = SegTree(300001,max,0)
# dp[i][j] = A1~Ai を用いて、末尾が j になり条件を満たす数列の長さの最大値
# dp[i][j] = 1+max(dp[i-1][Ai-K],…,dp[i-1][Ai+K]) if j == Ai else dp[i-1][j]
# この dp をセグメントツリーにのせて考える
for i in range(N):
a = I()
ST.set_val(a,1+ST.fold(max(0,a-K),min(300000,a+K)+1))
print(ST.fold(0,300001))
``` | output | 1 | 7,289 | 5 | 14,579 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7
Submitted Solution:
```
#import sys
#import numpy as np
import math
#from fractions import Fraction
import itertools
from collections import deque
from collections import Counter
import heapq
from fractions import gcd
#input=sys.stdin.readline
#import bisect
from fractions import gcd
n,k=map(int,input().split())
inf = 0
m=300001
num_min =2**(m-1).bit_length()
dat=[inf]*(2*num_min-1)
#初期化
#親のノード(n-1)//2
#子のノード2n+1,2n+2
def segfunc(x,y):
return max(x,y)
def update(i,x):
i+=num_min-1
dat[i]=x
while i>0:
i=(i-1)//2
dat[i]=segfunc(dat[2*i+1],dat[2*i+2])
def query(a,b): #半開区間、[a,b)の最小値
if b<=a:
return inf
res=inf
a += num_min-1
b += num_min-2
while b-a>1:
if a&1==0:
res = segfunc(res,dat[a])
if b&1==1:
res = segfunc(res,dat[b])
b-=1
a=a//2
b=(b-1)//2
if a==b:
res = segfunc(res,dat[a])
else:
res=segfunc(segfunc(res,dat[a]),dat[b])
return res
ans=0
for i in range(n):
x=int(input())
l=max(0,x-k)
r=min(300000,x+k)
tmp=query(l,r+1)+1
ans=max(tmp,ans)
update(x,tmp)
print(ans)
``` | instruction | 0 | 7,290 | 5 | 14,580 |
Yes | output | 1 | 7,290 | 5 | 14,581 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7
Submitted Solution:
```
import sys, math
import io, os
#data = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
from bisect import bisect_left as bl, bisect_right as br, insort
from heapq import heapify, heappush, heappop
from collections import defaultdict as dd, deque, Counter
# from itertools import permutations,combinations
def data(): return sys.stdin.readline().strip()
def mdata(): return list(map(int, data().split()))
def outl(var): sys.stdout.write('\n'.join(map(str, var)) + '\n')
def out(var): sys.stdout.write(str(var) + '\n')
from decimal import Decimal
# from fractions import Fraction
# sys.setrecursionlimit(100000)
mod = 998244353
INF=float('inf')
def construct_sum(segtree,a,n,func=max):
for i in range(n):
segtree[n + i] = a[i]
for i in range(n - 1, 0, -1):
segtree[i] = func(segtree[2 * i], segtree[2 * i + 1])
def update(pos, x, func=max):
pos += n-1
segtree[pos] = x
while (pos>1):
pos>>=1
segtree[pos] = func(segtree[2 * pos], segtree[2 * pos + 1])
def get(l, r, func=max):
l += n-1
r += n-1
s = 0
while (l <= r):
if l & 1:
s = func(segtree[l],s)
l+=1
if (r+1) & 1:
s = func(segtree[r],s)
r-=1
l >>= 1
r >>= 1
return s
n,k=mdata()
a=[int(data()) for i in range(n)]
n=max(a)+1
segtree = [0]*(2*n)
construct_sum(segtree,[0]*n,n)
ans=0
for i in a:
a1=get(max(i-k+1,1),min(i+k+1,n))+1
update(i+1,a1)
ans=max(ans,a1)
out(ans)
``` | instruction | 0 | 7,291 | 5 | 14,582 |
Yes | output | 1 | 7,291 | 5 | 14,583 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7
Submitted Solution:
```
import typing
class SegTree:
def __init__(self,
op: typing.Callable[[typing.Any, typing.Any], typing.Any],
e: typing.Any,
v: typing.Union[int, typing.List[typing.Any]]):
self._op = op
self._e = e
if isinstance(v, int):
v = [e] * v
self._n = len(v)
self._log = self._ceil_pow2(self._n)
self._size = 1 << self._log
self._d = [e] * (2 * self._size)
for i in range(self._n):
self._d[self._size + i] = v[i]
for i in range(self._size - 1, 0, -1):
self._update(i)
def set(self, p: int, x: typing.Any) -> None:
assert 0 <= p < self._n
p += self._size
self._d[p] = x
for i in range(1, self._log + 1):
self._update(p >> i)
def prod(self, left: int, right: int) -> typing.Any:
assert 0 <= left <= right <= self._n
sml = self._e
smr = self._e
left += self._size
right += self._size
while left < right:
if left & 1:
sml = self._op(sml, self._d[left])
left += 1
if right & 1:
right -= 1
smr = self._op(self._d[right], smr)
left >>= 1
right >>= 1
return self._op(sml, smr)
def all_prod(self) -> typing.Any:
return self._d[1]
def _update(self, k: int) -> None:
self._d[k] = self._op(self._d[2 * k], self._d[2 * k + 1])
def _ceil_pow2(self, n: int) -> int:
x = 0
while (1 << x) < n:
x += 1
return x
N, K = map(int, input().split())
A = list(int(input()) for _ in range(N))
max_A = max(A)
seg = SegTree(max, -1, [0]*(max_A+1))
for v in A:
l = max(0, v-K)
r = min(max_A, v+K)
seg.set(v, seg.prod(l, r+1)+1)
print(seg.all_prod())
``` | instruction | 0 | 7,292 | 5 | 14,584 |
Yes | output | 1 | 7,292 | 5 | 14,585 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7
Submitted Solution:
```
class SegTree:
X_unit = 0
X_f = max
def __init__(self, N):
self.N = N
self.X = [self.X_unit] * (N + N)
def build(self, seq):
for i, x in enumerate(seq, self.N):
self.X[i] = x
for i in range(self.N - 1, 0, -1):
self.X[i] = self.X_f(self.X[i << 1], self.X[i << 1 | 1])
def set_val(self, i, x):
i += self.N
self.X[i] = x
while i > 1:
i >>= 1
self.X[i] = self.X_f(self.X[i << 1], self.X[i << 1 | 1])
def fold(self, L, R):
L += self.N
R += self.N
vL = self.X_unit
vR = self.X_unit
while L < R:
if L & 1:
vL = self.X_f(vL, self.X[L])
L += 1
if R & 1:
R -= 1
vR = self.X_f(self.X[R], vR)
L >>= 1
R >>= 1
return self.X_f(vL, vR)
lim = 4*10**5
n,k = map(int,input().split())
seg = SegTree(lim)
# a = [0]*n
# seg.build(a)
for i in range(n):
a = int(input())
seg.set_val(a,seg.fold(max(0,a-k),min(lim,a+k+1)) + 1)
print(seg.fold(0,lim))
``` | instruction | 0 | 7,293 | 5 | 14,586 |
Yes | output | 1 | 7,293 | 5 | 14,587 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7
Submitted Solution:
```
#!/usr/bin/env python
import os
import sys
from io import BytesIO, IOBase
def ii(): return int(input())
def si(): return input()
def mi(): return map(int,input().strip().split(" "))
def li(): return list(mi())
def solve():
n, k = mi()
stack = []
for i in range(n):
z = ii()
if not stack:
stack.append(z)
else:
d = abs(stack[-1] - z)
if d <= k:
stack.append(z)
return len(stack)
def main():
# pass
print(solve())
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# endregion
if __name__ == "__main__":
main()
``` | instruction | 0 | 7,294 | 5 | 14,588 |
No | output | 1 | 7,294 | 5 | 14,589 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7
Submitted Solution:
```
class SegmentTree:
_op = None
_e = None
_size = None
_offset = None
_data = None
def __init__(self, size, op, e):
self._op = op
self._e = e
self._size = size
t = 1
while t < size:
t *= 2
self._offset = t - 1
self._data = [0] * (t * 2 - 1)
def build(self, iterable):
op = self._op
data = self._data
data[self._offset:self._offset + self._size] = iterable
for i in range(self._offset - 1, -1, -1):
data[i] = op(data[i * 2 + 1], data[i * 2 + 2])
def update(self, index, value):
op = self._op
data = self._data
i = self._offset + index
data[i] = value
while i >= 1:
i = (i - 1) // 2
data[i] = op(data[i * 2 + 1], data[i * 2 + 2])
def query(self, start, stop):
def iter_segments(data, l, r):
while l < r:
if l & 1 == 0:
yield data[l]
if r & 1 == 0:
yield data[r - 1]
l = l // 2
r = (r - 1) // 2
op = self._op
it = iter_segments(self._data, start + self._offset,
stop + self._offset)
result = self._e
for v in it:
result = op(result, v)
return result
N, K, *A = map(int, open(0).read().split())
st = SegmentTree(300000 + 1, max, 0)
for a in A:
st.update(a, st.query(max(a - K, 0), min(a + K + 1, 300000 + 1)) + 1)
print(st.query(0, 300000 + 1))
``` | instruction | 0 | 7,295 | 5 | 14,590 |
No | output | 1 | 7,295 | 5 | 14,591 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7
Submitted Solution:
```
import typing
def _ceil_pow2(n: int) -> int:
x = 0
while (1 << x) < n:
x += 1
return x
def _bsf(n: int) -> int:
x = 0
while n % 2 == 0:
x += 1
n //= 2
return x
class SegTree:
def __init__(self,
op: typing.Callable[[typing.Any, typing.Any], typing.Any],
e: typing.Any,
v: typing.Union[int, typing.List[typing.Any]]) -> None:
self._op = op
self._e = e
if isinstance(v, int):
v = [e] * v
self._n = len(v)
self._log = _ceil_pow2(self._n)
self._size = 1 << self._log
self._d = [e] * (2 * self._size)
for i in range(self._n):
self._d[self._size + i] = v[i]
for i in range(self._size - 1, 0, -1):
self._update(i)
def set(self, p: int, x: typing.Any) -> None:
assert 0 <= p < self._n
p += self._size
self._d[p] = x
for i in range(1, self._log + 1):
self._update(p >> i)
def get(self, p: int) -> typing.Any:
assert 0 <= p < self._n
return self._d[p + self._size]
def prod(self, left: int, right: int) -> typing.Any:
assert 0 <= left <= right <= self._n
sml = self._e
smr = self._e
left += self._size
right += self._size
while left < right:
if left & 1:
sml = self._op(sml, self._d[left])
left += 1
if right & 1:
right -= 1
smr = self._op(self._d[right], smr)
left >>= 1
right >>= 1
return self._op(sml, smr)
def all_prod(self) -> typing.Any:
return self._d[1]
def max_right(self, left: int,
f: typing.Callable[[typing.Any], bool]) -> int:
assert 0 <= left <= self._n
assert f(self._e)
if left == self._n:
return self._n
def _update(self, k: int) -> None:
self._d[k] = self._op(self._d[2 * k], self._d[2 * k + 1])
n, k, *A = map(int, open(0).read().split())
m = 303030
segtree = SegTree(op=max, e=0, v=m)
for a in A:
l, r = max(1, a-k), min(m, a+k+1)
segtree.set(a, segtree.prod(l, r)+1)
print(segtree.all_prod())
``` | instruction | 0 | 7,296 | 5 | 14,592 |
No | output | 1 | 7,296 | 5 | 14,593 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a sequence A_1, A_2, ..., A_N and an integer K.
Print the maximum possible length of a sequence B that satisfies the following conditions:
* B is a (not necessarily continuous) subsequence of A.
* For each pair of adjacents elements of B, the absolute difference of the elements is at most K.
Constraints
* 1 \leq N \leq 300,000
* 0 \leq A_i \leq 300,000
* 0 \leq K \leq 300,000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K
A_1
A_2
:
A_N
Output
Print the answer.
Example
Input
10 3
1
5
4
3
8
6
9
7
2
4
Output
7
Submitted Solution:
```
from math import ceil, log2
import sys
z=sys.stdin.readline
class SegTree:
ide_ele = 0
def __init__(self, init_val):
n = len(init_val)
self.num = 2**ceil(log2(n))
self.seg = [self.ide_ele] * (2 * self.num - 1)
def segfunc(self, x, y):
return max(x, y)
def update(self, k, x):
k += self.num - 1
self.seg[k] = x
while k:
k = (k - 1) // 2
self.seg[k] = self.segfunc(self.seg[k * 2 + 1], self.seg[k * 2 + 2])
def query(self, a, b, k, l, r):
if r <= a or b <= l:
return self.ide_ele
if a <= l and r <= b:
return self.seg[k]
else:
vl = self.query(a, b, k*2+1, l, (l+r)//2)
vr = self.query(a, b, k*2+2, (l+r)//2, r)
return self.segfunc(vl, vr)
n, k = map(int, z().split())
a = [int(z()) for _ in range(n)]
M=300001
st = SegTree([0]*M)
res = 0
for i in a:
min_a = max(i-k, 0)
max_a = min(i+k, M)
s = st.query(min_a, max_a+1, 0, 0, st.num)
st.update(i, max(s, 0)+1)
res = max(res, max(s, 0) + 1)
print(res)
``` | instruction | 0 | 7,297 | 5 | 14,594 |
No | output | 1 | 7,297 | 5 | 14,595 |
Provide a correct Python 3 solution for this coding contest problem.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70 | instruction | 0 | 7,302 | 5 | 14,604 |
"Correct Solution:
```
n,k,s = map(int, input().split())
if s < 10**9:
ans = [s+1] * n
else:
ans = [1]*n
ans[:k] = [s]*k
print(" ".join(map(str,ans)))
``` | output | 1 | 7,302 | 5 | 14,605 |
Provide a correct Python 3 solution for this coding contest problem.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70 | instruction | 0 | 7,303 | 5 | 14,606 |
"Correct Solution:
```
n, k, s= map(int,input().split())
if s == 10**9:
ans = [s]*k+[1]*(n-k)
else:
ans = [s]*k+[s+1]*(n-k)
print(*ans)
``` | output | 1 | 7,303 | 5 | 14,607 |
Provide a correct Python 3 solution for this coding contest problem.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70 | instruction | 0 | 7,304 | 5 | 14,608 |
"Correct Solution:
```
N,K,S=list(map(int, input().split()))
L=[0]*N
L[:K]=[S]*K
if S==10**9:
L[K:]=[1]*(N-K)
else:
L[K:]=[10**9]*(N-K)
print(*L)
``` | output | 1 | 7,304 | 5 | 14,609 |
Provide a correct Python 3 solution for this coding contest problem.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70 | instruction | 0 | 7,305 | 5 | 14,610 |
"Correct Solution:
```
N, K, S = map(int, open(0).read().split())
fill = 10 ** 9 - 1 if S == 10 ** 9 else 10 ** 9
ans = [S] * K + [fill] * (N - K)
print(*ans)
``` | output | 1 | 7,305 | 5 | 14,611 |
Provide a correct Python 3 solution for this coding contest problem.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70 | instruction | 0 | 7,306 | 5 | 14,612 |
"Correct Solution:
```
n, k, s = map(int, input().split())
a = [s] * k
b = [pow(10, 9) if not s == pow(10, 9) else 1] * (n - k)
print(" ".join(map(str, a + b)))
``` | output | 1 | 7,306 | 5 | 14,613 |
Provide a correct Python 3 solution for this coding contest problem.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70 | instruction | 0 | 7,307 | 5 | 14,614 |
"Correct Solution:
```
n, k, s = map(int, input().split())
if s == 10**9:
ans = [10**9]*k+[1]*(n-k)
else:
ans = [s]*k+[s+1]*(n-k)
print(*ans)
``` | output | 1 | 7,307 | 5 | 14,615 |
Provide a correct Python 3 solution for this coding contest problem.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70 | instruction | 0 | 7,308 | 5 | 14,616 |
"Correct Solution:
```
n,k,s=map(int,input().split())
a=[]
for i in range(k):
a.append(s)
for j in range(n-k):
a.append(s+1 if s==1 else s-1)
print(*a)
``` | output | 1 | 7,308 | 5 | 14,617 |
Provide a correct Python 3 solution for this coding contest problem.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70 | instruction | 0 | 7,309 | 5 | 14,618 |
"Correct Solution:
```
N,K,S = map(int,input().split())
w = 10**9
if S==w: w = 1
ans = [S]*K + [w]*(N-K)
print(*ans)
``` | output | 1 | 7,309 | 5 | 14,619 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70
Submitted Solution:
```
# C - Subarray Sum
n,k,s=map(int,input().split())
a=[]
a+=[s]*k
if s!=10**9:
a+=[s+1]*(n-k)
else:
a+=[1]*(n-k)
print(*a)
``` | instruction | 0 | 7,310 | 5 | 14,620 |
Yes | output | 1 | 7,310 | 5 | 14,621 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70
Submitted Solution:
```
N,K,S=map(int, input().split())
ans=[S]*K
if S!=10**9:
add=10**9
else:
add=10**9-1
ans=ans+[add]*(N-K)
print(*ans)
``` | instruction | 0 | 7,311 | 5 | 14,622 |
Yes | output | 1 | 7,311 | 5 | 14,623 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70
Submitted Solution:
```
N, K, S = map(int,input().split())
if S > N:
A = [S] * K + [1] * (N - K)
else:
A = [S] * K + [S + 1] * (N - K)
print(*A)
``` | instruction | 0 | 7,312 | 5 | 14,624 |
Yes | output | 1 | 7,312 | 5 | 14,625 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70
Submitted Solution:
```
N,K,S=map(int,input().split())
ans=[S]*K
if N-K>=S:
ans.extend([S+1]*(N-K))
else:
ans.extend([1]*(N-K))
print(*ans)
``` | instruction | 0 | 7,313 | 5 | 14,626 |
Yes | output | 1 | 7,313 | 5 | 14,627 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70
Submitted Solution:
```
#!/usr/bin/env python3
import sys
def solve(N: int, K: int, S: int):
if N==K:
print(' '.join([str(S) for _ in range(K)]))
else:
a = ' '.join([str(S) for _ in range(K)])
b = ' '.join([str(10**10) for _ in range(N-K-1)])
c = str(10**10)
print(a + ' ' + b + ' ' + c)
return
# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools (tips: You use the default template now. You can remove this line by using your custom template)
def main():
def iterate_tokens():
for line in sys.stdin:
for word in line.split():
yield word
tokens = iterate_tokens()
N = int(next(tokens)) # type: int
K = int(next(tokens)) # type: int
S = int(next(tokens)) # type: int
solve(N, K, S)
if __name__ == '__main__':
main()
``` | instruction | 0 | 7,314 | 5 | 14,628 |
No | output | 1 | 7,314 | 5 | 14,629 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70
Submitted Solution:
```
def main():
N, K, S = map(int, input().split())
MaxN = 10 ** 9
if S == MaxN:
A = [1] * N
elif K == N:
A = [S] * N
else:
A = [MaxN] * N
if K != 0 and K != N:
for i in range(K + 1):
if S % 2 == 0:
A[i] = S // 2
else:
if i % 2 == 0:
A[i] = S // 2 + 1
else:
A[i] = S // 2
print(" ".join(map(str, A)))
if __name__ == "__main__":
main()
``` | instruction | 0 | 7,315 | 5 | 14,630 |
No | output | 1 | 7,315 | 5 | 14,631 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70
Submitted Solution:
```
#template
from collections import Counter
def inputlist(): return [int(i) for i in input().split()]
#template
N,K,S = inputlist()
if N == 1 and K == 0 and S == 1:
print(2)
exit()
ans = []
for i in range(K):
ans.append(S)
for i in range(N-K):
ans.append(S-1)
print(*ans)
``` | instruction | 0 | 7,316 | 5 | 14,632 |
No | output | 1 | 7,316 | 5 | 14,633 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70
Submitted Solution:
```
import sys
input = sys.stdin.readline
ri = lambda: int(input())
rs = lambda: input().rstrip()
ril = lambda: list(map(int, input().split()))
rsl = lambda: input().rstrip().split()
ris = lambda n: [ri() for _ in range(n)]
rss = lambda n: [rs() for _ in range(n)]
rils = lambda n: [ril() for _ in range(n)]
rsls = lambda n: [rsl() for _ in range(n)]
n, k, s = ril()
res = [s] * k
if n - k == s:
res.extend([2] * (n - k))
else:
res.extend([1] * (n - k))
print(res)
``` | instruction | 0 | 7,317 | 5 | 14,634 |
No | output | 1 | 7,317 | 5 | 14,635 |
Provide a correct Python 3 solution for this coding contest problem.
Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7 | instruction | 0 | 7,445 | 5 | 14,890 |
"Correct Solution:
```
def parser(left, right):
if S[left] == '(' and S[right - 1] == ')':
cnt = 0
for i in range(left + 1, right - 1):
if S[i] == '(':
cnt += 1
elif S[i] == ')':
cnt -= 1
elif cnt == 0 and S[i] == '+':
return [max(x, y) for x, y in zip(parser(left + 1, i), parser(i + 1, right - 1))]
elif cnt == 0 and S[i] == '*':
return [min(x, y) for x, y in zip(parser(left + 1, i), parser(i + 1, right - 1))]
elif S[left] == '-':
return [2 - x for x in parser(left + 1, right)]
elif S[left] == 'P':
return [i // 9 % 3 for i in range(27)]
elif S[left] == 'Q':
return [i // 3 % 3 for i in range(27)]
elif S[left] == 'R':
return [i % 3 for i in range(27)]
else:
return [int(S[left]) for _ in range(27)]
while True:
S = input()
if S == '.':
break
print(parser(0, len(S)).count(2))
``` | output | 1 | 7,445 | 5 | 14,891 |
Provide a correct Python 3 solution for this coding contest problem.
Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7 | instruction | 0 | 7,446 | 5 | 14,892 |
"Correct Solution:
```
def parseParenthesis(formula):
pos = 0
count = 0
while True:
if formula[pos] == '(':
count += 1
elif formula[pos] == ')':
count -= 1
elif count == 1 and (formula[pos] == '+' or formula[pos] == '*'):
sign = formula[pos]
formulaA = formula[1:pos]
formulaB = formula[pos + 1: -1]
return formulaA, sign, formulaB
pos += 1
def eval_or(a, b):
if a == '0':
return b
elif a == '1':
return '1' if b == '0' else b
elif a == '2':
return '2'
def eval_and(a, b):
if a == '0':
return '0'
elif a == '1':
return '0' if b == '0' else '1'
elif a == '2':
return b
def eval_neg(a):
if a == '1':
return '1'
return '2' if a == '0' else '0'
def evaluate(formula, p, q, r):
if formula == '0' or formula == '1' or formula == '2':
return formula
if formula == 'P':
return p
if formula == 'Q':
return q
if formula == 'R':
return r
if formula[0] == '(':
formulaA, sign, formulaB = parseParenthesis(formula)
evalA = evaluate(formulaA, p, q, r)
evalB = evaluate(formulaB, p, q, r)
if sign == '+':
return eval_or(evalA, evalB)
elif sign == '*':
return eval_and(evalA, evalB)
elif formula[0] == '-':
return eval_neg(evaluate(formula[1:], p, q, r))
if __name__ == '__main__':
while True:
formula = input().strip()
if formula == '.':
break
count = 0
for p in range(3):
for q in range(3):
for r in range(3):
if evaluate(formula, str(p), str(q), str(r)) == '2':
count += 1
print(count)
``` | output | 1 | 7,446 | 5 | 14,893 |
Provide a correct Python 3 solution for this coding contest problem.
Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7 | instruction | 0 | 7,447 | 5 | 14,894 |
"Correct Solution:
```
def parse_formula(s, pointer):
head = s[pointer]
if head == "-":
pointer += 1
result, pointer = parse_formula(s, pointer)
result = 2 - result
elif head == "(":
pointer += 1
result_left, pointer = parse_formula(s, pointer)
op, pointer = parse_op(s, pointer)
result_right, pointer = parse_formula(s, pointer)
result = calc(op, result_left, result_right)
pointer += 1
else:
result = int(head)
pointer += 1
return result, pointer
def parse_op(s, pointer):
return s[pointer], pointer + 1
calc_table1 = {(0, 0):0, (0, 1):0, (0, 2):0,
(1, 0):0, (1, 1):1, (1, 2):1,
(2, 0):0, (2, 1):1, (2, 2):2}
calc_table2 = {(0, 0):0, (0, 1):1, (0, 2):2,
(1, 0):1, (1, 1):1, (1, 2):2,
(2, 0):2, (2, 1):2, (2, 2):2}
def calc(op, left, right):
if op == "*":return calc_table1[(left, right)]
if op == "+":return calc_table2[(left, right)]
while True:
formula = input()
if formula == ".":
break
ans = 0
for p in ("0", "1", "2"):
sp = formula.replace("P", p)
for q in ("0", "1", "2"):
sq = sp.replace("Q", q)
for r in ("0", "1", "2"):
sr = sq.replace("R", r)
if parse_formula(sr, 0)[0] == 2:
ans += 1
print(ans)
``` | output | 1 | 7,447 | 5 | 14,895 |
Provide a correct Python 3 solution for this coding contest problem.
Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7 | instruction | 0 | 7,448 | 5 | 14,896 |
"Correct Solution:
```
def multi(a, b) :
if a == 0 :
return 0
elif a == 1 :
if b == 0 :
return 0
else :
return 1
else :
return b
def add(a, b) :
if a == 0 :
return b
elif a == 1 :
if b == 2 :
return 2
else :
return 1
else :
return 2
def minus(a) :
return (2 - a)
def calc(l) : # '('、')'のない計算式
l = list(l)
#'-'を計算
i = len(l)-1
while True :
if i < 0 :
break
if l[i] == '-' :
print
l[i] = str(minus(int(l[i+1])))
del l[i+1]
i -= 1
#'*'を計算
i = 0
while True :
if i >= len(l) :
break
if l[i] == '*' :
l[i-1] = str(multi(int(l[i-1]), int(l[i+1])))
del l[i:i+2]
else :
i += 1
#'+'を計算
i = 0
while True :
if i >= len(l) :
break
if l[i] == '+' :
l[i-1] = str(add(int(l[i-1]), int(l[i+1])))
del l[i:i+2]
else :
i += 1
return ''.join(l)
def main(l) :
l = list(l)
while '(' in l :
for i in range(len(l)) :
if l[i] == '(' :
start = i
elif l[i] == ')' :
A = ''.join(l[start+1:i])
del l[start:i+1]
l.insert(start, calc(A))
break
if len(l) != 1 :
l = calc(l)
return ''.join(l)
while True :
input_l = input()
if input_l == '.' :
break
cnt = 0
for p in ['0', '1', '2'] :
for q in ['0', '1', '2'] :
for r in ['0', '1', '2'] :
l = input_l
if 'P' in l :
l = l.replace('P', p)
if 'Q' in l :
l = l.replace('Q', q)
if 'R' in l :
l = l.replace('R', r)
if main(l) == '2' :
cnt += 1
print(cnt)
``` | output | 1 | 7,448 | 5 | 14,897 |
Provide a correct Python 3 solution for this coding contest problem.
Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7 | instruction | 0 | 7,449 | 5 | 14,898 |
"Correct Solution:
```
# AOJ 1155: How can I satisfy thee? Let me count
# Python3 2018.7.17 bal4u
def term(idx):
x, idx = factor(idx)
op = buf[idx]
y, idx = factor(idx+1);
if op == '*':
if x == 2 and y == 2: x = 2
elif x == 0 or y == 0: x = 0
else: x = 1
else:
if x == 0 and y == 0: x = 0
elif x == 2 or y == 2: x = 2
else: x = 1
return [x, idx]
def factor(idx):
global p, q, r
if buf[idx] == '(': x, idx = term(idx+1)
elif buf[idx] == '-':
x, idx = factor(idx+1)
x = 2-x; idx -= 1
elif '0'<= buf[idx] <='9': x = int(buf[idx])
elif buf[idx] == 'P': x = p
elif buf[idx] == 'Q': x = q
else: x = r
return [x, idx+1]
while True:
buf = list(input())
if buf[0] == '.': break
ans = 0
for p in range(3):
for q in range(3):
for r in range(3):
if factor(0)[0] == 2: ans += 1
print(ans)
``` | output | 1 | 7,449 | 5 | 14,899 |
Provide a correct Python 3 solution for this coding contest problem.
Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7 | instruction | 0 | 7,450 | 5 | 14,900 |
"Correct Solution:
```
just_len = 60
import re
import collections
NUM = r'(?P<NUM>\d+)'
PLUS = r'(?P<PLUS>\+)'
MINUS = r'(?P<MINUS>-)'
TIMES = r'(?P<TIMES>\*)'
LPAREN = r'(?P<LPAREN>\()'
RPAREN = r'(?P<RPAREN>\))'
WS = r'(?P<WS>\s+)'
master_pattern = re.compile('|'.join((NUM, PLUS, MINUS, TIMES, LPAREN, RPAREN, WS)))
Token = collections.namedtuple('Token', ['type', 'value'])
def generate_tokens(pattern, text):
scanner = pattern.scanner(text)
for m in iter(scanner.match, None):
token = Token(m.lastgroup, m.group())
if token.type != 'WS':
yield token
def minus(x):
if x==0: ans=2
if x==1: ans=1
if x==2: ans=0
return ans
def mult(x,y):
if x==0:
a=0
if x==1:
if y==0: a=0
if y==1: a=1
if y==2: a=1
if x==2:
if y==0: a=0
if y==1: a=1
if y==2: a=2
return a
def add(x,y):
if x==0:
if y==0: a=0
if y==1: a=1
if y==2: a=2
if x==1:
if y==0: a=1
if y==1: a=1
if y==2: a=2
if x==2:
a=2
return a
class ExpressionEvaluator:
def parse(self, text):
self.tokens = generate_tokens(master_pattern, text)
self.current_token = None
self.next_token = None
self._advance()
# expr is the top level grammar. So we invoke that first.
# it will invoke other function to consume tokens according to grammar rule.
return self.expr()
def _advance(self):
self.current_token, self.next_token = self.next_token, next(self.tokens, None)
def _accept(self, token_type):
# if there is next token and token type matches
if self.next_token and self.next_token.type == token_type:
self._advance()
return True
else:
return False
def _expect(self, token_type):
if not self._accept(token_type):
raise SyntaxError('Expected ' + token_type)
def expr(self):
'''
expression ::= term { ( +|-) term } *
'''
expr_value = self.term()
while self._accept('PLUS') or self._accept('MINUS'):
op = self.current_token.type
right = self.term()
if op == 'PLUS':
#expr_value += right
expr_value = add(expr_value, right)
elif op == 'MINUS':
#expr_value -= right
expr_value = add(expr_value, minus(right))
else:
raise SyntaxError('Should not arrive here ' + op)
return expr_value
def term(self):
'''
term ::= factor { ('*') factor } *
'''
term_value = self.factor()
while self._accept('TIMES') or self._accept('DIVIDE'):
op = self.current_token.type
if op == 'TIMES':
#term_value *= self.factor()
term_value = mult(term_value, self.factor())
else:
raise SyntaxError('Should not arrive here ' + op)
return term_value
def factor(self):
'''
factor ::= NUM | (expr) | -(factor)
'''
# it can be a number
if self._accept('NUM'):
expr_value = int(self.current_token.value)
# or (expr)
elif self._accept('LPAREN'):
expr_value = self.expr()
self._expect('RPAREN')
elif self._accept('MINUS'):
expr_value = minus(self.factor())
else:
raise SyntaxError('Expect NUMBER or LPAREN')
return expr_value
e = ExpressionEvaluator()
# print('parse 2'.ljust(just_len),
# e.parse('2'))
#
# print('parse 2 + 3'.ljust(just_len),
# e.parse('2 + 3'))
# print('parse 2 + 3 * 4'.ljust(just_len),
# e.parse('2 + 3 * 4'))
#
# print('parse (2 + 3) * 4'.ljust(just_len),
# e.parse('(2 + 3) * 4'))
while True:
rS=input()
if rS=='.': break
ans=0
for p in range(3):
for q in range(3):
for r in range(3):
S = rS.replace('P',str(p))\
.replace('Q',str(q))\
.replace('R',str(r))
if e.parse(S)==2: ans+=1
print(ans)
``` | output | 1 | 7,450 | 5 | 14,901 |
Provide a correct Python 3 solution for this coding contest problem.
Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7 | instruction | 0 | 7,451 | 5 | 14,902 |
"Correct Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(0,-1),(1,0),(0,1),(-1,0)]
ddn = [(0,-1),(1,-1),(1,0),(1,1),(0,1),(-1,-1),(-1,0),(-1,1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
rr = []
m = {}
def f(s):
k = s
if k in m:
return m[k]
t = set(re.findall(r"\([^()]+\)", s))
while t:
for c in t:
s = s.replace(c, f(c[1:-1]))
t = set(re.findall(r"\([^()]+\)", s))
while '-' in s:
s = s.replace('-1', '1')
s = s.replace('-2', '0')
s = s.replace('-0', '2')
r = s[0]
for i in range(len(s)//2):
if s[i*2+1] == '*':
r = min(r,s[i*2+2])
else:
r = max(r,s[i*2+2])
m[k] = r
return r
while True:
s = S()
if s == '.':
break
tr = 0
for P,Q,R in itertools.product(['0', '1', '2'], repeat=3):
ts = s.replace('P', P)
ts = ts.replace('Q', Q)
ts = ts.replace('R', R)
if f(ts) == '2':
tr += 1
rr.append(tr)
return '\n'.join(map(str, rr))
print(main())
``` | output | 1 | 7,451 | 5 | 14,903 |
Provide a correct Python 3 solution for this coding contest problem.
Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7 | instruction | 0 | 7,452 | 5 | 14,904 |
"Correct Solution:
```
import re
# and
def and_def(a, b):
return str(min(int(a), int(b)))
# or
def or_def(a, b):
return str(max(int(a), int(b)))
# not
def not_def(a):
return str(2 - int(a))
def match(struct):
if re.fullmatch(r'\-[0,1,2]', struct):
return not_def(struct[-1])
if re.fullmatch(r'[0,1,2]\+[0,1,2]', struct):
return or_def(struct[0], struct[-1])
if re.fullmatch(r'[0,1,2]\*[0,1,2]', struct):
return and_def(struct[0], struct[-1])
if re.fullmatch(r'[0,1,2]', struct):
return struct
if re.fullmatch(r'\([0,1,2]\)', struct):
return struct[1]
return struct
def parse(struct):
tmpstruct = ''
check, minas = False, False
if len(struct) == 1:
return struct
for i in range(len(struct)):
if not check:
if struct[i] == '(':
check = [')', '(']
tmp = 1
num = i
elif struct[i] == '-':
check = ['0', '1', '2', '(']
minas = True
num = i
else:
tmpstruct += struct[i]
else:
if struct[i] in check:
if struct[i] == ')':
tmp -= 1
if not tmp:
if not minas:
tmpstruct += parse(struct[num+1: i])
else:
tmpstruct += not_def(parse(struct[num + 1: i + 1]))
minas = False
check = False
elif struct[i] == '(' and check == ['0', '1', '2', '(']:
check = [')', '(']
tmp = 1
elif struct[i] == '(':
tmp += 1
else:
tmpstruct += not_def(parse(struct[num + 1: i + 1]))
check = False
minas = False
tmpstruct = match(tmpstruct)
return tmpstruct
def change_PQR(string, P, Q, R):
ret = ''
for i in string:
if i == 'P':
ret += str(P)
elif i == 'Q':
ret += str(Q)
elif i == 'R':
ret += str(R)
else:
ret += i
return ret
while True:
struct = input()
if struct == '.':
break
ans = 0
for i in (0, 1, 2):
for j in (0, 1, 2):
for k in (0, 1, 2):
tmpstr = struct
if parse(change_PQR(tmpstr, i, j, k)) == '2':
ans += 1
print(ans)
``` | output | 1 | 7,452 | 5 | 14,905 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7
Submitted Solution:
```
# -*- coding: utf-8 -*-
from itertools import product
class thee(int):
def __add__(self, that):
return thee(max(int(self), int(that)))
def __mul__(self, that):
return thee(min(int(self), int(that)))
def __neg__(self):
T = [2, 1, 0]
return thee(T[int(self)])
S = input()
while S != ".":
for x in list("012PQR"):
S = S.replace(x, "thee({})".format(x))
ans = 0
for P, Q, R in product(range(3), repeat=3):
ans += 2 == int(eval(S))
print(ans)
S = input()
``` | instruction | 0 | 7,453 | 5 | 14,906 |
Yes | output | 1 | 7,453 | 5 | 14,907 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7
Submitted Solution:
```
class N:
def __init__(self, a):
self.a = a
def __mul__(self, b):
if self.a == 0:
return N(0)
elif self.a == 1:
return N((b.a >= 1) * 1)
else:
return b
def __add__(self, b):
if self.a == 0:
return b
elif self.a == 1:
return N((b.a > 1) + 1)
else:
return N(2)
def __neg__(self):
if self.a == 2:
return N(0)
elif self.a == 1:
return N(1)
else:
return N(2)
while True:
s = input().replace("-", "-").replace("0", "N(0)").replace("1", "N(1)").replace("2", "N(2)")
N(1) + N(2)
if s == ".": break
result = []
for P in map(N, range(3)):
for Q in map(N, range(3)):
for R in map(N, range(3)):
result.append(eval(s).a)
print(result.count(2))
``` | instruction | 0 | 7,454 | 5 | 14,908 |
Yes | output | 1 | 7,454 | 5 | 14,909 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7
Submitted Solution:
```
from collections import deque
def AND(a, b):
if a == "0" or b == "0":
return "0"
elif a == b == "2":
return "2"
else:
return "1"
def OR(a, b):
if a == "2" or b == "2":
return 2
elif a == b == "0":
return "0"
else:
return "1"
def NOT(a):
if a.count("-") % 2 == 1:
if a[0] == "0":
return "2"
elif a[0] == "2":
return "0"
else:
return "1"
else:
return a[0]
def solve(S):
que = deque()
for s in S:
if s == ")":
formula = ""
while True:
q = que.pop()
if q == "(":
break
formula += q
if "+" in formula:
a, b = formula.split("+")
a = NOT(a)
b = NOT(b)
que.append(str(OR(a, b)))
if "*" in formula:
a, b = formula.split("*")
a = NOT(a)
b = NOT(b)
que.append(str(AND(a, b)))
else:
que.append(s)
return NOT("".join(reversed(que)))
while True:
S = input()
if S == ".":
break
count = 0
for p in range(3):
for q in range(3):
for r in range(3):
if solve(S.replace("P", str(p)).replace("Q", str(q)).replace("R", str(r))) == "2":
count += 1
print(count)
``` | instruction | 0 | 7,455 | 5 | 14,910 |
Yes | output | 1 | 7,455 | 5 | 14,911 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
Define a function $ f $ that starts with $ 1 $ and takes a sequence of finite lengths as an argument as follows.
$ \ displaystyle f (\\ {a_1, a_2, \ ldots, a_n \\}) = \ sum_ {i = 1} ^ n {a_i} ^ i $
Given a sequence of length $ N $, $ X = \\ {x_1, x_2, \ ldots, x_N \\} $, $ f (X) for all subsequences $ X'$ except empty columns. ') Find $ and output the sum of them divided by $ 998244353 $. However, the subsequence subsequences shall be renumbered starting from $ 1 $ while maintaining the relative order in the original sequence. Also, even if two subsequences are the same as columns, if they are taken out at different positions, they shall be counted separately.
Constraints
The input satisfies the following conditions.
* $ 1 \ leq N \ leq 10 ^ 6 $
* $ 1 \ leq x_i \ leq 10 ^ 6 $
* All inputs are integers
Input
The input is given in the following format.
$ N $
$ x_1 $ $ \ ldots $ $ x_N $
The first line is given the length $ N $. In the second row, the elements of the sequence $ X $ are given, separated by blanks.
Output
Find $ f (X') $ for all subsequences $ X'$ except empty columns, and divide the sum by $ 998244353 $ to output the remainder.
Examples
Input
3
1 2 3
Output
64
Input
5
100 200 300 400 500
Output
935740429 | instruction | 0 | 7,504 | 5 | 15,008 |
"Correct Solution:
```
N = int(input())
X = list(map(int, input().split()))
ans = 0
mod = 998244353
for i, x in enumerate(X):
ans = (ans * 2 + x * pow(x+1, i, mod)) % mod
print(ans)
``` | output | 1 | 7,504 | 5 | 15,009 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1
Submitted Solution:
```
n = int(input())
num = [int(input()) for i in range(n)]
gra = [1]*n
for i in range(1,n):
Max = 1
for j in range(i):
if num[j]<num[i] and gra[j]>=Max:
Max = gra[j]
gra[i] = Max+1
print(max(gra))
``` | instruction | 0 | 7,517 | 5 | 15,034 |
No | output | 1 | 7,517 | 5 | 15,035 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a given sequence A = {a0, a1, ... , an-1}, find the length of the longest increasing subsequnece (LIS) in A.
An increasing subsequence of A is defined by a subsequence {ai0, ai1, ... , aik} where 0 ≤ i0 < i1 < ... < ik < n and ai0 < ai1 < ... < aik.
Constraints
* 1 ≤ n ≤ 100000
* 0 ≤ ai ≤ 109
Input
n
a0
a1
:
an-1
In the first line, an integer n is given. In the next n lines, elements of A are given.
Output
The length of the longest increasing subsequence of A.
Examples
Input
5
5
1
3
2
4
Output
3
Input
3
1
1
1
Output
1
Submitted Solution:
```
# fp = open("DPL_1_D-in11.txt")
# inlist = list(map(int, fp.read().splitlines()))
n = int(input())
A = []
dp = [0 for _ in range(n)]
dp[0] = 1
for i in range(n):
num = int(input())
A.append(num)
dpmax = 0
for j in range(i):
if A[j] < num and dp[j] > dpmax:
dpmax = dp[j]
dp[i] = max(dpmax + 1, 1)
print(dp[-1])
``` | instruction | 0 | 7,519 | 5 | 15,038 |
No | output | 1 | 7,519 | 5 | 15,039 |
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