message stringlengths 2 16.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 575 109k | cluster float64 16 16 | __index_level_0__ int64 1.15k 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (x_i,y_i).
Let R=10^{10^{10^{10}}}. Ringo performs the following operation:
* Randomly choose a point from the interior of a circle of radius R centered at the origin, and put Snuke there. Snuke will move to the hole with the smallest Euclidean distance from the point, and fall into that hole. If there are multiple such holes, the hole with the smallest index will be chosen.
For every i (1 \leq i \leq N), find the probability that Snuke falls into the i-th hole.
Here, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:
* Pick two real numbers x and y independently according to uniform distribution on [-R,R].
* If x^2+y^2\leq R^2, the point (x,y) is chosen. Otherwise, repeat picking the real numbers x,y until the condition is met.
Constraints
* 2 \leq N \leq 100
* |x_i|,|y_i| \leq 10^6(1\leq i\leq N)
* All given points are pairwise distinct.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print N real numbers. The i-th real number must represent the probability that Snuke falls into the i-th hole.
The output will be judged correct when, for all output values, the absolute or relative error is at most 10^{-5}.
Examples
Input
2
0 0
1 1
Output
0.5
0.5
Input
5
0 0
2 8
4 5
2 6
3 10
Output
0.43160120892732328768
0.03480224363653196956
0.13880483535586193855
0.00000000000000000000
0.39479171208028279727
Submitted Solution:
```
from sys import exit, stderr, setrecursionlimit
from functools import reduce
from itertools import *
from collections import defaultdict
from bisect import bisect
from math import atan2, pi
def read():
return int(input())
def reads():
return [int(x) for x in input().split()]
setrecursionlimit(1000000)
p = []
N = read()
for _ in range(N):
(x, y) = reads()
p.append((x, y))
for i in range(N):
(x, y) = p[i]
(b1, e1) = (0, pi)
(b2, e2) = (pi, 2*pi)
for j in range(N):
if j == i:
continue
(z, w) = p[j]
th = (atan2(w - y, z - x) + pi / 2) % (2*pi)
if th <= pi:
b1 = max(b1, th)
e2 = min(e2, th + pi)
else:
e1 = min(e1, th - pi)
b2 = max(b2, th)
result = (max(0, e1-b1) + max(0, e2-b2)) / 2 / pi
print("{:.20f}".format(result))
``` | instruction | 0 | 45,258 | 16 | 90,516 |
Yes | output | 1 | 45,258 | 16 | 90,517 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (x_i,y_i).
Let R=10^{10^{10^{10}}}. Ringo performs the following operation:
* Randomly choose a point from the interior of a circle of radius R centered at the origin, and put Snuke there. Snuke will move to the hole with the smallest Euclidean distance from the point, and fall into that hole. If there are multiple such holes, the hole with the smallest index will be chosen.
For every i (1 \leq i \leq N), find the probability that Snuke falls into the i-th hole.
Here, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:
* Pick two real numbers x and y independently according to uniform distribution on [-R,R].
* If x^2+y^2\leq R^2, the point (x,y) is chosen. Otherwise, repeat picking the real numbers x,y until the condition is met.
Constraints
* 2 \leq N \leq 100
* |x_i|,|y_i| \leq 10^6(1\leq i\leq N)
* All given points are pairwise distinct.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print N real numbers. The i-th real number must represent the probability that Snuke falls into the i-th hole.
The output will be judged correct when, for all output values, the absolute or relative error is at most 10^{-5}.
Examples
Input
2
0 0
1 1
Output
0.5
0.5
Input
5
0 0
2 8
4 5
2 6
3 10
Output
0.43160120892732328768
0.03480224363653196956
0.13880483535586193855
0.00000000000000000000
0.39479171208028279727
Submitted Solution:
```
import math
def angle(p1, p2):
x1, y1 = p1
x2, y2 = p2
return math.atan2(y2-y1, x2-x1)
def is_turn_right(p1, p2, p3):
x1, y1 = p1
x2, y2 = p2
x3, y3 = p3
return (y3 - y1) * (x2 - x1) < (y2 - y1) * (x3 - x1)
def find_convex_hull(points):
if len(points) < 2:
return points
P = sorted(points)
upper = [P[0], P[1]]
for p in P[2:]:
if not is_turn_right(upper[-2], upper[-1], p):
upper.pop()
upper.append(p)
lower = [P[-1], P[-2]]
for p in reversed(P[:-2]):
if not is_turn_right(lower[-2], lower[-1], p):
lower.pop()
lower.append(p)
if upper[-1] == lower[0]:
upper = upper[:-1]
if upper[0] == lower[-1]:
lower = lower[:-1]
ans = upper + lower
return ans
def main():
N = int(input())
P = [None] * N
for i in range(N):
x, y = map(int, input().split())
P[i] = (x, y)
ans = {p: 0.0 for p in P}
ch = find_convex_hull(P)
M = len(ch)
for i in range(M):
a1 = angle(ch[i], ch[(i-1) % M]) - math.pi / 2
a2 = angle(ch[i], ch[(i+1) % M]) + math.pi / 2
ratio = ((a1-a2) / (math.pi*2)) % 1.0
ans[ch[i]] = ratio
for p in P:
print(ans[p])
if __name__ == "__main__":
main()
``` | instruction | 0 | 45,259 | 16 | 90,518 |
No | output | 1 | 45,259 | 16 | 90,519 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (x_i,y_i).
Let R=10^{10^{10^{10}}}. Ringo performs the following operation:
* Randomly choose a point from the interior of a circle of radius R centered at the origin, and put Snuke there. Snuke will move to the hole with the smallest Euclidean distance from the point, and fall into that hole. If there are multiple such holes, the hole with the smallest index will be chosen.
For every i (1 \leq i \leq N), find the probability that Snuke falls into the i-th hole.
Here, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:
* Pick two real numbers x and y independently according to uniform distribution on [-R,R].
* If x^2+y^2\leq R^2, the point (x,y) is chosen. Otherwise, repeat picking the real numbers x,y until the condition is met.
Constraints
* 2 \leq N \leq 100
* |x_i|,|y_i| \leq 10^6(1\leq i\leq N)
* All given points are pairwise distinct.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print N real numbers. The i-th real number must represent the probability that Snuke falls into the i-th hole.
The output will be judged correct when, for all output values, the absolute or relative error is at most 10^{-5}.
Examples
Input
2
0 0
1 1
Output
0.5
0.5
Input
5
0 0
2 8
4 5
2 6
3 10
Output
0.43160120892732328768
0.03480224363653196956
0.13880483535586193855
0.00000000000000000000
0.39479171208028279727
Submitted Solution:
```
import math
N = int(input())
xys = [tuple(map(int, input().split())) for _ in range(N)]
if N == 2:
print(0.5)
print(0.5)
exit()
outside = []
for i in range(N):
x1, y1 = xys[i]
for j in range(i+1, N):
x2, y2 = xys[j]
sign = 0
for x3, y3 in xys:
tmp = (x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1)
if tmp == 0:
continue
elif tmp > 0:
if sign == 0:
sign = +1
elif sign == -1:
continue_flg = True
break
else:
continue
else:
if sign == 0:
sign = -1
elif sign == +1:
continue_flg = True
break
else:
continue
else:
outside.append(i)
outside.append(j)
continue_flg = False
break
if continue_flg == False:
break
delete_list = [False] * N
while True:
i = outside[-1]
x1, y1 = xys[i]
for j in range(N):
if j in outside:
continue
x2, y2 = xys[j]
sign = 0
for k, (x3, y3) in enumerate(xys):
if k == i or k == j:
continue
tmp = (x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1)
if tmp == 0:
if x1 < x3 < x2 or x1 > x3 > x2 or y1 < y3 < y2 or y1 > y3 > y2:
delete_list[k] = True
continue
elif x1 < x2 < x3 or x1 > x2 > x3 or y1 < y2 < y3 or y1 > y2 > y3:
delete_list[j] = True
continue
else:
delete_list[i] = True
continue
elif tmp > 0:
if sign == 0:
sign = +1
elif sign == -1:
continue_flg = True
break
else:
continue
else:
if sign == 0:
sign = -1
elif sign == +1:
continue_flg = True
break
else:
continue
else:
outside.append(j)
continue_flg = False
break
else: #when not found appropriate j
break #get out of while True
for i in range(N):
if delete_list[i] and i in outside:
outside.remove(i)
ans = [0.0] * N
for i in range(-1, len(outside) - 1):
x1, y1 = xys[outside[i-1]]
x2, y2 = xys[outside[i]]
x3, y3 = xys[outside[i+1]]
v1x, v1y = x2 - x1, y2 - y1
v2x, v2y = x3 - x2, y3 - y2
dot = v1x * v2x + v1y * v2y
len1 = (v1x ** 2 + v1y ** 2)
len2 = (v2x ** 2 + v2y ** 2)
ans[outside[i]] = math.acos( max(-1.0, min(1.0, dot / math.sqrt(len1 * len2))) ) / (2 * math.pi)
for a in ans:
print('{:.20f}'.format(a))
``` | instruction | 0 | 45,260 | 16 | 90,520 |
No | output | 1 | 45,260 | 16 | 90,521 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (x_i,y_i).
Let R=10^{10^{10^{10}}}. Ringo performs the following operation:
* Randomly choose a point from the interior of a circle of radius R centered at the origin, and put Snuke there. Snuke will move to the hole with the smallest Euclidean distance from the point, and fall into that hole. If there are multiple such holes, the hole with the smallest index will be chosen.
For every i (1 \leq i \leq N), find the probability that Snuke falls into the i-th hole.
Here, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:
* Pick two real numbers x and y independently according to uniform distribution on [-R,R].
* If x^2+y^2\leq R^2, the point (x,y) is chosen. Otherwise, repeat picking the real numbers x,y until the condition is met.
Constraints
* 2 \leq N \leq 100
* |x_i|,|y_i| \leq 10^6(1\leq i\leq N)
* All given points are pairwise distinct.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print N real numbers. The i-th real number must represent the probability that Snuke falls into the i-th hole.
The output will be judged correct when, for all output values, the absolute or relative error is at most 10^{-5}.
Examples
Input
2
0 0
1 1
Output
0.5
0.5
Input
5
0 0
2 8
4 5
2 6
3 10
Output
0.43160120892732328768
0.03480224363653196956
0.13880483535586193855
0.00000000000000000000
0.39479171208028279727
Submitted Solution:
```
import math
N = int(input())
x = [0 for i in range(N)]
y = [0 for i in range(N)]
for i in range(N):
x[i], y[i] = map(int, input().split())
def mindis(p, q):
j = 0
for i in range(N):
if (x[i]-p)**2+(y[i]-q)**2<(x[j]-p)**2+(y[j]-q)**2:
j = i
return j
r = [0 for i in range(N)]
M = 10*10**5
for i in range(M):
c = math.cos(2*math.pi*i/M)*10**10
s = math.sin(2*math.pi*i/M)*10**10
k = mindis(c, s)
r[k] += 1
S = sum(r)
for i in range(N):
print(r[i]/S)
``` | instruction | 0 | 45,261 | 16 | 90,522 |
No | output | 1 | 45,261 | 16 | 90,523 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (x_i,y_i).
Let R=10^{10^{10^{10}}}. Ringo performs the following operation:
* Randomly choose a point from the interior of a circle of radius R centered at the origin, and put Snuke there. Snuke will move to the hole with the smallest Euclidean distance from the point, and fall into that hole. If there are multiple such holes, the hole with the smallest index will be chosen.
For every i (1 \leq i \leq N), find the probability that Snuke falls into the i-th hole.
Here, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:
* Pick two real numbers x and y independently according to uniform distribution on [-R,R].
* If x^2+y^2\leq R^2, the point (x,y) is chosen. Otherwise, repeat picking the real numbers x,y until the condition is met.
Constraints
* 2 \leq N \leq 100
* |x_i|,|y_i| \leq 10^6(1\leq i\leq N)
* All given points are pairwise distinct.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print N real numbers. The i-th real number must represent the probability that Snuke falls into the i-th hole.
The output will be judged correct when, for all output values, the absolute or relative error is at most 10^{-5}.
Examples
Input
2
0 0
1 1
Output
0.5
0.5
Input
5
0 0
2 8
4 5
2 6
3 10
Output
0.43160120892732328768
0.03480224363653196956
0.13880483535586193855
0.00000000000000000000
0.39479171208028279727
Submitted Solution:
```
import sys
stdin = sys.stdin
def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x)-1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())
from math import acos
def ccw(p1,p2,p3):
return (p2[0]-p1[0])*(p3[1]-p1[1]) - (p2[1]-p1[1])*(p3[0]-p1[0])
def ConvexHull(points):
u = []
l = []
points.sort()
for p in points:
while len(u)>1 and ccw(u[-2], u[-1], p)>=0:
u.pop()
while len(l)>1 and ccw(l[-2], l[-1], p)<=0:
l.pop()
u.append(p)
l.append(p)
return u + l[-2:0:-1]
def angle(v1, v2):
inner = v1[0]*v2[0] + v1[1]*v2[1]
normv1 = (v1[0]**2 + v1[1]**2) ** 0.5
normv2 = (v2[0]**2 + v2[1]**2) ** 0.5
return acos(inner / (normv1*normv2))
n = ni()
if n == 1:
print(1)
elif n == 2:
print(0.5)
print(0.5)
else:
points = [list(li()) + [i] for i in range(n)]
ch = ConvexHull(points)
bsc = []
for i in range(len(ch)):
x1,y1,i1 = ch[i]
x2,y2,i2 = ch[i-1]
bsc.append((y1-y2, x2-x1))
if len(ch) == 2:
angles = [1,1]
else:
angles = [angle(bsc[i], bsc[i-1]) for i in range(len(ch))]
sm = sum(angles)
ans = [0]*n
for i in range(len(ch)):
x,y,ind = ch[i-1]
ans[ind] = angles[i] / sm
for x in ans:
print(x)
``` | instruction | 0 | 45,262 | 16 | 90,524 |
No | output | 1 | 45,262 | 16 | 90,525 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17 | instruction | 0 | 46,057 | 16 | 92,114 |
"Correct Solution:
```
from itertools import accumulate as acc
N, K, *a = map(int, open(0).read().split())
*b, = map(lambda x: max(x, 0), a)
*Sa, = acc([0] + a)
*Sb, = acc([0] + b)
print(max(Sb[i] + max(0,Sa[i+K]-Sa[i]) + Sb[N]-Sb[i+K] for i in range(N-K+1)))
``` | output | 1 | 46,057 | 16 | 92,115 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17 | instruction | 0 | 46,058 | 16 | 92,116 |
"Correct Solution:
```
from itertools import accumulate
N, K = map(int, input().split())
A = []
B = []
for a in map(int, input().split()):
A.append(a)
B.append( a if a > 0 else 0)
S = [0]+list(accumulate(A))
T = [0]+list(accumulate(B))
res = 0
for i in range(N-K+1):
res = max(T[i] + max(S[i+K] - S[i], 0) + T[N]-T[i+K], res)
print(res)
``` | output | 1 | 46,058 | 16 | 92,117 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17 | instruction | 0 | 46,059 | 16 | 92,118 |
"Correct Solution:
```
# -*- coding: utf-8 -*-
import sys
from itertools import accumulate
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10 ** 9)
INF = 10 ** 18
MOD = 10 ** 9 + 7
N, K = MAP()
A = LIST()
B = [0] * N
for i, a in enumerate(A):
if a > 0:
B[i] = a
acc = [0] + list(accumulate(A))
acc2 = [0] + list(accumulate(B))
acc2rev = [0] + list(accumulate(B[::-1]))[::-1] + [0]
ans = -INF
for i in range(1, N-K+2):
cnt = max(acc[i+K-1] - acc[i-1], 0)
cnt += acc2[i-1] + acc2rev[i+K]
ans = max(ans, cnt)
print(ans)
``` | output | 1 | 46,059 | 16 | 92,119 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17 | instruction | 0 | 46,060 | 16 | 92,120 |
"Correct Solution:
```
#!/usr/bin/env python3
N, K = map(int, input().split())
a = list(map(int, input().split()))
pl = [(x if (x > 0) else 0) for x in a]
s = sum(pl)
sk_a = [sum(a[:K])]
sk_pl = [sum(pl[:K])]
for i in range(1, N - K + 1):
sk_a.append(sk_a[-1] - a[i - 1] + a[K + i - 1])
sk_pl.append(sk_pl[-1] - pl[i - 1] + pl[K + i - 1])
ans = 0
if lambda x: x > 0 in a:
for i in range(N - K + 1):
ans = max(ans, s - sk_pl[i] + max(0, sk_a[i]))
print(ans)
``` | output | 1 | 46,060 | 16 | 92,121 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17 | instruction | 0 | 46,061 | 16 | 92,122 |
"Correct Solution:
```
from itertools import accumulate
n, k = map(int, input().split())
a = list(map(int, input().split()))
a_plus = [e if e > 0 else 0 for e in a]
acc = [0] + list(accumulate(a))
acc_plus = [0] + list(accumulate(a_plus))
ans = 0
for i in range(1, n - k + 2):
white = acc_plus[i-1] + acc_plus[n] - acc_plus[i+k-1]
black = white + acc[i+k-1] - acc[i-1]
ans = max(ans, white, black)
print(ans)
``` | output | 1 | 46,061 | 16 | 92,123 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17 | instruction | 0 | 46,062 | 16 | 92,124 |
"Correct Solution:
```
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
def readln(ch):
_res = list(map(int,str(input()).split(ch)))
return _res
s = readln(' ')
n,k = s[0],s[1]
a = [0 for i in range(0,n+1)]
a[1:] = readln(' ')
s = a[:]
r = a[:]
for i in range(1,n+1):
s[i] = s[i-1] + s[i]
if r[i] > 0:
r[i] = r[i-1] + r[i]
else:
r[i] = r[i-1]
ans = 0
for i in range(k,n+1):
ans = max(ans,r[n] - (r[i] - r[i-k]) + max(0,s[i] - s[i-k]))
print(ans)
``` | output | 1 | 46,062 | 16 | 92,125 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17 | instruction | 0 | 46,063 | 16 | 92,126 |
"Correct Solution:
```
N, K = map(int, input().split())
a = list(map(int, input().split()))
if N == K:
print(max(sum(a), 0))
exit()
a_plus = []
a_minus = []
for i in range(N):
if i == 0:
if a[i] > 0:
a_plus.append(a[i])
a_minus.append(0)
else:
a_plus.append(0)
a_minus.append(a[i])
else:
if a[i] > 0:
a_plus.append(a_plus[i-1] + a[i])
a_minus.append(a_minus[i-1])
else:
a_plus.append(a_plus[i-1])
a_minus.append(a_minus[i-1] + a[i])
ans = 0
for i in range(N-K):
ans = max(ans,
a_plus[N-1] + (a_minus[i+K] - a_minus[i]),
a_plus[N-1] - (a_plus[i+K] - a_plus[i]))
print(ans)
``` | output | 1 | 46,063 | 16 | 92,127 |
Provide a correct Python 3 solution for this coding contest problem.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17 | instruction | 0 | 46,064 | 16 | 92,128 |
"Correct Solution:
```
from itertools import accumulate as ac
n,k=map(int,input().split())
a=list(map(int,input().split()))
b=[0]+list(ac(a))
c=[0]+list(ac([(0 if i<0 else i)for i in a]))
d=0
for i in range(n-k+1):
d=max(d,max(b[i+k]-b[i],0)+c[i]+c[-1]-c[i+k])
print(d)
``` | output | 1 | 46,064 | 16 | 92,129 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17
Submitted Solution:
```
from itertools import accumulate
n,k = map(int, input().split())
a = list(map(int, input().split()))
b = [max(0,i) for i in a]
cumsum_a = [0] + list(accumulate(a))
cumsum_b = [0] + list(accumulate(b))
ans = 0
for i in range(n-k+1):
tmp = max(0,cumsum_a[i+k]-cumsum_a[i]) + cumsum_b[i] + cumsum_b[n] - cumsum_b[i+k]
ans = max(ans,tmp)
print(ans)
``` | instruction | 0 | 46,065 | 16 | 92,130 |
Yes | output | 1 | 46,065 | 16 | 92,131 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17
Submitted Solution:
```
# B - Contiguous Repainting
N,K = map(int,input().split())
a = [0] + list(map(int,input().split()))
ans = 0
tmp = [0,0]
for i in range(1,K+1):
ans += max(0,a[i])
tmp[a[i]>=0] += abs(a[i])
loss = min(tmp)
for i in range(K+1,N+1):
ans += max(0,a[i])
tmp[a[i-K]>=0] -= abs(a[i-K])
tmp[a[i]>=0] += abs(a[i])
loss = min(loss,min(tmp))
print(ans-loss)
``` | instruction | 0 | 46,066 | 16 | 92,132 |
Yes | output | 1 | 46,066 | 16 | 92,133 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17
Submitted Solution:
```
N, K = map(int, input().split())
a = list(map(int, input().split()))
mae = 0
naka = sum(a[:K])
usiro = 0
for i in range(K, N):
if a[i]>0:
usiro+=a[i]
ans = max(mae+naka+usiro, mae+usiro)
for i in range(N-K):
naka+=a[i+K]-a[i]
if a[i]>0:
mae+=a[i]
if a[i+K]>0:
usiro-=a[i+K]
ans = max(ans, mae+naka+usiro, mae+usiro)
print(ans)
``` | instruction | 0 | 46,067 | 16 | 92,134 |
Yes | output | 1 | 46,067 | 16 | 92,135 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17
Submitted Solution:
```
N,K=map(int,input().split())
a=[int(i) for i in input().split()]
S=[0]
p=[0]
for i in range(1,N+1):
S.append(S[i-1]+a[i-1])
if a[i-1]>0:
p.append(p[i-1]+a[i-1])
else:
p.append(p[i-1])
ans=0
for i in range(1,N-K+2):
res=0
res+=max(S[i+K-1]-S[i-1],0)
res+=p[i-1]
res+=p[-1]-p[i+K-1]
ans=max(res,ans)
print(ans)
``` | instruction | 0 | 46,068 | 16 | 92,136 |
Yes | output | 1 | 46,068 | 16 | 92,137 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17
Submitted Solution:
```
N,K = map(int,input().split())
a = list(map(int,input().split()))
A = [0]*(N+1)
S = [0]*(N+1)
for i in range(N):
A[i+1] = A[i]+max(0,a[i])
S[i+1] = S[i]+a[i]
ans = -inf
for i in range(0,N-K+1):
ans = max(ans,A[i]+max(0,S[i+K]-S[i])+(A[N]-A[i+K]))
print(ans)
``` | instruction | 0 | 46,069 | 16 | 92,138 |
No | output | 1 | 46,069 | 16 | 92,139 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17
Submitted Solution:
```
import sys
input = sys.stdin.readline
def main():
N,K = map(int,input().split())
a = list(map(int,input().split()))
rt = 0
rf = 0
for i in range(N-K):
if a[i] > 0:
rt += a[i]
if a[-1-i] > 0:
rf += a[-1-i]
rt = max(rt,rt+sum(a[N-K:]))
rf = max(rf,rf+sum(a[:K-1]))
print(max(rt,rf))
if __name__ == "__main__":
main()
``` | instruction | 0 | 46,070 | 16 | 92,140 |
No | output | 1 | 46,070 | 16 | 92,141 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17
Submitted Solution:
```
from itertools import accumulate
import sys
def main():
input = sys.stdin.readline
N, K = map(int, input().split())
*A, = map(int, input().split())
ans = solve1(A, K)
ans = max(ans, solve2(A, K))
A.reverse()
ans = max(ans, solve2(A, K))
print(ans)
def solve1(A, K):
N = len(A)
C = [0] + list(accumulate(A))
D = [0] * (N + 1)
for i, a in enumerate(A):
D[i + 1] = D[i] + (a if a > 0 else 0)
res = -10 ** 10
for i in range(1, N - K + 1):
s = D[i] + D[N] - D[i + K]
t = C[i + K] - C[i - 1]
s += t if t > 0 else 0
res = max(res, s)
return res
def solve2(A, K):
s = sum(A[:K])
if s < 0: s = 0
for i in range(K, len(A)):
if A[i] > 0: s += A[i]
return s
if __name__ == '__main__':
main()
``` | instruction | 0 | 46,071 | 16 | 92,142 |
No | output | 1 | 46,071 | 16 | 92,143 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N squares aligned in a row. The i-th square from the left contains an integer a_i.
Initially, all the squares are white. Snuke will perform the following operation some number of times:
* Select K consecutive squares. Then, paint all of them white, or paint all of them black. Here, the colors of the squares are overwritten.
After Snuke finishes performing the operation, the score will be calculated as the sum of the integers contained in the black squares. Find the maximum possible score.
Constraints
* 1≤N≤10^5
* 1≤K≤N
* a_i is an integer.
* |a_i|≤10^9
Input
The input is given from Standard Input in the following format:
N K
a_1 a_2 ... a_N
Output
Print the maximum possible score.
Examples
Input
5 3
-10 10 -10 10 -10
Output
10
Input
4 2
10 -10 -10 10
Output
20
Input
1 1
-10
Output
0
Input
10 5
5 -4 -5 -8 -4 7 2 -4 0 7
Output
17
Submitted Solution:
```
N, K = map(int, input().split())
A = [int(i) for i in input().split()]
ans = 0
for i in range(N):
if A[i] > 0:
ans += A[i]
A[i] = 0
m = sum(A[:K])
for i in range(N-K):
M = m - A[i] + A[i+K]
m = max(M,m)
print(max(ans+m,0))
``` | instruction | 0 | 46,072 | 16 | 92,144 |
No | output | 1 | 46,072 | 16 | 92,145 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10 | instruction | 0 | 46,073 | 16 | 92,146 |
"Correct Solution:
```
n,x=map(int,input().split())
A=[int(i) for i in input().split()]
B=[float("inf")]*n
ans=float("inf")
for i in range(n):
ans_i=i*x
for j in range(n):
B[j]=min(B[j],A[j-i])
ans_i+=B[j]
ans=min(ans,ans_i)
print(ans)
``` | output | 1 | 46,073 | 16 | 92,147 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10 | instruction | 0 | 46,074 | 16 | 92,148 |
"Correct Solution:
```
N,x=map(int,input().split())
a=[int(i) for i in input().split()]
for i in range(N):
a.append(a[i])
dp=[[float("inf")]*N for i in range(N)]
ans=float("inf")
for k in range(N):
for i in range(N):
if k==0:
dp[k][i]=a[N+i]
else:
dp[k][i]=min(dp[k-1][i],a[N+i-k])
ans=min(ans,k*x+sum(dp[k]))
print(ans)
``` | output | 1 | 46,074 | 16 | 92,149 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10 | instruction | 0 | 46,075 | 16 | 92,150 |
"Correct Solution:
```
N,x = map(int,input().split())
*A, = map(int,input().split())
c = [A[:] for _ in [0]*(N)]
ans = sum(A)
for i in range(1,N):
for j in range(N):
c[i][j] = min(c[i-1][j-1],c[i][j])
ans = min(ans,sum(c[i])+x*i)
print(ans)
``` | output | 1 | 46,075 | 16 | 92,151 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10 | instruction | 0 | 46,076 | 16 | 92,152 |
"Correct Solution:
```
def read():
return [int(i) for i in input().split(" ")]
N, x = read()
A = read()
ans = sum(A)
tempcost = ans
BC = A[:]
for i in range(1, N):
BC = [BC[j - 1] if BC[j - 1] < BC[j] else BC[j] for j in range(N)]
tempcost = x * i + sum(BC)
if(ans > tempcost):
ans = tempcost
print(ans)
``` | output | 1 | 46,076 | 16 | 92,153 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10 | instruction | 0 | 46,077 | 16 | 92,154 |
"Correct Solution:
```
import sys
import copy
input = sys.stdin.readline
def main():
N, x = map(int, input().split())
a = list(map(int, input().split()))
min_ = copy.deepcopy(a)
ans = int(1e15)
# 魔法を唱える回数 k
for k in range(N):
tmp = k * x
for i in range(N):
min_[i] = min(min_[i], a[(i-k)%N])
tmp += min_[i]
# print(min_)
ans = min(ans, tmp)
print(ans)
if __name__ == "__main__":
main()
``` | output | 1 | 46,077 | 16 | 92,155 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10 | instruction | 0 | 46,078 | 16 | 92,156 |
"Correct Solution:
```
from itertools import accumulate
from functools import reduce
N,x,*A = map(int, open(0).read().split())
dp = [0]*N
for i in range(N):
dp[i] = list(accumulate((A[i-j] for j in range(N)),min))
ans = reduce(min, (i*x+sum(a) for i,a in enumerate(zip(*dp))))
print(ans)
``` | output | 1 | 46,078 | 16 | 92,157 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10 | instruction | 0 | 46,079 | 16 | 92,158 |
"Correct Solution:
```
prev=lambda n,i,d: i-d if i-d>=0 else n+i-d
N,x=map(int,input().split())
A=list(map(int,input().split()))
dp = A[:]
ans=sum(dp)
for d in range(1,N+1):
for i in range(N):
p = prev(N,i,d)
dp[i]=min(dp[i], A[p])
ans=min(ans,sum(dp)+d*x)
print(ans)
``` | output | 1 | 46,079 | 16 | 92,159 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10 | instruction | 0 | 46,080 | 16 | 92,160 |
"Correct Solution:
```
n,x = map(int, input().split())
a = list(map(int, input().split()))
ans = sum(a)
b = [a[i] for i in range(n)]
for i in range(1,n):
c = [b[j] for j in range(n)]
for k in range(n):
b[k] = min(c[k],c[k-1])
ans = min(ans, sum(b)+i*x)
print(ans)
``` | output | 1 | 46,080 | 16 | 92,161 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10
Submitted Solution:
```
def read():
return [int(i) for i in input().split(" ")]
N, x = read()
A = read()
ans = sum(A)
tempcost = ans
xt = 0
BC = A
for i in range(1, N):
xt += x
A = [A[-1]] + A[0:-1]
BC = [v if v < BC[i] else BC[i] for (i, v) in enumerate(A)]
tempcost = xt + sum(BC)
if(ans > tempcost):
ans = tempcost
print(ans)
``` | instruction | 0 | 46,081 | 16 | 92,162 |
Yes | output | 1 | 46,081 | 16 | 92,163 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10
Submitted Solution:
```
#b faster
#m_i(k) = min(m_i(k-1), a_(i-k))
# http://agc004.contest.atcoder.jp/data/agc/004/editorial.pdf
n,x = [int(i) for i in input().split()]
a = [int(i) for i in input().split()]
m = a[::]
a.extend(a)
min_cost = sum(a)
for k in range(n):
#cost = x * k
for i in range(n,2*n):
m[i-n] = min(m[i-n], a[i-k])
#cost += mini
min_cost = min(min_cost, x*k + sum(m))
print(min_cost)
``` | instruction | 0 | 46,082 | 16 | 92,164 |
Yes | output | 1 | 46,082 | 16 | 92,165 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10
Submitted Solution:
```
N, x = map(int, input().split())
a = [int(i) for i in input().split()]
ret = float('inf')
dp = [float('inf')] * N
for i in range(N) :
for j in range(N) :
dp[(j+i)%N] = min(dp[(j+i)%N], a[j])
ret = min(ret, sum(dp) + x * i)
print(ret)
``` | instruction | 0 | 46,083 | 16 | 92,166 |
Yes | output | 1 | 46,083 | 16 | 92,167 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10
Submitted Solution:
```
# -*- coding: utf-8 -*-
def inpl(): return list(map(int, input().split()))
N, x = inpl()
A = inpl()
ans = sum(A)
for i in range(1, N):
A = [min(A[j], A[(j-1)%N]) for j in range(N)]
ans = min(ans, sum(A) + x*i)
print(ans)
``` | instruction | 0 | 46,084 | 16 | 92,168 |
Yes | output | 1 | 46,084 | 16 | 92,169 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10
Submitted Solution:
```
n,x=map(int,input().split())
a=list(map(int,input().split()))
a*=2
INF=10**15
cost=[INF]*n
b=[(c,d) for i in enumerate(a)]
b.sort(key=lambda x:x[1])
start=b[0][1]
cost[start]=a[start]
for i in range(start+1,start+n):
cost[i%n]=min(cost[(i-1)%n]+x,cost[i%n])
ans=0
for i in cost:
if i==INF:continue
ans+=i
print(ans)
``` | instruction | 0 | 46,085 | 16 | 92,170 |
No | output | 1 | 46,085 | 16 | 92,171 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10
Submitted Solution:
```
import sys
stdin = sys.stdin
sys.setrecursionlimit(10**5)
def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x)-1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())
n,x = li()
a = list(li())
a = a+a
mins = [-1]*n
idxs = [-1]*n
for i in range(n,2*n):
lst = [a[i-j] + j*x for j in range(n)]
mins[i-n] = min(lst)
idxs[i-n] = lst.index(mins[i-n])
ans = x*max(idxs)
idxs = idxs+idxs
first_zero = idxs.index(0)
for ai, idx in zip(a[first_zero:first_zero+n],idxs[first_zero:first_zero+n]):
if idx == 0:
temp = ai
ans += temp
else:
ans += temp
print(ans)
``` | instruction | 0 | 46,086 | 16 | 92,172 |
No | output | 1 | 46,086 | 16 | 92,173 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10
Submitted Solution:
```
n, x = [int(i) for i in input().split()]
a = [int(i) for i in input().split()]
ans = 0
b = []
for k in range(n):
if k == 0:
b = a.copy()
else:
for i in range(n):
b[i] = min(a[(i-k)%n],b[i])
cost = k*x+sum(b)
if k == 0:
ans = cost
else:
ans = min(ans,cost)
if ans != cost:
break
if ans < (k+1)*x:
break
print(ans)
``` | instruction | 0 | 46,087 | 16 | 92,174 |
No | output | 1 | 46,087 | 16 | 92,175 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.
Snuke can perform the following two actions:
* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.
* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.
Find the minimum time that Snuke needs to have slimes in all N colors.
Constraints
* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9
Input
The input is given from Standard Input in the following format:
N x
a_1 a_2 ... a_N
Output
Find the minimum time that Snuke needs to have slimes in all N colors.
Examples
Input
2 10
1 100
Output
12
Input
3 10
100 1 100
Output
23
Input
4 10
1 2 3 4
Output
10
Submitted Solution:
```
loop, magic_cost = map(int, input().split(" "))
cost = [n for n in map(int, input().split(" "))]
answer = float("inf")
for i in range(loop):
min_catch_cost = cost[i]
last_catch_index = i
sum_cost = 0
for j in range(i, i + loop):
if cost[j % loop] > (magic_cost * (j - last_catch_index)):
sum_cost += magic_cost * (j - last_catch_index)
else:
min_catch_cost = cost[j % loop]
last_catch_index = j
sum_cost += cost[j % loop]
answer = min(answer, sum_cost)
print(answer)
``` | instruction | 0 | 46,088 | 16 | 92,176 |
No | output | 1 | 46,088 | 16 | 92,177 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A + B balls are arranged in a row. The leftmost A balls are colored red, and the rightmost B balls are colored blue.
You perform the following operation:
* First, you choose two integers s, t such that 1 \leq s, t \leq A + B.
* Then, you repeat the following step A + B times: In each step, you remove the first ball or the s-th ball (if it exists) or the t-th ball (if it exists, all indices are 1-based) from left in the row, and give it to Snuke.
In how many ways can you give the balls to Snuke? Compute the answer modulo 10^9 + 7.
Here, we consider two ways to be different if for some k, the k-th ball given to Snuke has different colors. In particular, the choice of s, t doesn't matter. Also, we don't distinguish two balls of the same color.
Constraints
* 1 \leq A, B \leq 2000
Input
Input is given from Standard Input in the following format:
A B
Output
Print the answer.
Examples
Input
3 3
Output
20
Input
4 4
Output
67
Input
7 9
Output
7772
Input
1987 1789
Output
456315553
Submitted Solution:
```
from numpy import *
A,B=map(int,input().split())
M=10**9+7
U=2001
C=zeros((U,U),int64)
C[0,0]=1
for n in range(1,U):
C[n,1:]+=C[n-1,:-1]
C[n,:-1]+=C[n-1,:-1]
C[n]%=M
S=zeros_like(C)
S[0]=1
S[1:]=(C[:-1].cumsum(axis=1)%M).cumsum(axis=1)%M
print(sum(C[B-1,k]*(sum(S[k,:A-k+1])%M)%M for k in range(A+1)))
``` | instruction | 0 | 46,924 | 16 | 93,848 |
No | output | 1 | 46,924 | 16 | 93,849 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has an integer sequence A of length N.
He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E. The positions of the cuts can be freely chosen.
Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively. Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller. Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Constraints
* 4 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Examples
Input
5
3 2 4 1 2
Output
2
Input
10
10 71 84 33 6 47 23 25 52 64
Output
36
Input
7
1 2 3 1000000000 4 5 6
Output
999999994 | instruction | 0 | 47,768 | 16 | 95,536 |
"Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
cumsum = [a[0]]
for i in range(1, n):
cumsum.append(cumsum[i-1] + a[i])
i, k = 0, 2
ans = 10**18
for j in range(1, n-2):
while i < j:
p = cumsum[i]
q = cumsum[j] - cumsum[i]
p_new = cumsum[i+1]
q_new = cumsum[j] - cumsum[i+1]
if abs(q_new - p_new) > abs(q - p):
break
else:
i += 1
while k < n-1:
r = cumsum[k] - cumsum[j]
s = cumsum[n-1] - cumsum[k]
r_new = cumsum[k+1] - cumsum[j]
s_new = cumsum[n-1] - cumsum[k+1]
if abs(s_new - r_new) > abs(s - r):
break
else:
k += 1
pqrs = [p, q, r, s]
ans = min(ans, abs(max(pqrs) - min(pqrs)))
# print(i, j, k, ans, pqrs)
print(ans)
``` | output | 1 | 47,768 | 16 | 95,537 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has an integer sequence A of length N.
He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E. The positions of the cuts can be freely chosen.
Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively. Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller. Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Constraints
* 4 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Examples
Input
5
3 2 4 1 2
Output
2
Input
10
10 71 84 33 6 47 23 25 52 64
Output
36
Input
7
1 2 3 1000000000 4 5 6
Output
999999994 | instruction | 0 | 47,769 | 16 | 95,538 |
"Correct Solution:
```
from bisect import bisect_left
from itertools import accumulate
n = int(input())
a = tuple(map(int, input().split()))
cumsum = (0,) + tuple(accumulate(a))
# print(cumsum)
# PQ := [0, cut)
# RS = [cut, n)
ans = cumsum[-1]
for cut in range(2, n - 1):
# cumsum[cut] : PQ区間和
# cumsum[lc], cumsum[lc_1] : P区間和の候補
# cumsum[n] - cumsum[cut] : RS区間和
# cumsum[rc], cumsum[rc_1] : R区間和 + sPQの候補
sPQ = cumsum[cut]
sRS = cumsum[n] - cumsum[cut]
lc = bisect_left(cumsum, sPQ // 2)
# x以上で最小, 累積和のindexは、aの1-indexedに対応
lc_1 = lc - 1
# x未満で最大
if abs((sPQ - cumsum[lc]) - cumsum[lc]) < abs((sPQ - cumsum[lc_1]) - cumsum[lc_1]):
sP = cumsum[lc]
# print('sP', sP, lc, cumsum)
else:
sP = cumsum[lc_1]
# print('sP', sP, lc_1, cumsum)
sQ = sPQ - sP
# print('sQ', sQ)
rc = bisect_left(cumsum, sPQ + (sRS // 2))
# x以上で最小, 累積和のindexは、aの1-indexedに対応
rc_1 = rc - 1
# x未満で最大
if abs((sRS - (cumsum[rc] - sPQ)) - (cumsum[rc] - sPQ)) < abs((sRS - (cumsum[rc_1] - sPQ)) - (cumsum[rc_1] - sPQ)):
sR = cumsum[rc] - sPQ
# print('sR', sR, rc, cumsum)
else:
sR = cumsum[rc_1] - sPQ
# print('sR', sR, rc_1, cumsum)
sS = sRS - sR
# print('sS', sS)
t = (sP, sQ, sR, sS)
ans = min(ans, max(t) - min(t))
# print(t)
print(ans)
``` | output | 1 | 47,769 | 16 | 95,539 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has an integer sequence A of length N.
He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E. The positions of the cuts can be freely chosen.
Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively. Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller. Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Constraints
* 4 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Examples
Input
5
3 2 4 1 2
Output
2
Input
10
10 71 84 33 6 47 23 25 52 64
Output
36
Input
7
1 2 3 1000000000 4 5 6
Output
999999994 | instruction | 0 | 47,770 | 16 | 95,540 |
"Correct Solution:
```
n=int(input())
s=list(map(int,input().split()))
a=[0]
c=0
for si in s:
c+=si
a.append(c)
ans=[]
f=1
g=3
for i in range(2,n-1):
while abs(a[f]-(a[i]-a[f])) > abs(a[f+1]-(a[i]-a[f+1])):
f+=1
while abs(a[g]-a[i]-(a[n]-a[g])) > abs(a[g+1]-a[i]-(a[n]-a[g+1])):
g+=1
ls=[a[f],a[i]-a[f],a[g]-a[i],a[n]-a[g]]
ans.append(max(ls)-min(ls))
print(min(ans))
``` | output | 1 | 47,770 | 16 | 95,541 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has an integer sequence A of length N.
He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E. The positions of the cuts can be freely chosen.
Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively. Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller. Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Constraints
* 4 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Examples
Input
5
3 2 4 1 2
Output
2
Input
10
10 71 84 33 6 47 23 25 52 64
Output
36
Input
7
1 2 3 1000000000 4 5 6
Output
999999994 | instruction | 0 | 47,771 | 16 | 95,542 |
"Correct Solution:
```
# 写経AC
N = int(input())
A = tuple(map(int, input().split()))
# P,Q,R,S に対応
score = [A[0], A[1], A[2], sum(A[3:])]
ans = float("inf")
left, right = 1, 3
""" 尺取り法 """
# 真ん中
for mid in range(2, N-1):
# 左側
while left < mid and abs(score[0] - score[1]) > abs((score[0] + A[left]) - (score[1] - A[left])):
score[0] += A[left]
score[1] -= A[left]
left += 1
# 右側
while right < N and abs(score[2] - score[3]) > abs((score[2] + A[right]) - (score[3] - A[right])):
score[2] += A[right]
score[3] -= A[right]
right += 1
ans = min(ans, max(score) - min(score))
score[1] += A[mid]
score[2] -= A[mid]
print(ans)
``` | output | 1 | 47,771 | 16 | 95,543 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has an integer sequence A of length N.
He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E. The positions of the cuts can be freely chosen.
Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively. Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller. Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Constraints
* 4 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Examples
Input
5
3 2 4 1 2
Output
2
Input
10
10 71 84 33 6 47 23 25 52 64
Output
36
Input
7
1 2 3 1000000000 4 5 6
Output
999999994 | instruction | 0 | 47,772 | 16 | 95,544 |
"Correct Solution:
```
import bisect
N = int(input())
A = list(map(int,input().split()))
S = [A[0]]
for i in range(1,N):
S.append(S[i-1]+A[i])
ans = 1e18
for i in range(2, N-1):
# 左側 [0,i)
left_sum = S[i-1]
m = bisect.bisect(S, left_sum/2)
L = [S[m], left_sum-S[m]]
if m != 0:
L2 = [S[m-1], left_sum - S[m-1]]
if(abs(L[0]-L[1]) > abs(L2[0]-L2[1])): L = L2
# 右側 [i,N)
m = bisect.bisect(S, (S[-1]+left_sum)/2)
R = [S[m]-left_sum, S[-1]-S[m]]
if m != i:
R2 = [S[m-1]-left_sum, S[-1]-S[m-1]]
if(abs(R[0]-R[1]) > abs(R2[0]-R2[1])): R = R2
ans = min(ans, max(L[0],L[1],R[0],R[1]) - min(L[0],L[1],R[0],R[1]))
print(ans)
``` | output | 1 | 47,772 | 16 | 95,545 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has an integer sequence A of length N.
He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E. The positions of the cuts can be freely chosen.
Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively. Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller. Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Constraints
* 4 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Examples
Input
5
3 2 4 1 2
Output
2
Input
10
10 71 84 33 6 47 23 25 52 64
Output
36
Input
7
1 2 3 1000000000 4 5 6
Output
999999994 | instruction | 0 | 47,773 | 16 | 95,546 |
"Correct Solution:
```
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)
N = int(input())
As = list(mapint())
from itertools import accumulate
from bisect import bisect_right
cum = list(accumulate(As))
ans = 10**18
for i in range(1, N-2):
c = cum[i]
l_target = c/2
r_target = (cum[-1]+c)/2
l_idx = bisect_right(cum, l_target)
r_idx = bisect_right(cum, r_target)
if abs(l_target-cum[l_idx])<=abs(l_target-cum[l_idx-1]):
first = cum[l_idx]
else:
first = cum[l_idx-1]
second = c-first
if abs(r_target-cum[r_idx])<=abs(r_target-cum[r_idx-1]):
third = cum[r_idx]-c
forth = cum[-1]-cum[r_idx]
else:
third = cum[r_idx-1]-c
forth = cum[-1]-cum[r_idx-1]
lis = [first, second, third, forth]
ans = min(ans, max(lis)-min(lis))
print(ans)
``` | output | 1 | 47,773 | 16 | 95,547 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has an integer sequence A of length N.
He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E. The positions of the cuts can be freely chosen.
Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively. Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller. Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Constraints
* 4 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Examples
Input
5
3 2 4 1 2
Output
2
Input
10
10 71 84 33 6 47 23 25 52 64
Output
36
Input
7
1 2 3 1000000000 4 5 6
Output
999999994 | instruction | 0 | 47,774 | 16 | 95,548 |
"Correct Solution:
```
n=int(input())
l=[0]+list(map(int,input().split()))
from itertools import accumulate
l=list(accumulate(l))
from bisect import bisect, bisect_left, bisect_right
ans=10**15
for i in range(2,n-1):
x=bisect_left(l,l[i]//2)
p1=l[x]
p2=l[x-1]
if abs(l[i]-p1*2)>=abs(l[i]-p2*2):
p=p2
else:
p=p1
q=l[i]-p
x=bisect_left(l,(l[n]-l[i])//2+l[i])
r1=l[x]-l[i]
r2=l[x-1]-l[i]
if abs(l[n]-l[i]-r1*2)>=abs(l[n]-l[i]-r2*2):
r=r2
else:
r=r1
s=l[n]-l[i]-r
ans=min(ans,max(p,q,r,s)-min(p,q,r,s))
print(ans)
``` | output | 1 | 47,774 | 16 | 95,549 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke has an integer sequence A of length N.
He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E. The positions of the cuts can be freely chosen.
Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively. Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller. Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Constraints
* 4 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Examples
Input
5
3 2 4 1 2
Output
2
Input
10
10 71 84 33 6 47 23 25 52 64
Output
36
Input
7
1 2 3 1000000000 4 5 6
Output
999999994 | instruction | 0 | 47,775 | 16 | 95,550 |
"Correct Solution:
```
import functools
N = int(input())
A = [int(x) for x in input().split()]
P = A[0]
Q = A[1]
R = A[2]
S = functools.reduce(lambda x, y: x + y, A[3:])
i = 1
k = 3
SR_pre = abs(S - R)
for m in range(k, N - 1):
SR_post = abs(S - R - 2 * A[m])
if SR_post <= SR_pre:
SR_pre = SR_post
R += A[m]
S -= A[m]
k = m + 1
else:
break
ans = max(P, Q, R, S) - min(P, Q, R, S)
for j in range(2, N - 2):
Q += A[j]
QP_pre = abs(Q - P)
for l in range(i, j):
QP_post = abs(Q - P - 2 * A[l])
if QP_post <= QP_pre:
QP_pre = QP_post
P += A[l]
Q -= A[l]
i = l + 1
else:
break
R -= A[j]
SR_pre = abs(S - R)
for m in range(k, N - 1):
SR_post = abs(S - R - 2 * A[m])
if SR_post <= SR_pre:
SR_pre = SR_post
R += A[m]
S -= A[m]
k = m + 1
else:
break
ans = min(ans, max(P,Q, R, S) - min(P, Q, R, S))
print(ans)
``` | output | 1 | 47,775 | 16 | 95,551 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has an integer sequence A of length N.
He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E. The positions of the cuts can be freely chosen.
Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively. Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller. Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Constraints
* 4 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Examples
Input
5
3 2 4 1 2
Output
2
Input
10
10 71 84 33 6 47 23 25 52 64
Output
36
Input
7
1 2 3 1000000000 4 5 6
Output
999999994
Submitted Solution:
```
N = int(input())
ai = list(map(int,input().split()))
sumai = []
s = 0
for i in ai:
s += i
sumai.append(s)
lcut = 0 # l1 = sumai[lcut]
rcut = 2 # r2 = sumai[N-1]-sumai[rcut]
l1 = sumai[lcut]
r2 = sumai[N-1]-sumai[rcut]
ans = []
for i in range(1,N-2):
while abs(sumai[lcut]-(sumai[i]-sumai[lcut]))>abs(sumai[lcut+1]-(sumai[i]-sumai[lcut+1])):
lcut += 1
while abs((sumai[N-1]-sumai[rcut])-(sumai[rcut]-sumai[i]))>abs((sumai[N-1]-sumai[rcut+1])-(sumai[rcut+1]-sumai[i])):
rcut += 1
ans.append(max(sumai[lcut],sumai[i]-sumai[lcut],sumai[N-1]-sumai[rcut],sumai[rcut]-sumai[i])-min(sumai[lcut],sumai[i]-sumai[lcut],sumai[N-1]-sumai[rcut],sumai[rcut]-sumai[i]))
print(min(ans))
``` | instruction | 0 | 47,776 | 16 | 95,552 |
Yes | output | 1 | 47,776 | 16 | 95,553 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has an integer sequence A of length N.
He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E. The positions of the cuts can be freely chosen.
Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively. Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller. Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Constraints
* 4 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Examples
Input
5
3 2 4 1 2
Output
2
Input
10
10 71 84 33 6 47 23 25 52 64
Output
36
Input
7
1 2 3 1000000000 4 5 6
Output
999999994
Submitted Solution:
```
N = int(input())
A = list(map(int,input().split()))
SUM = sum(A)
left = 0
right = 0
L = 0
M = 0
R = 0
ans = float('inf')
for mid in range(N):
while abs(M - 2 * L) > abs(M - 2 * L - 2 * A[left]):
L += A[left]
left += 1
while right < N and abs(SUM + M - 2 * R) > abs(SUM + M - 2 * R - 2 * A[right]):
R += A[right]
right += 1
ans = min(ans, max(L, M - L, R - M, SUM - R) - min(L, M - L, R - M, SUM - R))
M += A[mid]
print(ans)
``` | instruction | 0 | 47,777 | 16 | 95,554 |
Yes | output | 1 | 47,777 | 16 | 95,555 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has an integer sequence A of length N.
He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E. The positions of the cuts can be freely chosen.
Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively. Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller. Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Constraints
* 4 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Examples
Input
5
3 2 4 1 2
Output
2
Input
10
10 71 84 33 6 47 23 25 52 64
Output
36
Input
7
1 2 3 1000000000 4 5 6
Output
999999994
Submitted Solution:
```
from itertools import accumulate
from bisect import bisect_right
N = int(input())
A = list(map(int, input().split()))
# 累積和を前計算
cumsum = list(accumulate(A))
cumsum.insert(0, 0)
#print(cumsum)
ans = float('inf')
# 真ん中を全探索
for i in range(2, N-1):
#print(A[:i], A[i:])
# 左の真ん中
LC = cumsum[i] / 2
LX = bisect_right(cumsum, LC)
#print(LX)
# 超えるべきか超えないべきか
if abs(cumsum[LX-1] - LC) < abs(cumsum[LX] - LC):
LX -= 1
# 右の真ん中
RC = (cumsum[N] + cumsum[i]) / 2
RX = bisect_right(cumsum, RC)
# 超えるべきか超えないべきか
if abs(cumsum[RX-1] - RC) < abs(cumsum[RX] - RC):
RX -= 1
P, Q, R, S = cumsum[LX], cumsum[i]-cumsum[LX], cumsum[RX]-cumsum[i], cumsum[N]-cumsum[RX]
ans = min(ans, max(P, Q, R, S) - min(P, Q, R, S))
print(ans)
``` | instruction | 0 | 47,778 | 16 | 95,556 |
Yes | output | 1 | 47,778 | 16 | 95,557 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke has an integer sequence A of length N.
He will make three cuts in A and divide it into four (non-empty) contiguous subsequences B, C, D and E. The positions of the cuts can be freely chosen.
Let P,Q,R,S be the sums of the elements in B,C,D,E, respectively. Snuke is happier when the absolute difference of the maximum and the minimum among P,Q,R,S is smaller. Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Constraints
* 4 \leq N \leq 2 \times 10^5
* 1 \leq A_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Find the minimum possible absolute difference of the maximum and the minimum among P,Q,R,S.
Examples
Input
5
3 2 4 1 2
Output
2
Input
10
10 71 84 33 6 47 23 25 52 64
Output
36
Input
7
1 2 3 1000000000 4 5 6
Output
999999994
Submitted Solution:
```
N = int(input())
A = list(map(int, input().split()))
from itertools import accumulate
ans = float("inf")
if N == 4:
ans = min(ans, (max(A) - min(A)))
else:
cs = list(accumulate(A))
l = 0
r = 0
for i in range(1, N - 2):
while cs[i] > cs[l] + cs[l+1]:
l += 1
while cs[-1] + cs[i] > cs[r] + cs[r+1]:
r += 1
P = cs[l]
Q = cs[i] - P
R = cs[r] - P - Q
S = cs[-1] - cs[r]
ans = min(ans, (max(P, Q, R, S) - min(P, Q, R, S)))
print(ans)
``` | instruction | 0 | 47,779 | 16 | 95,558 |
Yes | output | 1 | 47,779 | 16 | 95,559 |
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