message stringlengths 2 433k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 113 108k | cluster float64 12 12 | __index_level_0__ int64 226 217k |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1]. | instruction | 0 | 92,790 | 12 | 185,580 |
Tags: greedy, two pointers
Correct Solution:
```
t=int(input())
while t>0 :
n=int(input())
l=list(map(int,input().split()))
ans=[0,abs(l[1]-l[0])]
a=[l[0]]
for i in range(2,n) :
if ans[i-1]+abs(l[i]-l[i-1]) > ans[i-2]+abs(l[i]-l[i-2]) :
ans.append(ans[i-1]+abs(l[i]-l[i-1]))
a.append(l[i-1])
else :
ans.append(ans[i-2]+abs(l[i]-l[i-2]))
a.append(l[-1])
print(len(a))
for i in a :
print(i,end=" ")
print()
#print(ans)
#print(ans[n-1])
t-=1
``` | output | 1 | 92,790 | 12 | 185,581 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1]. | instruction | 0 | 92,791 | 12 | 185,582 |
Tags: greedy, two pointers
Correct Solution:
```
import sys
input = sys.stdin.readline
for T in range(int(input())) :
n = int(input())
arr = list(map(int ,input().split()))
inc = False
dec = False
res =[arr[0]]
for i in range(1,n):
if arr[i] < arr[i-1] :
if dec :
res.pop()
res.append(arr[i])
dec = True
inc = False
elif arr[i] > arr[i-1]:
if inc :
res.pop()
res.append(arr[i])
dec = False
inc = True
print(len(res))
print(*res)
``` | output | 1 | 92,791 | 12 | 185,583 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1]. | instruction | 0 | 92,792 | 12 | 185,584 |
Tags: greedy, two pointers
Correct Solution:
```
for _ in range(int(input())):
n=int(input())
ar=list(map(int,input().split()))
ans=[ar[0]]
for i in range(1,n-1):
if ar[i]>ar[i-1] and ar[i]>ar[i+1]:
ans.append(ar[i])
elif ar[i]<ar[i-1] and ar[i]<ar[i+1]:
ans.append(ar[i])
ans.append(ar[-1])
print(len(ans))
for i in ans:
print(i,end= ' ')
print('')
``` | output | 1 | 92,792 | 12 | 185,585 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1]. | instruction | 0 | 92,793 | 12 | 185,586 |
Tags: greedy, two pointers
Correct Solution:
```
for _ in range(int(input())):
n = int(input())
l = list(map(int,input().split()))
k = [] # new list after removing
c = ''
if l[0] < l[1]:
c = 'i' # increasing
else:
c = 'd' # decreasing
# x = 1 # start of sequence
# count = 0
# for i in range(0,n-1):
# if (l[i] <= l[i+1] and c == 'd') or (l[i] >= l[i+1] and c == 'i'): # change in increse/decrease
# # sequence: 1 -> i
# k.append(str(x)) # 1st element
# k.append(str(i)) # last element
# x = i # reset first element to last element of previous sequence
# count += 1
#
# if count == 0:
# print(2)
# print(l[0],l[-1])
k.append(l[0])
k.append(l[1])
for i in range(1,n-1):
if l[i] <= l[i+1]:
if c == 'i':
k[len(k)-1] = l[i+1]
else:
k.append(l[i+1])
c = 'i'
elif l[i] >= l[i+1]:
if c == 'd':
k[len(k)-1] = l[i+1]
else:
k.append(l[i+1])
c = 'd'
print(len(k))
print(' '.join(map(str,k)))
# 3 7 2 4 5 6 1
# 4 5 2 1 1 5 = 18
# 3 7 2 x x 6 1
``` | output | 1 | 92,793 | 12 | 185,587 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1]. | instruction | 0 | 92,794 | 12 | 185,588 |
Tags: greedy, two pointers
Correct Solution:
```
import sys
max_int = 1000000001 # 10^9+1
min_int = -max_int
t = int(input())
for _t in range(t):
n = int(sys.stdin.readline())
p = list(map(int, sys.stdin.readline().split()))
d = prev_d = 0
out = [p[0]]
for i in range(1, n):
if p[i] == p[i - 1]:
continue
if p[i] > p[i - 1]:
d = 1
else:
d = -1
if not prev_d:
prev_d = d
if d and d != prev_d:
out.append(p[i - 1])
prev_d = d
out.append(p[-1])
print(len(out))
print(' '.join(map(str, out)))
``` | output | 1 | 92,794 | 12 | 185,589 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1]. | instruction | 0 | 92,795 | 12 | 185,590 |
Tags: greedy, two pointers
Correct Solution:
```
import re
import sys
from bisect import bisect, bisect_left, insort, insort_left
from collections import Counter, defaultdict, deque
from copy import deepcopy
from decimal import Decimal
from itertools import (
accumulate, combinations, combinations_with_replacement, groupby,
permutations, product)
from math import (acos, asin, atan, ceil, cos, degrees, factorial, gcd, hypot,
log2, pi, radians, sin, sqrt, tan)
from operator import itemgetter, mul
from string import ascii_lowercase, ascii_uppercase, digits
def inp():
return(int(input()))
def inlist():
return(list(map(int, input().split())))
def instr():
s = input()
return(list(s[:len(s)]))
def invr():
return(map(int, input().split()))
t = inp()
for _ in range(t):
n = inp()
a = inlist()
res = []
res.append(a[0])
flip = 0
if a[1] < a[0]:
flip = 1
for i in range(1, n):
if flip == 0 and a[i] < a[i-1]:
res.append(a[i-1])
flip = 1
elif flip == 1 and a[i] >= a[i-1]:
res.append(a[i-1])
flip = 0
res.append(a[n-1])
print(len(res))
print(*res)
``` | output | 1 | 92,795 | 12 | 185,591 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1]. | instruction | 0 | 92,796 | 12 | 185,592 |
Tags: greedy, two pointers
Correct Solution:
```
import sys
from sys import stdin
input = sys.stdin.readline
for _ in range(int(input())):
n=int(input())
arr=[int(j) for j in input().split()]
res=[]
res.append(arr[0])
count=0
for i in range(1,n-1):
if (arr[i-1]<arr[i] and arr[i]>arr[i+1]) or (arr[i-1]>arr[i] and arr[i]<arr[i+1]) :
res.append(arr[i])
res.append(arr[-1])
print(len(res))
print(*res)
``` | output | 1 | 92,796 | 12 | 185,593 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1]. | instruction | 0 | 92,797 | 12 | 185,594 |
Tags: greedy, two pointers
Correct Solution:
```
t = int(input())
for _ in range(t):
n1 = int(input())
a= list(map(int,input().split()))
g = []
inc = -1
c=0
n=0
# f = a[i-1]
for i in range(1,n1):
if a[i]>a[i-1]:
if n>0:
g.append(f)
# g.append(a[i-1])
n=0
c=1
inc=0
f=a[i-1]
elif inc==0:
c+=1
elif c==0:
inc=0
c=1
f = a[i-1]
else:
if c>0:
g.append(f)
# g.append(a[i-1])
inc=1
c=0
n=1
inc=1
f=a[i-1]
elif inc==1:
n+=1
elif n==0:
inc=1
n=1
f=a[i-1]
if n==0 and c>=1:
g.append(f)
g.append(a[i])
if c==0 and n>=1:
g.append(f)
g.append(a[i])
print(len(g))
print(*g, sep=" ")
``` | output | 1 | 92,797 | 12 | 185,595 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1].
Submitted Solution:
```
def main():
t = int(input())
for i in range(t):
solve()
def solve():
n = int(input())
arr = list(map(int, input().split(" ")))
if n == 2:
print(n)
print(*arr)
return
prev = arr.pop(0)
numbers = [prev]
amount = 1
while len(arr) > 1:
current = arr.pop(0)
if (current > numbers[amount - 1] and current > arr[0]) or (current < numbers[amount - 1] and current < arr[0]):
amount += 1
prev = current
numbers.append(current)
numbers.append(arr.pop(0))
amount += 1
print(amount)
print(*numbers)
main()
``` | instruction | 0 | 92,798 | 12 | 185,596 |
Yes | output | 1 | 92,798 | 12 | 185,597 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1].
Submitted Solution:
```
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,copy,functools
# import time,random,resource
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
mod2 = 998244353
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(): return [list(map(int, l.split())) for l in sys.stdin.readlines()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def pe(s): return print(str(s), file=sys.stderr)
def JA(a, sep): return sep.join(map(str, a))
def JAA(a, s, t): return s.join(t.join(map(str, b)) for b in a)
def IF(c, t, f): return t if c else f
def YES(c): return IF(c, "YES", "NO")
def main():
t = I()
rr = []
for _ in range(t):
n = I()
a = LI()
t = set()
for i in range(1,n-1):
if a[i] == a[i-1]:
t.add(i)
elif a[i-1] < a[i] < a[i+1]:
t.add(i)
elif a[i-1] > a[i] > a[i+1]:
t.add(i)
if a[-1] == a[-2]:
t.add(n-1)
r = [a[i] for i in range(n) if i not in t]
rr.append(len(r))
rr.append(JA(r, " "))
return JA(rr, "\n")
print(main())
``` | instruction | 0 | 92,799 | 12 | 185,598 |
Yes | output | 1 | 92,799 | 12 | 185,599 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1].
Submitted Solution:
```
t = int(input())
for i in range(t):
n= int(input())
ar = [int(i) for i in input().split()]
seq= [ar[0]]
run = ar[0]
count = False
for j in range(n-1):
if (run>ar[j+1]):
run = ar[j+1]
if count==False:
seq.append(run)
sign=False
count=True
elif sign==False:
seq[-1]=run
else:
seq.append(run)
sign=False
elif (run<ar[j+1]):
run = ar[j+1]
if count== False:
seq.append(run)
sign=True
count=True
elif sign==True:
seq[-1]=run
else:
seq.append(run)
sign=True
else:
pass
print(len(seq))
print(' '.join(str(i) for i in seq))
``` | instruction | 0 | 92,800 | 12 | 185,600 |
Yes | output | 1 | 92,800 | 12 | 185,601 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1].
Submitted Solution:
```
import math
t = int(input())
for cnt in range(t):
n = map(int, input().split())
a = list(map(int, input().split()))
num = max(a)
b = list()
sum = 0
for i in a:
temp = len(b)
if(temp == 0):
b.append(i)
if(temp>=1):
if(i!=b[temp-1]):
b.append(i)
temp = len(b)
if(temp>2):
if(abs(b[temp-1]-b[temp-2]) +abs(b[temp-2]-b[temp-3]) <= abs(b[temp-1]-b[temp-3])):
b.pop(temp-2)
print(len(b))
print(*b,sep=" ")
``` | instruction | 0 | 92,801 | 12 | 185,602 |
Yes | output | 1 | 92,801 | 12 | 185,603 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1].
Submitted Solution:
```
#BECAUSE ONE TRUTH PREVAILS
import sys
input=sys.stdin.readline
from collections import defaultdict
for _ in range(int(input())):
N=int(input())
L=list(map(int,input().split()))
i=0
ans=[]
while i<N-1:
pp=L[i]
ans.append(pp)
if L[i]<L[i+1]:
while i<N-1 and L[i]<L[i+1]:
i+=1
ans.append(L[i])
else:
while i<N-1 and L[i]>L[i+1]:
i+=1
ans.append(L[i])
i+=1
if(ans[-1]!=L[N-1]):
ans.append(L[N-1])
print(len(ans))
print(*ans)
``` | instruction | 0 | 92,802 | 12 | 185,604 |
No | output | 1 | 92,802 | 12 | 185,605 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1].
Submitted Solution:
```
for i in range(int(input())):
a=int(input())
b=list(map(int,input().strip().split()))[:a]
j=0
while j<len(b)-2:
if b[j]==b[j+1]:
b.remove(b[j])
elif b[j]>b[j+1]>b[j+2]:
b.remove(b[j+1])
elif b[j]<b[j+1]<b[j+2]:
b.remove(b[j+1])
else:
j+=1
if j+2==len(b):
break
for k in b:
print(k,end=" ")
print(" ")
``` | instruction | 0 | 92,803 | 12 | 185,606 |
No | output | 1 | 92,803 | 12 | 185,607 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1].
Submitted Solution:
```
for _ in range(int(input())):
n = int(input())
l = list(map(int,input().split()))
l1 = l.copy()
if n==2:
print(n)
print(*l)
else:
for i in range(n-2):
if ((l[i]-l[i+1])>0 and (l[i+1]-l[i+2])>0) or ((l[i]-l[i+1])<0 and (l[i+1]-l[i+2])<0) or ((l[i]-l[i+1])+(l[i+1]-l[i+2])==0):
l1.remove(l[i+1])
print(*l1)
``` | instruction | 0 | 92,804 | 12 | 185,608 |
No | output | 1 | 92,804 | 12 | 185,609 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given a permutation p of length n, find its subsequence s_1, s_2, β¦, s_k of length at least 2 such that:
* |s_1-s_2|+|s_2-s_3|+β¦+|s_{k-1}-s_k| is as big as possible over all subsequences of p with length at least 2.
* Among all such subsequences, choose the one whose length, k, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence a is a subsequence of an array b if a can be obtained from b by deleting some (possibly, zero or all) elements.
A permutation of length n is an array of length n in which every element from 1 to n occurs exactly once.
Input
The first line contains an integer t (1 β€ t β€ 2 β
10^4) β the number of test cases. The description of the test cases follows.
The first line of each test case contains an integer n (2 β€ n β€ 10^5) β the length of the permutation p.
The second line of each test case contains n integers p_1, p_2, β¦, p_{n} (1 β€ p_i β€ n, p_i are distinct) β the elements of the permutation p.
The sum of n across the test cases doesn't exceed 10^5.
Output
For each test case, the first line should contain the length of the found subsequence, k. The second line should contain s_1, s_2, β¦, s_k β its elements.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
Example
Input
2
3
3 2 1
4
1 3 4 2
Output
2
3 1
3
1 4 2
Note
In the first test case, there are 4 subsequences of length at least 2:
* [3,2] which gives us |3-2|=1.
* [3,1] which gives us |3-1|=2.
* [2,1] which gives us |2-1|=1.
* [3,2,1] which gives us |3-2|+|2-1|=2.
So the answer is either [3,1] or [3,2,1]. Since we want the subsequence to be as short as possible, the answer is [3,1].
Submitted Solution:
```
t = int(input())
for _ in range(t):
# n, x = map(int, input().split(' '))
# a = list(map(int, input().split(' ')))
n = int(input())
a = list(map(int, input().split(' ')))
ans = [a[0]]
if a[0] > a[1]:
temp = 'small'
else:
temp = 'big'
for i in range(1, n-1):
if (temp == 'big'):
if (a[i] < a[i+1]):
continue
else:
ans.append(a[i])
else:
if (a[i] > a[i+1]):
continue
else:
ans.append(a[i])
if a[i] > a[i+1]:
temp = 'small'
else:
temp = 'big'
ans.append(a[-1])
print(*ans)
``` | instruction | 0 | 92,805 | 12 | 185,610 |
No | output | 1 | 92,805 | 12 | 185,611 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let a_1, β¦, a_n be an array of n positive integers. In one operation, you can choose an index i such that a_i = i, and remove a_i from the array (after the removal, the remaining parts are concatenated).
The weight of a is defined as the maximum number of elements you can remove.
You must answer q independent queries (x, y): after replacing the x first elements of a and the y last elements of a by n+1 (making them impossible to remove), what would be the weight of a?
Input
The first line contains two integers n and q (1 β€ n, q β€ 3 β
10^5) β the length of the array and the number of queries.
The second line contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ n) β elements of the array.
The i-th of the next q lines contains two integers x and y (x, y β₯ 0 and x+y < n).
Output
Print q lines, i-th line should contain a single integer β the answer to the i-th query.
Examples
Input
13 5
2 2 3 9 5 4 6 5 7 8 3 11 13
3 1
0 0
2 4
5 0
0 12
Output
5
11
6
1
0
Input
5 2
1 4 1 2 4
0 0
1 0
Output
2
0
Note
Explanation of the first query:
After making first x = 3 and last y = 1 elements impossible to remove, a becomes [Γ, Γ, Γ, 9, 5, 4, 6, 5, 7, 8, 3, 11, Γ] (we represent 14 as Γ for clarity).
Here is a strategy that removes 5 elements (the element removed is colored in red):
* [Γ, Γ, Γ, 9, \color{red}{5}, 4, 6, 5, 7, 8, 3, 11, Γ]
* [Γ, Γ, Γ, 9, 4, 6, 5, 7, 8, 3, \color{red}{11}, Γ]
* [Γ, Γ, Γ, 9, 4, \color{red}{6}, 5, 7, 8, 3, Γ]
* [Γ, Γ, Γ, 9, 4, 5, 7, \color{red}{8}, 3, Γ]
* [Γ, Γ, Γ, 9, 4, 5, \color{red}{7}, 3, Γ]
* [Γ, Γ, Γ, 9, 4, 5, 3, Γ] (final state)
It is impossible to remove more than 5 elements, hence the weight is 5. | instruction | 0 | 92,822 | 12 | 185,644 |
Tags: binary search, constructive algorithms, data structures, greedy, two pointers
Correct Solution:
```
class Fenwick:
def __init__(self, size):
self.size = size
self.tree = [0] * (size + 1)
def add(self, idx, val):
idx = int(idx)
while idx <= self.size:
self.tree[idx] += val
idx += idx & (-idx)
def sum(self, idx):
ret = 0
idx = int(idx)
while idx > 0:
ret += self.tree[idx]
idx -= idx & (-idx)
return ret
n, q = map(int, input().split())
A = [int(x) for x in input().split()]
A = [A[i] - (i + 1) for i in range(n)]
query = [[] for _ in range(n + 1)]
for i in range(q):
x, y = map(int, input().split())
l, r = x, n - y - 1
query[r].append((l, i))
ft = Fenwick(n + 1)
# ans = [0 for _ in range(q + 3)]
# for r in range(n):
# ob = A[r]
# if ob <= 0:
# if ft.sum(1) >= -ob:
# low, high = 0, r
# while low + 1 < high:
# mid = low + high >> 1;
# if ft.sum(mid + 1) >= -ob:
# low = mid
# else: high = mid
# idx = low
# if ft.sum(high + 1) >= -ob:
# idx = max(idx, high)
# ft.add(1, 1)
# ft.add(idx + 2, -1)
# for qr in query[r]:
# ans[qr[1]] = ft.sum(qr[0] + 1)
#
# for _ in range(q):
# print(ans[_])
ans = [0 for _ in range(q + 3)]
for r in range(n):
ob = A[r]
if ob <= 0:
if ft.sum(1) >= -ob:
low, high = 0, r
while low + 1 < high:
mid = low + high >> 1
if ft.sum(mid + 1) >= -ob:
low = mid
else: high = mid
idx = high if ft.sum(high + 1) >= -ob else low
ft.add(1, 1)
ft.add(idx + 2, -1)
for qr in query[r]:
ans[qr[1]] = ft.sum(qr[0] + 1)
for _ in range(q):
print(ans[_])
``` | output | 1 | 92,822 | 12 | 185,645 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let a_1, β¦, a_n be an array of n positive integers. In one operation, you can choose an index i such that a_i = i, and remove a_i from the array (after the removal, the remaining parts are concatenated).
The weight of a is defined as the maximum number of elements you can remove.
You must answer q independent queries (x, y): after replacing the x first elements of a and the y last elements of a by n+1 (making them impossible to remove), what would be the weight of a?
Input
The first line contains two integers n and q (1 β€ n, q β€ 3 β
10^5) β the length of the array and the number of queries.
The second line contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ n) β elements of the array.
The i-th of the next q lines contains two integers x and y (x, y β₯ 0 and x+y < n).
Output
Print q lines, i-th line should contain a single integer β the answer to the i-th query.
Examples
Input
13 5
2 2 3 9 5 4 6 5 7 8 3 11 13
3 1
0 0
2 4
5 0
0 12
Output
5
11
6
1
0
Input
5 2
1 4 1 2 4
0 0
1 0
Output
2
0
Note
Explanation of the first query:
After making first x = 3 and last y = 1 elements impossible to remove, a becomes [Γ, Γ, Γ, 9, 5, 4, 6, 5, 7, 8, 3, 11, Γ] (we represent 14 as Γ for clarity).
Here is a strategy that removes 5 elements (the element removed is colored in red):
* [Γ, Γ, Γ, 9, \color{red}{5}, 4, 6, 5, 7, 8, 3, 11, Γ]
* [Γ, Γ, Γ, 9, 4, 6, 5, 7, 8, 3, \color{red}{11}, Γ]
* [Γ, Γ, Γ, 9, 4, \color{red}{6}, 5, 7, 8, 3, Γ]
* [Γ, Γ, Γ, 9, 4, 5, 7, \color{red}{8}, 3, Γ]
* [Γ, Γ, Γ, 9, 4, 5, \color{red}{7}, 3, Γ]
* [Γ, Γ, Γ, 9, 4, 5, 3, Γ] (final state)
It is impossible to remove more than 5 elements, hence the weight is 5. | instruction | 0 | 92,823 | 12 | 185,646 |
Tags: binary search, constructive algorithms, data structures, greedy, two pointers
Correct Solution:
```
from sys import stdin
def bitadd(a,w,bit):
x = a
while x <= (len(bit)-1):
bit[x] += w
x += x & (-1 * x)
def bitsum(a,bit):
ret = 0
x = a
while x > 0:
ret += bit[x]
x -= x & (-1 * x)
return ret
class RangeBIT:
def __init__(self,N,indexed):
self.bit1 = [0] * (N+2)
self.bit2 = [0] * (N+2)
self.mode = indexed
def bitadd(self,a,w,bit):
x = a
while x <= (len(bit)-1):
bit[x] += w
x += x & (-1 * x)
def bitsum(self,a,bit):
ret = 0
x = a
while x > 0:
ret += bit[x]
x -= x & (-1 * x)
return ret
def add(self,l,r,w):
l = l + (1-self.mode)
r = r + (1-self.mode)
self.bitadd(l,-1*w*l,self.bit1)
self.bitadd(r,w*r,self.bit1)
self.bitadd(l,w,self.bit2)
self.bitadd(r,-1*w,self.bit2)
def sum(self,l,r):
l = l + (1-self.mode)
r = r + (1-self.mode)
ret = self.bitsum(r,self.bit1) + r * self.bitsum(r,self.bit2)
ret -= self.bitsum(l,self.bit1) + l * self.bitsum(l,self.bit2)
return ret
n,q = map(int,stdin.readline().split());a = list(map(int,stdin.readline().split()));qs = [ [] for i in range(n+1) ];ans = [None] * q;BIT = [0] * (n+1)
for loop in range(q):x,y = map(int,stdin.readline().split());l = x+1;r = n-y;qs[r].append((l,loop))
for r in range(1,n+1):
b = r-a[r-1]
if b >= 0:
L = 1;R = r+1
while R-L != 1:
M = (L+R)//2
if bitsum(M,BIT) >= b:L = M
else:R = M
if bitsum(L,BIT) >= b:bitadd(1,1,BIT);bitadd(L+1,-1,BIT)
for ql,qind in qs[r]:ans[qind] = bitsum(ql,BIT)
for i in ans:print (i)
``` | output | 1 | 92,823 | 12 | 185,647 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let a_1, β¦, a_n be an array of n positive integers. In one operation, you can choose an index i such that a_i = i, and remove a_i from the array (after the removal, the remaining parts are concatenated).
The weight of a is defined as the maximum number of elements you can remove.
You must answer q independent queries (x, y): after replacing the x first elements of a and the y last elements of a by n+1 (making them impossible to remove), what would be the weight of a?
Input
The first line contains two integers n and q (1 β€ n, q β€ 3 β
10^5) β the length of the array and the number of queries.
The second line contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ n) β elements of the array.
The i-th of the next q lines contains two integers x and y (x, y β₯ 0 and x+y < n).
Output
Print q lines, i-th line should contain a single integer β the answer to the i-th query.
Examples
Input
13 5
2 2 3 9 5 4 6 5 7 8 3 11 13
3 1
0 0
2 4
5 0
0 12
Output
5
11
6
1
0
Input
5 2
1 4 1 2 4
0 0
1 0
Output
2
0
Note
Explanation of the first query:
After making first x = 3 and last y = 1 elements impossible to remove, a becomes [Γ, Γ, Γ, 9, 5, 4, 6, 5, 7, 8, 3, 11, Γ] (we represent 14 as Γ for clarity).
Here is a strategy that removes 5 elements (the element removed is colored in red):
* [Γ, Γ, Γ, 9, \color{red}{5}, 4, 6, 5, 7, 8, 3, 11, Γ]
* [Γ, Γ, Γ, 9, 4, 6, 5, 7, 8, 3, \color{red}{11}, Γ]
* [Γ, Γ, Γ, 9, 4, \color{red}{6}, 5, 7, 8, 3, Γ]
* [Γ, Γ, Γ, 9, 4, 5, 7, \color{red}{8}, 3, Γ]
* [Γ, Γ, Γ, 9, 4, 5, \color{red}{7}, 3, Γ]
* [Γ, Γ, Γ, 9, 4, 5, 3, Γ] (final state)
It is impossible to remove more than 5 elements, hence the weight is 5. | instruction | 0 | 92,824 | 12 | 185,648 |
Tags: binary search, constructive algorithms, data structures, greedy, two pointers
Correct Solution:
```
from sys import stdin
def bitadd(a,w,bit):
x = a
while x <= (len(bit)-1):
bit[x] += w
x += x & (-1 * x)
def bitsum(a,bit):
ret = 0
x = a
while x > 0:
ret += bit[x]
x -= x & (-1 * x)
return ret
class RangeBIT:
def __init__(self,N,indexed):
self.bit1 = [0] * (N+2)
self.bit2 = [0] * (N+2)
self.mode = indexed
def bitadd(self,a,w,bit):
x = a
while x <= (len(bit)-1):
bit[x] += w
x += x & (-1 * x)
def bitsum(self,a,bit):
ret = 0
x = a
while x > 0:
ret += bit[x]
x -= x & (-1 * x)
return ret
def add(self,l,r,w):
l = l + (1-self.mode)
r = r + (1-self.mode)
self.bitadd(l,-1*w*l,self.bit1)
self.bitadd(r,w*r,self.bit1)
self.bitadd(l,w,self.bit2)
self.bitadd(r,-1*w,self.bit2)
def sum(self,l,r):
l = l + (1-self.mode)
r = r + (1-self.mode)
ret = self.bitsum(r,self.bit1) + r * self.bitsum(r,self.bit2)
ret -= self.bitsum(l,self.bit1) + l * self.bitsum(l,self.bit2)
return ret
n,q = map(int,stdin.readline().split())
a = list(map(int,stdin.readline().split()))
qs = [ [] for i in range(n+1) ]
ans = [None] * q
for loop in range(q):
x,y = map(int,stdin.readline().split())
l = x+1
r = n-y
qs[r].append((l,loop))
BIT = [0] * (n+1)
for r in range(1,n+1):
b = r-a[r-1]
if b >= 0:
L = 1
R = r+1
while R-L != 1:
M = (L+R)//2
if bitsum(M,BIT) >= b:
L = M
else:
R = M
if bitsum(L,BIT) >= b:
bitadd(1,1,BIT)
bitadd(L+1,-1,BIT)
for ql,qind in qs[r]:
ans[qind] = bitsum(ql,BIT)
for i in ans:
print (i)
``` | output | 1 | 92,824 | 12 | 185,649 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let a_1, β¦, a_n be an array of n positive integers. In one operation, you can choose an index i such that a_i = i, and remove a_i from the array (after the removal, the remaining parts are concatenated).
The weight of a is defined as the maximum number of elements you can remove.
You must answer q independent queries (x, y): after replacing the x first elements of a and the y last elements of a by n+1 (making them impossible to remove), what would be the weight of a?
Input
The first line contains two integers n and q (1 β€ n, q β€ 3 β
10^5) β the length of the array and the number of queries.
The second line contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ n) β elements of the array.
The i-th of the next q lines contains two integers x and y (x, y β₯ 0 and x+y < n).
Output
Print q lines, i-th line should contain a single integer β the answer to the i-th query.
Examples
Input
13 5
2 2 3 9 5 4 6 5 7 8 3 11 13
3 1
0 0
2 4
5 0
0 12
Output
5
11
6
1
0
Input
5 2
1 4 1 2 4
0 0
1 0
Output
2
0
Note
Explanation of the first query:
After making first x = 3 and last y = 1 elements impossible to remove, a becomes [Γ, Γ, Γ, 9, 5, 4, 6, 5, 7, 8, 3, 11, Γ] (we represent 14 as Γ for clarity).
Here is a strategy that removes 5 elements (the element removed is colored in red):
* [Γ, Γ, Γ, 9, \color{red}{5}, 4, 6, 5, 7, 8, 3, 11, Γ]
* [Γ, Γ, Γ, 9, 4, 6, 5, 7, 8, 3, \color{red}{11}, Γ]
* [Γ, Γ, Γ, 9, 4, \color{red}{6}, 5, 7, 8, 3, Γ]
* [Γ, Γ, Γ, 9, 4, 5, 7, \color{red}{8}, 3, Γ]
* [Γ, Γ, Γ, 9, 4, 5, \color{red}{7}, 3, Γ]
* [Γ, Γ, Γ, 9, 4, 5, 3, Γ] (final state)
It is impossible to remove more than 5 elements, hence the weight is 5. | instruction | 0 | 92,825 | 12 | 185,650 |
Tags: binary search, constructive algorithms, data structures, greedy, two pointers
Correct Solution:
```
from sys import stdin
def bitadd(a,w,bit):
x = a
while x <= (len(bit)-1):bit[x] += w;x += x & (-1 * x)
def bitsum(a,bit):
ret = 0;x = a
while x > 0:ret += bit[x];x -= x & (-1 * x)
return ret
class RangeBIT:
def __init__(self,N,indexed):self.bit1 = [0] * (N+2);self.bit2 = [0] * (N+2);self.mode = indexed
def bitadd(self,a,w,bit):
x = a
while x <= (len(bit)-1):bit[x] += w;x += x & (-1 * x)
def bitsum(self,a,bit):
ret = 0;x = a
while x > 0:ret += bit[x];x -= x & (-1 * x)
return ret
def add(self,l,r,w):l = l + (1-self.mode);r = r + (1-self.mode);self.bitadd(l,-1*w*l,self.bit1);self.bitadd(r,w*r,self.bit1);self.bitadd(l,w,self.bit2);self.bitadd(r,-1*w,self.bit2)
def sum(self,l,r):l = l + (1-self.mode);r = r + (1-self.mode);ret = self.bitsum(r,self.bit1) + r * self.bitsum(r,self.bit2);ret -= self.bitsum(l,self.bit1) + l * self.bitsum(l,self.bit2);return ret
n,q = map(int,stdin.readline().split());a = list(map(int,stdin.readline().split()));qs = [ [] for i in range(n+1) ];ans = [None] * q;BIT = [0] * (n+1)
for loop in range(q):x,y = map(int,stdin.readline().split());l = x+1;r = n-y;qs[r].append((l,loop))
for r in range(1,n+1):
b = r-a[r-1]
if b >= 0:
L = 1;R = r+1
while R-L != 1:
M = (L+R)//2
if bitsum(M,BIT) >= b:L = M
else:R = M
if bitsum(L,BIT) >= b:bitadd(1,1,BIT);bitadd(L+1,-1,BIT)
for ql,qind in qs[r]:ans[qind] = bitsum(ql,BIT)
for i in ans:print (i)
``` | output | 1 | 92,825 | 12 | 185,651 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27. | instruction | 0 | 92,826 | 12 | 185,652 |
Tags: math, sortings
Correct Solution:
```
for _ in range(int(input())):
input();a = list(map(int, input().split()))
s = sum(a)
if s==0:print('NO')
else:
print('YES')
if s>0: print(*sorted(a, reverse=True))
else: print(*sorted(a))
``` | output | 1 | 92,826 | 12 | 185,653 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27. | instruction | 0 | 92,827 | 12 | 185,654 |
Tags: math, sortings
Correct Solution:
```
t = int(input())
q = []
for i in range(t):
n = int(input())
l = list(map(int, list(input().split())))
if sum(l) == 0:
q.append(["NO"])
else:
l.sort()
q.append(["YES"])
if sum(l) > 0:
q.append(l[::-1])
else:
q.append(l)
for i in q:
for j in i:
print(j, end=" ")
print()
``` | output | 1 | 92,827 | 12 | 185,655 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27. | instruction | 0 | 92,828 | 12 | 185,656 |
Tags: math, sortings
Correct Solution:
```
t = int(input())
for _ in range(t):
n = int(input())
a = list(map(int, input().split()))
if sum(a) == 0:
print('NO')
elif sum(a) > 0:
print('YES')
print(*sorted(a, reverse=True))
else:
print('YES')
print(*sorted(a))
``` | output | 1 | 92,828 | 12 | 185,657 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27. | instruction | 0 | 92,829 | 12 | 185,658 |
Tags: math, sortings
Correct Solution:
```
t = int(input())
for _ in range(t):
n = int(input())
a = list(sorted(map(int,input().split())))
def judge(a):
cum = 0
for i in range(n):
cum += a[i]
if cum == 0:
flag = True
for k in range(i+1,n):
if a[k] != a[i]:
cum += a[k] - a[i]
tmp = a[i]
a[i] = a[k]
a[k] = tmp
flag = False
break
if flag:
return False
return True
if judge(a):
print("YES")
print(*a)
elif judge(a[::-1]):
print("YES")
print(*a[::-1])
else:
print("NO")
``` | output | 1 | 92,829 | 12 | 185,659 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27. | instruction | 0 | 92,830 | 12 | 185,660 |
Tags: math, sortings
Correct Solution:
```
def function():
n=int(input())
a=list(map(int,input().split()))
temp=[]
b=[]
flag=0
if sum(a)==0:
print("NO")
else:
sum1=0
sum2=0
for i in a:
if i>0:
sum1=sum1+i
temp.append(i)
for i in a:
if i<0:
sum2=sum2+i
temp.append(i)
if abs(sum1)<abs(sum2):
temp.reverse()
# print(temp)
for i in a:
if i==0:
temp.append(i)
s_um=0
for value in temp:
s_um=s_um+value
if s_um==0:
print("NO")
flag=1
return
if flag==0:
print("YES")
print(*temp)
return
if __name__=="__main__":
tests=int(input())
for test in range(tests):
function()
``` | output | 1 | 92,830 | 12 | 185,661 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27. | instruction | 0 | 92,831 | 12 | 185,662 |
Tags: math, sortings
Correct Solution:
```
T = int( input() )
for t in range(T):
n = int( input() )
st = input().split()
A = []
s = 0
for i in range(n):
A.append( int( st[i] ) )
s += A[i]
if s == 0:
print("NO")
continue
else:
print("YES")
if s > 0:
A = sorted(A, reverse=True)
else:
A = sorted(A)
if A[0] == 0:
for i in range(n):
if A[i] != 0:
A[0], A[i] = A[i], A[0]
break
for i in range(n):
print(A[i], end = " ")
print()
``` | output | 1 | 92,831 | 12 | 185,663 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27. | instruction | 0 | 92,832 | 12 | 185,664 |
Tags: math, sortings
Correct Solution:
```
for test in range(int(input())):
n = int(input())
a = list(map(int, input().split()))
a.sort()
if sum(a)==0:
print("NO")
elif sum(a)>0:
print("YES")
print(*a[::-1])
else:
print("YES")
print(*a)
``` | output | 1 | 92,832 | 12 | 185,665 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27. | instruction | 0 | 92,833 | 12 | 185,666 |
Tags: math, sortings
Correct Solution:
```
t = int(input())
for i in range(t):
n = int(input())
a = list(map(int, input().split()))
arr = []
if sum(a) == 0:
print("NO")
elif sum(a) > 0:
a.sort(reverse=True)
print("YES")
print(*a)
elif sum(a) < 0:
a.sort()
print("YES")
print(*a)
``` | output | 1 | 92,833 | 12 | 185,667 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27.
Submitted Solution:
```
import sys
input = sys.stdin.readline
def main():
n = int(input())
alst = list(map(int, input().split()))
total = sum(alst)
if total == 0:
print("NO")
return
print("YES")
alst.sort()
if total > 0:
print(*alst[::-1])
else:
print(*alst)
for _ in range(int(input())):
main()
``` | instruction | 0 | 92,834 | 12 | 185,668 |
Yes | output | 1 | 92,834 | 12 | 185,669 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27.
Submitted Solution:
```
t = int(input())
for _ in range(t):
n = int(input())
arr = list(map(int, input().split()))
if sum(arr) == 0:
print('NO')
elif sum(arr) > 0:
print('YES')
arr = sorted(arr, reverse=True)
print(' '.join(list(map(str, arr))))
elif sum(arr) < 0:
print('YES')
arr = sorted(arr)
print(' '.join(list(map(str, arr))))
``` | instruction | 0 | 92,835 | 12 | 185,670 |
Yes | output | 1 | 92,835 | 12 | 185,671 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27.
Submitted Solution:
```
import os
import sys
from io import BytesIO, IOBase
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")
##########################################################
import math
import bisect
# for _ in range(int(input())):
from collections import Counter
# sys.setrecursionlimit(10**6)
# dp=[[-1 for i in range(n+5)]for j in range(cap+5)]
# arr= list(map(int, input().split()))
# n,m= map(int, input().split())
# arr= list(map(int, input().split()))
# for _ in range(int(input())):
import bisect
# n=int(input())
for _ in range(int(input())):
n=int(input())
#n,m=map(int, input().split())
arr= list(map(int, input().split()))
#arr=[0]*50
#ls=sorted(arr)
#ls=ls[::-1]
if sum(arr)==0:
print("NO")
else:
ne=[]
p=[]
z=[]
for i in range(n):
if arr[i]>0:
p.append(arr[i])
elif arr[i]==0:
z.append(0)
else:
ne.append(arr[i])
if sum(p)>abs(sum(ne)):
ans=p+ne+z
print("YES")
print(*ans)
elif sum(p)<abs(sum(ne)):
ans=ne+p+z
print("YES")
print(*ans)
else:
print("NO")
``` | instruction | 0 | 92,836 | 12 | 185,672 |
Yes | output | 1 | 92,836 | 12 | 185,673 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27.
Submitted Solution:
```
for _ in range(int(input())):
n=int(input())
a=list(map(int,input().split()))
if(sum(a)==0):
print("NO")
else:
l1=[]
l2=[]
print("YES")
pos=0
neg=0
z=[]
for i in range(n):
if(a[i]>0):
l1.append(a[i])
pos=pos+a[i]
elif(a[i]<0):
l2.append(a[i])
neg=neg+a[i]
else:
z.append(a[i])
if(pos>abs(neg)):
print(*l1,*l2,*z)
else:
print(*l2,*l1,*z)
``` | instruction | 0 | 92,837 | 12 | 185,674 |
Yes | output | 1 | 92,837 | 12 | 185,675 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27.
Submitted Solution:
```
# ========== //\\ //|| ||====//||
# || // \\ || || // ||
# || //====\\ || || // ||
# || // \\ || || // ||
# ========== // \\ ======== ||//====||
# code
def solve():
n = int(input())
a = list(map(int, input().split()))
if sum(a) == 0:
print('NO')
return
a.sort(reverse = True)
b = []
c = []
s = 0
for i in a:
s += i
if s == 0:
s -= i
c.append(i)
else:
b.append(i)
print('YES')
print(*(b + c))
return
def main():
t = 1
t = int(input())
for _ in range(t):
solve()
if __name__ == "__main__":
main()
``` | instruction | 0 | 92,838 | 12 | 185,676 |
No | output | 1 | 92,838 | 12 | 185,677 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27.
Submitted Solution:
```
# import sys; input = sys.stdin.buffer.readline
# sys.setrecursionlimit(10**7)
from collections import defaultdict
mod = 10 ** 9 + 7; INF = float("inf")
def getlist():
return list(map(int, input().split()))
def main():
T = int(input())
for _ in range(T):
N = int(input())
A = getlist()
S = sum(A)
if S == 0:
print("NO")
elif S < 0:
A.sort()
print("YES")
print(*A)
else:
print(A.sort(reverse=True))
print("YES")
print(*A)
if __name__ == '__main__':
main()
``` | instruction | 0 | 92,839 | 12 | 185,678 |
No | output | 1 | 92,839 | 12 | 185,679 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27.
Submitted Solution:
```
def main():
for _ in range(int(input())):
n=int(input())
a=list(map(int,input().split()))
if(sum(a)==0):
print('NO')
else:
print('YES')
l=[]
i,s=0,0
while(i<n):
for j in range(len(a)):
if(s+a[j]!=0):
l.append(a[j])
s+=a[j]
del a[j]
break
i+=1
print(*l)
main()
``` | instruction | 0 | 92,840 | 12 | 185,680 |
No | output | 1 | 92,840 | 12 | 185,681 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array of n integers a_1,a_2,...,a_n.
You have to create an array of n integers b_1,b_2,...,b_n such that:
* The array b is a rearrangement of the array a, that is, it contains the same values and each value appears the same number of times in the two arrays. In other words, the multisets \\{a_1,a_2,...,a_n\} and \\{b_1,b_2,...,b_n\} are equal.
For example, if a=[1,-1,0,1], then b=[-1,1,1,0] and b=[0,1,-1,1] are rearrangements of a, but b=[1,-1,-1,0] and b=[1,0,2,-3] are not rearrangements of a.
* For all k=1,2,...,n the sum of the first k elements of b is nonzero. Formally, for all k=1,2,...,n, it must hold $$$b_1+b_2+β
β
β
+b_knot=0 .$$$
If an array b_1,b_2,..., b_n with the required properties does not exist, you have to print NO.
Input
Each test contains multiple test cases. The first line contains an integer t (1β€ t β€ 1000) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains one integer n (1β€ nβ€ 50) β the length of the array a.
The second line of each testcase contains n integers a_1,a_2,..., a_n (-50β€ a_iβ€ 50) β the elements of a.
Output
For each testcase, if there is not an array b_1,b_2,...,b_n with the required properties, print a single line with the word NO.
Otherwise print a line with the word YES, followed by a line with the n integers b_1,b_2,...,b_n.
If there is more than one array b_1,b_2,...,b_n satisfying the required properties, you can print any of them.
Example
Input
4
4
1 -2 3 -4
3
0 0 0
5
1 -1 1 -1 1
6
40 -31 -9 0 13 -40
Output
YES
1 -2 3 -4
NO
YES
1 1 -1 1 -1
YES
-40 13 40 0 -9 -31
Note
Explanation of the first testcase: An array with the desired properties is b=[1,-2,3,-4]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is -1.
* The sum of the first three elements of b is 2.
* The sum of the first four elements of b is -2.
Explanation of the second testcase: Since all values in a are 0, any rearrangement b of a will have all elements equal to 0 and therefore it clearly cannot satisfy the second property described in the statement (for example because b_1=0). Hence in this case the answer is NO.
Explanation of the third testcase: An array with the desired properties is b=[1, 1, -1, 1, -1]. For this array, it holds:
* The first element of b is 1.
* The sum of the first two elements of b is 2.
* The sum of the first three elements of b is 1.
* The sum of the first four elements of b is 2.
* The sum of the first five elements of b is 1.
Explanation of the fourth testcase: An array with the desired properties is b=[-40,13,40,0,-9,-31]. For this array, it holds:
* The first element of b is -40.
* The sum of the first two elements of b is -27.
* The sum of the first three elements of b is 13.
* The sum of the first four elements of b is 13.
* The sum of the first five elements of b is 4.
* The sum of the first six elements of b is -27.
Submitted Solution:
```
for _ in range(int(input())):
n=int(input())
l=list(map(int,input().split()))
if set(l)=={0}:
print('NO')
else:
pos,neg=[],[]
s=0
for x in range(n):
if l[x] >=0:
pos.append(l[x])
s+=l[x]
else:
neg.append(l[x])
for x in pos:
if -x not in pos:
print('YES')
pos=pos[::-1]
for x in range(len(neg)):
if neg[x]==-(s) and s!=0:
pos.append(neg[x])
pos[x],pos[x-1]=pos[x-1],pos[x]
else:pos.append(neg[x])
print(*pos)
break
else:
print('NO')
``` | instruction | 0 | 92,841 | 12 | 185,682 |
No | output | 1 | 92,841 | 12 | 185,683 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Note that the memory limit is unusual.
You are given an integer n and two sequences a_1, a_2, ..., a_n and b_1, b_2, ..., b_n.
Let's call a set of integers S such that S β \{1, 2, 3, ..., n\} strange, if, for every element i of S, the following condition is met: for every j β [1, i - 1], if a_j divides a_i, then j is also included in S. An empty set is always strange.
The cost of the set S is β_{i β S} b_i. You have to calculate the maximum possible cost of a strange set.
Input
The first line contains one integer n (1 β€ n β€ 3000).
The second line contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100).
The third line contains n integers b_1, b_2, ..., b_n (-10^5 β€ b_i β€ 10^5).
Output
Print one integer β the maximum cost of a strange set.
Examples
Input
9
4 7 3 4 5 6 7 8 13
-2 3 -19 5 -6 7 -8 9 1
Output
16
Input
2
42 42
-37 13
Output
0
Input
2
42 42
13 -37
Output
13
Note
The strange set with the maximum cost in the first example is \{1, 2, 4, 8, 9\}.
The strange set with the maximum cost in the second example is empty. | instruction | 0 | 92,859 | 12 | 185,718 |
Tags: flows, math
Correct Solution:
```
# Author: yumtam
# Created at: 2021-03-02 20:19
def main():
n = int(input())
A = [int(t) for t in input().split()]
cost = [int(t) for t in input().split()]
g = Flow(n+2)
s, t = n, n+1
last = [-1] * 101
for i, x in enumerate(A):
for d in range(1, 101):
if x % d == 0 and last[d] >= 0:
g.add_edge(i, last[d], float('inf'))
last[x] = i
if cost[i] >= 0:
g.add_edge(s, i, cost[i])
else:
g.add_edge(i, t, -cost[i])
min_cut = g.calc(s, t)
ans = sum(max(c, 0) for c in cost) - min_cut
print(ans)
class Flow:
def __init__(self, n):
self.n = n
self.g = [dict() for _ in range(n)]
def add_edge(self, u, v, w):
self.g[u][v] = w
self.g[v][u] = 0
def bfs(self, s, t):
q = [s]
vis = [0] * self.n
vis[s] = 1
prev = [-1] * self.n
found = False
for ver in q:
for nei, w in self.g[ver].items():
if not vis[nei] and w > 0:
vis[nei] = 1
prev[nei] = ver
q.append(nei)
if nei == t:
found = True
break
if found:
break
if not vis[t]:
return 0
flow = float('inf')
ver = t
while ver != s:
p = prev[ver]
flow = min(flow, self.g[p][ver])
ver = p
ver = t
while ver != s:
p = prev[ver]
self.g[p][ver] -= flow
self.g[ver][p] += flow
ver = p
return flow
def calc(self, s, t):
res = 0
while True:
flow = self.bfs(s, t)
res += flow
if not flow:
return res
main()
``` | output | 1 | 92,859 | 12 | 185,719 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Note that the memory limit is unusual.
You are given an integer n and two sequences a_1, a_2, ..., a_n and b_1, b_2, ..., b_n.
Let's call a set of integers S such that S β \{1, 2, 3, ..., n\} strange, if, for every element i of S, the following condition is met: for every j β [1, i - 1], if a_j divides a_i, then j is also included in S. An empty set is always strange.
The cost of the set S is β_{i β S} b_i. You have to calculate the maximum possible cost of a strange set.
Input
The first line contains one integer n (1 β€ n β€ 3000).
The second line contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100).
The third line contains n integers b_1, b_2, ..., b_n (-10^5 β€ b_i β€ 10^5).
Output
Print one integer β the maximum cost of a strange set.
Examples
Input
9
4 7 3 4 5 6 7 8 13
-2 3 -19 5 -6 7 -8 9 1
Output
16
Input
2
42 42
-37 13
Output
0
Input
2
42 42
13 -37
Output
13
Note
The strange set with the maximum cost in the first example is \{1, 2, 4, 8, 9\}.
The strange set with the maximum cost in the second example is empty. | instruction | 0 | 92,860 | 12 | 185,720 |
Tags: flows, math
Correct Solution:
```
from collections import deque
class Dinic:
def __init__(self, N):
self.N = N
self.G = [[] for i in range(N)]
# 1ζΉε
def add_edge(self, fr, to, cap):
forward = [to, cap, None]
forward[2] = backward = [fr, 0, forward]
self.G[fr].append(forward)
self.G[to].append(backward)
# δΈ‘ζΉε
def add_multi_edge(self, v1, v2, cap1, cap2):
edge1 = [v2, cap1, None]
edge1[2] = edge2 = [v1, cap2, edge1]
self.G[v1].append(edge1)
self.G[v2].append(edge2)
def bfs(self, s, t):
self.level = level = [None]*self.N
deq = deque([s])
level[s] = 0
G = self.G
while deq:
v = deq.popleft()
lv = level[v] + 1
for w, cap, _ in G[v]:
if cap and level[w] is None:
level[w] = lv
deq.append(w)
return level[t] is not None
def dfs(self, v, t, f):
if v == t:
return f
level = self.level
for e in self.it[v]:
w, cap, rev = e
if cap and level[v] < level[w]:
d = self.dfs(w, t, min(f, cap))
if d:
e[1] -= d
rev[1] += d
return d
return 0
def flow(self, s, t):
flow = 0
INF = 10**9 + 7
G = self.G
while self.bfs(s, t):
*self.it, = map(iter, self.G)
f = INF
while f:
f = self.dfs(s, t, INF)
flow += f
return flow
import sys
input = sys.stdin.readline
n = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
# s:n+1,g:0
f = Dinic(n+2)
INF = 10**15
for i in range(n):
if b[i] > 0:
f.add_edge(n+1,i+1,b[i])
elif b[i] < 0:
f.add_edge(i+1,0,-b[i])
for i in range(n):
used = [False]*101
for j in reversed(range(i)):
if a[i] % a[j] == 0 and not used[a[j]]:
f.add_edge(i+1,j+1,INF)
used[a[j]] = True
ans = sum(b[i]*(b[i] > 0) for i in range(n)) - f.flow(n+1,0)
print(ans)
``` | output | 1 | 92,860 | 12 | 185,721 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Note that the memory limit is unusual.
You are given an integer n and two sequences a_1, a_2, ..., a_n and b_1, b_2, ..., b_n.
Let's call a set of integers S such that S β \{1, 2, 3, ..., n\} strange, if, for every element i of S, the following condition is met: for every j β [1, i - 1], if a_j divides a_i, then j is also included in S. An empty set is always strange.
The cost of the set S is β_{i β S} b_i. You have to calculate the maximum possible cost of a strange set.
Input
The first line contains one integer n (1 β€ n β€ 3000).
The second line contains n integers a_1, a_2, ..., a_n (1 β€ a_i β€ 100).
The third line contains n integers b_1, b_2, ..., b_n (-10^5 β€ b_i β€ 10^5).
Output
Print one integer β the maximum cost of a strange set.
Examples
Input
9
4 7 3 4 5 6 7 8 13
-2 3 -19 5 -6 7 -8 9 1
Output
16
Input
2
42 42
-37 13
Output
0
Input
2
42 42
13 -37
Output
13
Note
The strange set with the maximum cost in the first example is \{1, 2, 4, 8, 9\}.
The strange set with the maximum cost in the second example is empty.
Submitted Solution:
```
from bisect import bisect_left as bl
from bisect import bisect_right as br
from heapq import heappush,heappop
import math
from collections import *
from functools import reduce,cmp_to_key, lru_cache
import sys
input = sys.stdin.readline
M = mod = 10 ** 9 + 7
def factors(n):return sorted(set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))
def inv_mod(n):return pow(n, mod - 2, mod)
def li():return [int(i) for i in input().rstrip('\n').split()]
def st():return input().rstrip('\n')
def val():return int(input().rstrip('\n'))
def li2():return [i for i in input().rstrip('\n')]
def li3():return [int(i) for i in input().rstrip('\n')]
n = val()
a = li()
b = li()
dp = [set() for i in range(n)]
for i in range(n):
dp[i].add(i)
for j in range(i - 1, -1, -1):
if j in dp[i]:continue
if a[i] % a[j] == 0:
dp[i] |= dp[j]
# print(dp)
l = []
for i in dp:
l.append(sum(b[j] for j in i))
currset = set()
for i in range(n):
if l[i] > 0:
currset |= dp[i]
print(sum(b[i] for i in currset))
``` | instruction | 0 | 92,864 | 12 | 185,728 |
No | output | 1 | 92,864 | 12 | 185,729 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kefa decided to make some money doing business on the Internet for exactly n days. He knows that on the i-th day (1 β€ i β€ n) he makes ai money. Kefa loves progress, that's why he wants to know the length of the maximum non-decreasing subsegment in sequence ai. Let us remind you that the subsegment of the sequence is its continuous fragment. A subsegment of numbers is called non-decreasing if all numbers in it follow in the non-decreasing order.
Help Kefa cope with this task!
Input
The first line contains integer n (1 β€ n β€ 105).
The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print a single integer β the length of the maximum non-decreasing subsegment of sequence a.
Examples
Input
6
2 2 1 3 4 1
Output
3
Input
3
2 2 9
Output
3
Note
In the first test the maximum non-decreasing subsegment is the numbers from the third to the fifth one.
In the second test the maximum non-decreasing subsegment is the numbers from the first to the third one. | instruction | 0 | 93,099 | 12 | 186,198 |
Tags: brute force, dp, implementation
Correct Solution:
```
n=int(input())
l=list(map(int,input().split()))
c=1
t=[]
f=0
for i in range(0,n-1):
if (l[i]<=l[i+1]):
c=c+1
else:
f=1
c=1
t.append(c)
if f==0:
print(c)
else:
print(max(t))
``` | output | 1 | 93,099 | 12 | 186,199 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kefa decided to make some money doing business on the Internet for exactly n days. He knows that on the i-th day (1 β€ i β€ n) he makes ai money. Kefa loves progress, that's why he wants to know the length of the maximum non-decreasing subsegment in sequence ai. Let us remind you that the subsegment of the sequence is its continuous fragment. A subsegment of numbers is called non-decreasing if all numbers in it follow in the non-decreasing order.
Help Kefa cope with this task!
Input
The first line contains integer n (1 β€ n β€ 105).
The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print a single integer β the length of the maximum non-decreasing subsegment of sequence a.
Examples
Input
6
2 2 1 3 4 1
Output
3
Input
3
2 2 9
Output
3
Note
In the first test the maximum non-decreasing subsegment is the numbers from the third to the fifth one.
In the second test the maximum non-decreasing subsegment is the numbers from the first to the third one. | instruction | 0 | 93,100 | 12 | 186,200 |
Tags: brute force, dp, implementation
Correct Solution:
```
n = int(input())
c = list(map(int, input().split()))
most = 0
tmp = 0
for i, num in enumerate(c):
if num >= c[i - 1] and i > 0:
tmp += 1
else:
if tmp > most:
most = tmp
tmp = 0
if tmp > most:
most = tmp
print(most+1)
``` | output | 1 | 93,100 | 12 | 186,201 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kefa decided to make some money doing business on the Internet for exactly n days. He knows that on the i-th day (1 β€ i β€ n) he makes ai money. Kefa loves progress, that's why he wants to know the length of the maximum non-decreasing subsegment in sequence ai. Let us remind you that the subsegment of the sequence is its continuous fragment. A subsegment of numbers is called non-decreasing if all numbers in it follow in the non-decreasing order.
Help Kefa cope with this task!
Input
The first line contains integer n (1 β€ n β€ 105).
The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print a single integer β the length of the maximum non-decreasing subsegment of sequence a.
Examples
Input
6
2 2 1 3 4 1
Output
3
Input
3
2 2 9
Output
3
Note
In the first test the maximum non-decreasing subsegment is the numbers from the third to the fifth one.
In the second test the maximum non-decreasing subsegment is the numbers from the first to the third one. | instruction | 0 | 93,101 | 12 | 186,202 |
Tags: brute force, dp, implementation
Correct Solution:
```
n = int(input())
s = list(map(int, input().split(' ')))
m = 1
l = 1
for i in range(n-1):
if s[i] <= s[i+1]:
l += 1
m = max(l, m)
else:
m = max(l, m)
l = 1
print(m)
``` | output | 1 | 93,101 | 12 | 186,203 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kefa decided to make some money doing business on the Internet for exactly n days. He knows that on the i-th day (1 β€ i β€ n) he makes ai money. Kefa loves progress, that's why he wants to know the length of the maximum non-decreasing subsegment in sequence ai. Let us remind you that the subsegment of the sequence is its continuous fragment. A subsegment of numbers is called non-decreasing if all numbers in it follow in the non-decreasing order.
Help Kefa cope with this task!
Input
The first line contains integer n (1 β€ n β€ 105).
The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print a single integer β the length of the maximum non-decreasing subsegment of sequence a.
Examples
Input
6
2 2 1 3 4 1
Output
3
Input
3
2 2 9
Output
3
Note
In the first test the maximum non-decreasing subsegment is the numbers from the third to the fifth one.
In the second test the maximum non-decreasing subsegment is the numbers from the first to the third one. | instruction | 0 | 93,102 | 12 | 186,204 |
Tags: brute force, dp, implementation
Correct Solution:
```
n=int(input())
s=list(map(int,input().split()))
number=[]
c=0
for i in range(n-1):
if s[i]<=s[i+1]:
c+=1
else:
number.append(c+1)
c=0
number.append(c+1)
if c+1==n:
print(c+1)
else:
result=sorted(number)
print(result[-1])
``` | output | 1 | 93,102 | 12 | 186,205 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kefa decided to make some money doing business on the Internet for exactly n days. He knows that on the i-th day (1 β€ i β€ n) he makes ai money. Kefa loves progress, that's why he wants to know the length of the maximum non-decreasing subsegment in sequence ai. Let us remind you that the subsegment of the sequence is its continuous fragment. A subsegment of numbers is called non-decreasing if all numbers in it follow in the non-decreasing order.
Help Kefa cope with this task!
Input
The first line contains integer n (1 β€ n β€ 105).
The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print a single integer β the length of the maximum non-decreasing subsegment of sequence a.
Examples
Input
6
2 2 1 3 4 1
Output
3
Input
3
2 2 9
Output
3
Note
In the first test the maximum non-decreasing subsegment is the numbers from the third to the fifth one.
In the second test the maximum non-decreasing subsegment is the numbers from the first to the third one. | instruction | 0 | 93,103 | 12 | 186,206 |
Tags: brute force, dp, implementation
Correct Solution:
```
n = int(input())
a = [0] + [int(s) for s in input().split()]
dp = [0] * (n+2)
for i in range(1, n+1):
if a[i] >= a[i-1]:
dp[i] = dp[i-1] + 1
else:
dp[i] = 1
print(max(dp))
``` | output | 1 | 93,103 | 12 | 186,207 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kefa decided to make some money doing business on the Internet for exactly n days. He knows that on the i-th day (1 β€ i β€ n) he makes ai money. Kefa loves progress, that's why he wants to know the length of the maximum non-decreasing subsegment in sequence ai. Let us remind you that the subsegment of the sequence is its continuous fragment. A subsegment of numbers is called non-decreasing if all numbers in it follow in the non-decreasing order.
Help Kefa cope with this task!
Input
The first line contains integer n (1 β€ n β€ 105).
The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print a single integer β the length of the maximum non-decreasing subsegment of sequence a.
Examples
Input
6
2 2 1 3 4 1
Output
3
Input
3
2 2 9
Output
3
Note
In the first test the maximum non-decreasing subsegment is the numbers from the third to the fifth one.
In the second test the maximum non-decreasing subsegment is the numbers from the first to the third one. | instruction | 0 | 93,104 | 12 | 186,208 |
Tags: brute force, dp, implementation
Correct Solution:
```
n=input()
l=input().split()
count=1
ans=0
for i in range (0,int(n)-1):
if(int(l[i])<=int(l[i+1])):
count=count+1
else:
if(count>ans):
ans=count
count=1
print(max(ans,count))
``` | output | 1 | 93,104 | 12 | 186,209 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kefa decided to make some money doing business on the Internet for exactly n days. He knows that on the i-th day (1 β€ i β€ n) he makes ai money. Kefa loves progress, that's why he wants to know the length of the maximum non-decreasing subsegment in sequence ai. Let us remind you that the subsegment of the sequence is its continuous fragment. A subsegment of numbers is called non-decreasing if all numbers in it follow in the non-decreasing order.
Help Kefa cope with this task!
Input
The first line contains integer n (1 β€ n β€ 105).
The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print a single integer β the length of the maximum non-decreasing subsegment of sequence a.
Examples
Input
6
2 2 1 3 4 1
Output
3
Input
3
2 2 9
Output
3
Note
In the first test the maximum non-decreasing subsegment is the numbers from the third to the fifth one.
In the second test the maximum non-decreasing subsegment is the numbers from the first to the third one. | instruction | 0 | 93,105 | 12 | 186,210 |
Tags: brute force, dp, implementation
Correct Solution:
```
n = int(input())
l = list(map(int, input().split()))
ans, cnt = 0, 1
for i in range(1, n):
if l[i] >= l[i - 1]: cnt -= -1
else:
ans = max(ans, cnt)
cnt = 1
ans = max(ans, cnt)
print(ans)
``` | output | 1 | 93,105 | 12 | 186,211 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kefa decided to make some money doing business on the Internet for exactly n days. He knows that on the i-th day (1 β€ i β€ n) he makes ai money. Kefa loves progress, that's why he wants to know the length of the maximum non-decreasing subsegment in sequence ai. Let us remind you that the subsegment of the sequence is its continuous fragment. A subsegment of numbers is called non-decreasing if all numbers in it follow in the non-decreasing order.
Help Kefa cope with this task!
Input
The first line contains integer n (1 β€ n β€ 105).
The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print a single integer β the length of the maximum non-decreasing subsegment of sequence a.
Examples
Input
6
2 2 1 3 4 1
Output
3
Input
3
2 2 9
Output
3
Note
In the first test the maximum non-decreasing subsegment is the numbers from the third to the fifth one.
In the second test the maximum non-decreasing subsegment is the numbers from the first to the third one. | instruction | 0 | 93,106 | 12 | 186,212 |
Tags: brute force, dp, implementation
Correct Solution:
```
n = int(input())
a = list(map(int,input().split(' ')))
tmp = 1
max_tmp = 1
for i in range(n-1):
if a[i] <= a[i+1]:
tmp+=1
if tmp > max_tmp:
max_tmp = tmp
# print(a[i])
else:
tmp = 1
print(max_tmp)
``` | output | 1 | 93,106 | 12 | 186,213 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kefa decided to make some money doing business on the Internet for exactly n days. He knows that on the i-th day (1 β€ i β€ n) he makes ai money. Kefa loves progress, that's why he wants to know the length of the maximum non-decreasing subsegment in sequence ai. Let us remind you that the subsegment of the sequence is its continuous fragment. A subsegment of numbers is called non-decreasing if all numbers in it follow in the non-decreasing order.
Help Kefa cope with this task!
Input
The first line contains integer n (1 β€ n β€ 105).
The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print a single integer β the length of the maximum non-decreasing subsegment of sequence a.
Examples
Input
6
2 2 1 3 4 1
Output
3
Input
3
2 2 9
Output
3
Note
In the first test the maximum non-decreasing subsegment is the numbers from the third to the fifth one.
In the second test the maximum non-decreasing subsegment is the numbers from the first to the third one.
Submitted Solution:
```
n = int(input())
s = [int(i) for i in input().split()]
k, m = 1, 0
for i in range(n-1):
if s[i] <= s[i+1]:
k += 1
else:
if k > m:
m = k
k = 1
if k > m:
print(k)
else:
print(m)
``` | instruction | 0 | 93,107 | 12 | 186,214 |
Yes | output | 1 | 93,107 | 12 | 186,215 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kefa decided to make some money doing business on the Internet for exactly n days. He knows that on the i-th day (1 β€ i β€ n) he makes ai money. Kefa loves progress, that's why he wants to know the length of the maximum non-decreasing subsegment in sequence ai. Let us remind you that the subsegment of the sequence is its continuous fragment. A subsegment of numbers is called non-decreasing if all numbers in it follow in the non-decreasing order.
Help Kefa cope with this task!
Input
The first line contains integer n (1 β€ n β€ 105).
The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print a single integer β the length of the maximum non-decreasing subsegment of sequence a.
Examples
Input
6
2 2 1 3 4 1
Output
3
Input
3
2 2 9
Output
3
Note
In the first test the maximum non-decreasing subsegment is the numbers from the third to the fifth one.
In the second test the maximum non-decreasing subsegment is the numbers from the first to the third one.
Submitted Solution:
```
t = int(input())
arr = [int(x) for x in input().split()]
count = 1
prev = 0
for i in range(1,t):
if arr[i-1] <= arr[i]:
count += 1
prev = max(prev, count)
else:
count = 1
print(max(prev,count))
``` | instruction | 0 | 93,108 | 12 | 186,216 |
Yes | output | 1 | 93,108 | 12 | 186,217 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kefa decided to make some money doing business on the Internet for exactly n days. He knows that on the i-th day (1 β€ i β€ n) he makes ai money. Kefa loves progress, that's why he wants to know the length of the maximum non-decreasing subsegment in sequence ai. Let us remind you that the subsegment of the sequence is its continuous fragment. A subsegment of numbers is called non-decreasing if all numbers in it follow in the non-decreasing order.
Help Kefa cope with this task!
Input
The first line contains integer n (1 β€ n β€ 105).
The second line contains n integers a1, a2, ..., an (1 β€ ai β€ 109).
Output
Print a single integer β the length of the maximum non-decreasing subsegment of sequence a.
Examples
Input
6
2 2 1 3 4 1
Output
3
Input
3
2 2 9
Output
3
Note
In the first test the maximum non-decreasing subsegment is the numbers from the third to the fifth one.
In the second test the maximum non-decreasing subsegment is the numbers from the first to the third one.
Submitted Solution:
```
n = int(input())
A = list(map(int, input().split()))
def crossLength(l, m, r):
count = 0
if A[m] > A[m + 1]:
return count
else:
count += 1
for i in range(m - l):
if A[m - i] >= A[m - i - 1]:
count += 1
else:
break
for i in range(r - m):
if A[m + i + 1] >= A[m + i]:
count += 1
else:
break
return count
def findSubsegmentLength(l, r):
if l == r:
return 1
m = (r + l) // 2
left_length = findSubsegmentLength(l, m)
right_length = findSubsegmentLength(m + 1, r)
mid_legth = crossLength(l, m, r)
return max(left_length, right_length, mid_legth)
print(findSubsegmentLength(0, len(A) - 1))
``` | instruction | 0 | 93,109 | 12 | 186,218 |
Yes | output | 1 | 93,109 | 12 | 186,219 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.