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.
You are given an array a consisting of n positive integers. You pick two integer numbers l and r from 1 to n, inclusive (numbers are picked randomly, equiprobably and independently). If l > r, then you swap values of l and r. You have to calculate the expected value of the number of unique elements in segment of the array from index l to index r, inclusive (1-indexed).
Input
The first line contains one integer number n (1 ≤ n ≤ 106). The second line contains n integer numbers a1, a2, ... an (1 ≤ ai ≤ 106) — elements of the array.
Output
Print one number — the expected number of unique elements in chosen segment.
Your answer will be considered correct if its absolute or relative error doesn't exceed 10 - 4 — formally, the answer is correct if <image>, where x is jury's answer, and y is your answer.
Examples
Input
2
1 2
Output
1.500000
Input
2
2 2
Output
1.000000 | instruction | 0 | 19,046 | 12 | 38,092 |
Tags: data structures, math, probabilities, two pointers
Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
lastocc=[0]*1000006
ans=[0]*n
ans[0]=1
lastocc[a[0]]=1
for i in range(1,n):
ans[i]=ans[i-1]+(i+1-lastocc[a[i]])
lastocc[a[i]]=i+1
print((2*sum(ans)-n)/(n*n))
``` | output | 1 | 19,046 | 12 | 38,093 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a consisting of n positive integers. You pick two integer numbers l and r from 1 to n, inclusive (numbers are picked randomly, equiprobably and independently). If l > r, then you swap values of l and r. You have to calculate the expected value of the number of unique elements in segment of the array from index l to index r, inclusive (1-indexed).
Input
The first line contains one integer number n (1 ≤ n ≤ 106). The second line contains n integer numbers a1, a2, ... an (1 ≤ ai ≤ 106) — elements of the array.
Output
Print one number — the expected number of unique elements in chosen segment.
Your answer will be considered correct if its absolute or relative error doesn't exceed 10 - 4 — formally, the answer is correct if <image>, where x is jury's answer, and y is your answer.
Examples
Input
2
1 2
Output
1.500000
Input
2
2 2
Output
1.000000 | instruction | 0 | 19,047 | 12 | 38,094 |
Tags: data structures, math, probabilities, two pointers
Correct Solution:
```
n = int(input())
arr = [0]
arr = arr + list(map(int, input().split(' ')))
def getCounts(arr):
last = {}
ans = 0.0
prev = 0.0
res = 0.0
for i in range(1, len(arr)):
if arr[i] not in last:
ans = prev + i
else:
ans = prev + i - last[arr[i]]
prev = ans
res += ans
last[arr[i]] = i
return res
ans = (2 * getCounts(arr) - n)/(n*n)
print("%.6f" % ans)
``` | output | 1 | 19,047 | 12 | 38,095 |
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 a consisting of n positive integers. You pick two integer numbers l and r from 1 to n, inclusive (numbers are picked randomly, equiprobably and independently). If l > r, then you swap values of l and r. You have to calculate the expected value of the number of unique elements in segment of the array from index l to index r, inclusive (1-indexed).
Input
The first line contains one integer number n (1 ≤ n ≤ 106). The second line contains n integer numbers a1, a2, ... an (1 ≤ ai ≤ 106) — elements of the array.
Output
Print one number — the expected number of unique elements in chosen segment.
Your answer will be considered correct if its absolute or relative error doesn't exceed 10 - 4 — formally, the answer is correct if <image>, where x is jury's answer, and y is your answer.
Examples
Input
2
1 2
Output
1.500000
Input
2
2 2
Output
1.000000
Submitted Solution:
```
n = int(input())
arr = list(map(int,input().split()))
array = [None for i in range(n+1)]
for i in range(1,n+1):
array[i] = arr[i-1]
last_occ = {}
ans = [0 for i in range(n+1)]
ans[0] = 0
summ = 0.0
for i in range(1,n+1):
ele = array[i]
if last_occ.get(ele) == None:
last_occ[ele] = 0
ans[i] = ans[i-1] + (i - last_occ[ele])
last_occ[ele]=i
print(ans[i])
summ = summ + float(ans[i])
final_ans = (2*(summ) - n)/(n*n*1.0)
print("{:.6f}".format(final_ans))
``` | instruction | 0 | 19,048 | 12 | 38,096 |
No | output | 1 | 19,048 | 12 | 38,097 |
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 a consisting of n positive integers. You pick two integer numbers l and r from 1 to n, inclusive (numbers are picked randomly, equiprobably and independently). If l > r, then you swap values of l and r. You have to calculate the expected value of the number of unique elements in segment of the array from index l to index r, inclusive (1-indexed).
Input
The first line contains one integer number n (1 ≤ n ≤ 106). The second line contains n integer numbers a1, a2, ... an (1 ≤ ai ≤ 106) — elements of the array.
Output
Print one number — the expected number of unique elements in chosen segment.
Your answer will be considered correct if its absolute or relative error doesn't exceed 10 - 4 — formally, the answer is correct if <image>, where x is jury's answer, and y is your answer.
Examples
Input
2
1 2
Output
1.500000
Input
2
2 2
Output
1.000000
Submitted Solution:
```
from sys import stdin, stdout
from math import factorial
from math import log10
n = int(stdin.readline())
values = list(map(int, stdin.readline().split()))
ans = 0
for i in range(n):
s = set()
for j in range(i, n):
s.add(values[j])
ans += len(s)
stdout.write(str(ans * 2 / (n * n)))
``` | instruction | 0 | 19,049 | 12 | 38,098 |
No | output | 1 | 19,049 | 12 | 38,099 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote a m-free matrix as a binary (that is, consisting of only 1's and 0's) matrix such that every square submatrix of size m × m of this matrix contains at least one zero.
Consider the following problem:
You are given two integers n and m. You have to construct an m-free square matrix of size n × n such that the number of 1's in this matrix is maximum possible. Print the maximum possible number of 1's in such matrix.
You don't have to solve this problem. Instead, you have to construct a few tests for it.
You will be given t numbers x1, x2, ..., xt. For every <image>, find two integers ni and mi (ni ≥ mi) such that the answer for the aforementioned problem is exactly xi if we set n = ni and m = mi.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of tests you have to construct.
Then t lines follow, i-th line containing one integer xi (0 ≤ xi ≤ 109).
Note that in hacks you have to set t = 1.
Output
For each test you have to construct, output two positive numbers ni and mi (1 ≤ mi ≤ ni ≤ 109) such that the maximum number of 1's in a mi-free ni × ni matrix is exactly xi. If there are multiple solutions, you may output any of them; and if this is impossible to construct a test, output a single integer - 1.
Example
Input
3
21
0
1
Output
5 2
1 1
-1 | instruction | 0 | 19,091 | 12 | 38,182 |
Tags: binary search, brute force, constructive algorithms
Correct Solution:
```
import math
t = int(input())
for rr in range(t):
oc = int(input())
fl = False
if oc != 0:
for i in range(2,40000):
sq1 = i
v1 = sq1*sq1 - oc
if v1 > 0 and int(math.sqrt(v1))**2 == v1:
sv1 = int(math.sqrt(v1))
l = 2
r = sq1
while (r-l) > 1:
mid = int((l+r)/2)
vc = int(sq1/mid)
if (sq1*sq1 - vc*vc) > oc:
r = mid - 1
else:
l = mid
cr = int(sq1/r)
cl = int(sq1/l)
if (sq1*sq1 - cr*cr) == oc and r <= sq1:
fl = True
st = str(sq1) +' '+ str(r)
print(st)
break
elif (sq1*sq1 - cl*cl) == oc and l <= sq1:
fl = True
st = str(sq1) +' '+ str(l)
print(st)
break
if not fl:
if oc == 0:
print("1 1")
else:
print(-1)
``` | output | 1 | 19,091 | 12 | 38,183 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote a m-free matrix as a binary (that is, consisting of only 1's and 0's) matrix such that every square submatrix of size m × m of this matrix contains at least one zero.
Consider the following problem:
You are given two integers n and m. You have to construct an m-free square matrix of size n × n such that the number of 1's in this matrix is maximum possible. Print the maximum possible number of 1's in such matrix.
You don't have to solve this problem. Instead, you have to construct a few tests for it.
You will be given t numbers x1, x2, ..., xt. For every <image>, find two integers ni and mi (ni ≥ mi) such that the answer for the aforementioned problem is exactly xi if we set n = ni and m = mi.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of tests you have to construct.
Then t lines follow, i-th line containing one integer xi (0 ≤ xi ≤ 109).
Note that in hacks you have to set t = 1.
Output
For each test you have to construct, output two positive numbers ni and mi (1 ≤ mi ≤ ni ≤ 109) such that the maximum number of 1's in a mi-free ni × ni matrix is exactly xi. If there are multiple solutions, you may output any of them; and if this is impossible to construct a test, output a single integer - 1.
Example
Input
3
21
0
1
Output
5 2
1 1
-1 | instruction | 0 | 19,092 | 12 | 38,184 |
Tags: binary search, brute force, constructive algorithms
Correct Solution:
```
from math import ceil
t = int(input())
for _ in range(t):
x = int(input())
if x == 1 or x % 4 == 2:
print(-1)
elif x == 0:
print(1,1)
else:
z = 0
for i in range(ceil((x/3)**0.5),ceil(x**0.5)):
if x % i == 0 and (x//i-i) % 2 == 0:
n = (i + x//i)//2
k = (x//i - i)//2
m = n//k
if n//m == k:
print(n,m)
z = 1
break
if z == 0:
print(-1)
``` | output | 1 | 19,092 | 12 | 38,185 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote a m-free matrix as a binary (that is, consisting of only 1's and 0's) matrix such that every square submatrix of size m × m of this matrix contains at least one zero.
Consider the following problem:
You are given two integers n and m. You have to construct an m-free square matrix of size n × n such that the number of 1's in this matrix is maximum possible. Print the maximum possible number of 1's in such matrix.
You don't have to solve this problem. Instead, you have to construct a few tests for it.
You will be given t numbers x1, x2, ..., xt. For every <image>, find two integers ni and mi (ni ≥ mi) such that the answer for the aforementioned problem is exactly xi if we set n = ni and m = mi.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of tests you have to construct.
Then t lines follow, i-th line containing one integer xi (0 ≤ xi ≤ 109).
Note that in hacks you have to set t = 1.
Output
For each test you have to construct, output two positive numbers ni and mi (1 ≤ mi ≤ ni ≤ 109) such that the maximum number of 1's in a mi-free ni × ni matrix is exactly xi. If there are multiple solutions, you may output any of them; and if this is impossible to construct a test, output a single integer - 1.
Example
Input
3
21
0
1
Output
5 2
1 1
-1 | instruction | 0 | 19,094 | 12 | 38,188 |
Tags: binary search, brute force, constructive algorithms
Correct Solution:
```
from math import*
def get(x):
if x==0:
print(1,1)
return
i=1
while i*i<=x:
if not(x%i):
a,b=int(x/i),i
if(not((a+b)%2)):
n=int((a+b)/2)
n_m=int((a-b)/2)
if n_m:
m=int(n/n_m)
if(int(n/m)==n_m and m<=n):
print(n,m)
return
i+=1
print(-1)
return
n=int(input())
for i in range(n):get(int(input()))
# Made By Mostafa_Khaled
``` | output | 1 | 19,094 | 12 | 38,189 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote a m-free matrix as a binary (that is, consisting of only 1's and 0's) matrix such that every square submatrix of size m × m of this matrix contains at least one zero.
Consider the following problem:
You are given two integers n and m. You have to construct an m-free square matrix of size n × n such that the number of 1's in this matrix is maximum possible. Print the maximum possible number of 1's in such matrix.
You don't have to solve this problem. Instead, you have to construct a few tests for it.
You will be given t numbers x1, x2, ..., xt. For every <image>, find two integers ni and mi (ni ≥ mi) such that the answer for the aforementioned problem is exactly xi if we set n = ni and m = mi.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of tests you have to construct.
Then t lines follow, i-th line containing one integer xi (0 ≤ xi ≤ 109).
Note that in hacks you have to set t = 1.
Output
For each test you have to construct, output two positive numbers ni and mi (1 ≤ mi ≤ ni ≤ 109) such that the maximum number of 1's in a mi-free ni × ni matrix is exactly xi. If there are multiple solutions, you may output any of them; and if this is impossible to construct a test, output a single integer - 1.
Example
Input
3
21
0
1
Output
5 2
1 1
-1 | instruction | 0 | 19,095 | 12 | 38,190 |
Tags: binary search, brute force, constructive algorithms
Correct Solution:
```
import math
t = int(input())
for _ in range(t):
suc = False
x = int(input())
for n in range(int(x**0.5)+1,int((4*x/3)**0.5)+2):
if int((n**2-x)**0.5)**2 == n**2-x:
mm = int((n**2-x)**0.5)
m = math.floor(n/mm)
if n**2-(n//m)**2 == x:
print(n,m)
suc = True
break
if not suc: print(-1)
``` | output | 1 | 19,095 | 12 | 38,191 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote a m-free matrix as a binary (that is, consisting of only 1's and 0's) matrix such that every square submatrix of size m × m of this matrix contains at least one zero.
Consider the following problem:
You are given two integers n and m. You have to construct an m-free square matrix of size n × n such that the number of 1's in this matrix is maximum possible. Print the maximum possible number of 1's in such matrix.
You don't have to solve this problem. Instead, you have to construct a few tests for it.
You will be given t numbers x1, x2, ..., xt. For every <image>, find two integers ni and mi (ni ≥ mi) such that the answer for the aforementioned problem is exactly xi if we set n = ni and m = mi.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of tests you have to construct.
Then t lines follow, i-th line containing one integer xi (0 ≤ xi ≤ 109).
Note that in hacks you have to set t = 1.
Output
For each test you have to construct, output two positive numbers ni and mi (1 ≤ mi ≤ ni ≤ 109) such that the maximum number of 1's in a mi-free ni × ni matrix is exactly xi. If there are multiple solutions, you may output any of them; and if this is impossible to construct a test, output a single integer - 1.
Example
Input
3
21
0
1
Output
5 2
1 1
-1 | instruction | 0 | 19,096 | 12 | 38,192 |
Tags: binary search, brute force, constructive algorithms
Correct Solution:
```
from math import sqrt,ceil
def func(x,):
a = int(ceil(sqrt(x)))
b = int(ceil(sqrt(2*x)))
for n in range(a,b+1):
if n == 0:
return 1,1
temp = sqrt((n**2 - x))
if temp%1 != 0 or temp == 0:
pass
else:
m = int(n/temp)
if int(n/m) == int(temp):
return n,m
return -1,-1
t = int(input())
for i in range(t):
x = int(input())
n,m = func(x)
if n == -1:
print(-1)
else:
print(n,m)
``` | output | 1 | 19,096 | 12 | 38,193 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote a m-free matrix as a binary (that is, consisting of only 1's and 0's) matrix such that every square submatrix of size m × m of this matrix contains at least one zero.
Consider the following problem:
You are given two integers n and m. You have to construct an m-free square matrix of size n × n such that the number of 1's in this matrix is maximum possible. Print the maximum possible number of 1's in such matrix.
You don't have to solve this problem. Instead, you have to construct a few tests for it.
You will be given t numbers x1, x2, ..., xt. For every <image>, find two integers ni and mi (ni ≥ mi) such that the answer for the aforementioned problem is exactly xi if we set n = ni and m = mi.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of tests you have to construct.
Then t lines follow, i-th line containing one integer xi (0 ≤ xi ≤ 109).
Note that in hacks you have to set t = 1.
Output
For each test you have to construct, output two positive numbers ni and mi (1 ≤ mi ≤ ni ≤ 109) such that the maximum number of 1's in a mi-free ni × ni matrix is exactly xi. If there are multiple solutions, you may output any of them; and if this is impossible to construct a test, output a single integer - 1.
Example
Input
3
21
0
1
Output
5 2
1 1
-1 | instruction | 0 | 19,097 | 12 | 38,194 |
Tags: binary search, brute force, constructive algorithms
Correct Solution:
```
"""Codeforces P938C. Constructing Tests
(http://codeforces.com/problemset/problem/938/C)
Problem tags: binary search, brute force
Time Complexity: O(sqrt(x))
"""
import atexit
import io
import math
import sys
# IO Buffering
_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER
@atexit.register
def write():
sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
def main():
t = int(input())
for _ in range(t):
x = int(input())
if x== 0:
print(1, 1)
continue
n = math.ceil(x ** 0.5)
while True:
if n * n - (n // 2) ** 2 > x:
print(-1)
break
t = math.floor((n * n - x) ** 0.5)
if t > 0 and t * t == n * n - x:
m = n // t
if t == n // m:
print(n, m)
break
n += 1
if __name__ == '__main__':
main()
``` | output | 1 | 19,097 | 12 | 38,195 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Let's denote a m-free matrix as a binary (that is, consisting of only 1's and 0's) matrix such that every square submatrix of size m × m of this matrix contains at least one zero.
Consider the following problem:
You are given two integers n and m. You have to construct an m-free square matrix of size n × n such that the number of 1's in this matrix is maximum possible. Print the maximum possible number of 1's in such matrix.
You don't have to solve this problem. Instead, you have to construct a few tests for it.
You will be given t numbers x1, x2, ..., xt. For every <image>, find two integers ni and mi (ni ≥ mi) such that the answer for the aforementioned problem is exactly xi if we set n = ni and m = mi.
Input
The first line contains one integer t (1 ≤ t ≤ 100) — the number of tests you have to construct.
Then t lines follow, i-th line containing one integer xi (0 ≤ xi ≤ 109).
Note that in hacks you have to set t = 1.
Output
For each test you have to construct, output two positive numbers ni and mi (1 ≤ mi ≤ ni ≤ 109) such that the maximum number of 1's in a mi-free ni × ni matrix is exactly xi. If there are multiple solutions, you may output any of them; and if this is impossible to construct a test, output a single integer - 1.
Example
Input
3
21
0
1
Output
5 2
1 1
-1 | instruction | 0 | 19,098 | 12 | 38,196 |
Tags: binary search, brute force, constructive algorithms
Correct Solution:
```
t = int(input())
for k in range(t):
x = int(input())
if x == 0:
print(1, 1)
continue
for i in range(1, int(x ** 0.5) + 2):
if x % i == 0 and (x // i - i) % 2 == 0 and (x // i - (x // i - i) // 2) ** 2 >= x:
a, b = x // i, i
y = (a - b) // 2
n = a - y
if y == 0:
continue
m = n // y
if n // m != y:
continue
print(n, m)
break
else:
print(-1)
``` | output | 1 | 19,098 | 12 | 38,197 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8 | instruction | 0 | 19,506 | 12 | 39,012 |
Tags: greedy, sortings
Correct Solution:
```
def main():
buf = input()
buflist = buf.split()
n = int(buflist[0])
k = int(buflist[1])
buf = input()
buflist = buf.split()
a = list(map(int, buflist))
a_sum = []
for i in range(1, len(a)+1):
if not a_sum:
a_sum.append(a[-i])
else:
a_sum.append(a[-i]+a_sum[-1])
cost = a_sum.pop()
a_sum.sort(reverse=True)
for i in range(k-1):
cost += a_sum[i]
print(cost)
if __name__ == '__main__':
main()
``` | output | 1 | 19,506 | 12 | 39,013 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8 | instruction | 0 | 19,507 | 12 | 39,014 |
Tags: greedy, sortings
Correct Solution:
```
n, k = map(int, input().split())
mass = [int(i) for i in input().split()]
mass = mass[::-1]
summ = 0
m = []
for i in range(n - 1):
summ += mass[i]
m.append(summ)
m = sorted(m, reverse = True)
print(sum(mass) + sum(m[:k - 1]))
``` | output | 1 | 19,507 | 12 | 39,015 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8 | instruction | 0 | 19,508 | 12 | 39,016 |
Tags: greedy, sortings
Correct Solution:
```
import heapq
n, k = map(int, input().split())
a = list(map(int, input().split()))
for i in range(n - 2, -1, -1):
a[i] += a[i + 1]
res = a[0] + sum(heapq.nlargest(k - 1, a[1:]))
print(res)
``` | output | 1 | 19,508 | 12 | 39,017 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8 | instruction | 0 | 19,509 | 12 | 39,018 |
Tags: greedy, sortings
Correct Solution:
```
import math
n,k=[int(x) for x in input().split()]
a=[int(x) for x in input().split()]
b=[]
a.reverse()
counter=0
for i in range(n-1):
counter+=a[i]
b.append(counter)
b.sort(reverse=True)
print(sum(b[:k-1])+sum(a))
``` | output | 1 | 19,509 | 12 | 39,019 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8 | instruction | 0 | 19,510 | 12 | 39,020 |
Tags: greedy, sortings
Correct Solution:
```
N,K = map(int, input().split())
A = list(map(int, input().split()))
L = [0]
for i in A[::-1]:
L.append(L[-1] + i)
k = L[-1] + sum(sorted(L[1:-1])[N-K:])
print(k)
``` | output | 1 | 19,510 | 12 | 39,021 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8 | instruction | 0 | 19,511 | 12 | 39,022 |
Tags: greedy, sortings
Correct Solution:
```
# https://codeforces.com/contest/1175/problem/D
n, k = map(int, input().split())
a = list(map(int, input().split()))
s = [0 for i in range(n)]
for i in range(n - 1, -1, -1):
s[i] = a[i] if i == n - 1 else a[i] + s[i + 1]
s0 = s[0]
s1 = s[1:]
s1.sort()
res = 0
for i in range(n-2, n-k-1, -1):
res += s1[i]
print(res + s0)
``` | output | 1 | 19,511 | 12 | 39,023 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8 | instruction | 0 | 19,512 | 12 | 39,024 |
Tags: greedy, sortings
Correct Solution:
```
n, k = map(int, input().strip().split(' '))
a = list(map(int, input().strip().split(' ')))
cnt = []
cnt.append(a[-1])
for i in range(1, n):
cnt.append(cnt[i-1] + a[-(i+1)])
ans = cnt[-1]
del cnt[-1]
cnt.sort(reverse=True)
ans += sum(cnt[:(k-1)])
print(ans)
``` | output | 1 | 19,512 | 12 | 39,025 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an array a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8 | instruction | 0 | 19,513 | 12 | 39,026 |
Tags: greedy, sortings
Correct Solution:
```
#########################################################################################################\
#########################################################################################################
###################################The_Apurv_Rathore#####################################################
#########################################################################################################
#########################################################################################################
import sys,os,io
from sys import stdin
from math import log, gcd, ceil
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop
from bisect import bisect_left , bisect_right
import math
alphabets = list('abcdefghijklmnopqrstuvwxyz')
def ncr(n, r, p):
num = den = 1
for i in range(r):
num = (num * (n - i)) % p
den = (den * (i + 1)) % p
return (num * pow(den,
p - 2, p)) % p
def primeFactors(n):
l = []
while n % 2 == 0:
l.append(2)
n = n / 2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
l.append(int(i))
n = n / i
if n > 2:
l.append(n)
return list(set(l))
def power(x, y, p) :
res = 1
x = x % p
if (x == 0) :
return 0
while (y > 0) :
if ((y & 1) == 1) :
res = (res * x) % p
y = y >> 1 # y = y/2
x = (x * x) % p
return res
def SieveOfEratosthenes(n):
prime = [True for i in range(n+1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
return prime
def countdig(n):
c = 0
while (n > 0):
n //= 10
c += 1
return c
def si():
return input()
def prefix_sum(arr):
r = [0] * (len(arr)+1)
for i, el in enumerate(arr):
r[i+1] = r[i] + el
return r
def divideCeil(n,x):
if (n%x==0):
return n//x
return n//x+1
def ii():
return int(input())
def li():
return list(map(int,input().split()))
def ws(s): sys.stdout.write(s + '\n')
def wi(n): sys.stdout.write(str(n) + '\n')
def wia(a): sys.stdout.write(''.join([str(x) for x in a]) + '\n')
#__________________________TEMPLATE__________________OVER_______________________________________________________
if(os.path.exists('input.txt')):
sys.stdin = open("input.txt","r") ; sys.stdout = open("output.txt","w")
else:
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
t = 1
# t = int(input())
for _ in range(t):
n,k = li()
a =li()
suf = []
cur = 0
for i in range(n-1,-1,-1):
cur+=a[i]
suf.append(cur)
ans = suf[-1]
suf = suf[::-1]
suf = suf[1:]
suf.sort(reverse=True)
for i in range(k-1):
ans+=suf[i]
print(ans)
``` | output | 1 | 19,513 | 12 | 39,027 |
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 a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8
Submitted Solution:
```
from collections import Counter, OrderedDict
from itertools import permutations as perm
from collections import deque
from sys import stdin
from bisect import *
from heapq import *
import math
g = lambda : stdin.readline().strip()
gl = lambda : g().split()
gil = lambda : [int(var) for var in gl()]
gfl = lambda : [float(var) for var in gl()]
gcl = lambda : list(g())
gbs = lambda : [int(var) for var in g()]
mod = int(1e9)+7
inf = float("inf")
n, k = gil()
a = gil()
for i in range(1, n):
a[i] += a[i-1]
ans = a.pop()
a.sort()
print(k*ans - sum(a[:k-1]))
``` | instruction | 0 | 19,514 | 12 | 39,028 |
Yes | output | 1 | 19,514 | 12 | 39,029 |
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 a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8
Submitted Solution:
```
# cf_contests E66
import sys
input = sys.stdin.readline
n, k = map(int, input().split())
a = list(map(int, input().split()))
s = 0
p = []
for i in range(n - 1, 0, -1):
s += a[i]
p.append(s)
p.sort()
p.reverse()
res = s + a[0]
for i in range(k-1):
res += p[i]
print(res)
``` | instruction | 0 | 19,515 | 12 | 39,030 |
Yes | output | 1 | 19,515 | 12 | 39,031 |
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 a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8
Submitted Solution:
```
n,k=map(int,input().split())
A=[int(i) for i in input().split()]
suff=[]
sumi=0
for i in range(n-1,0,-1):
sumi+=A[i]
suff.append(sumi)
# print(suff)
suff.sort(reverse=True)
ans=sum(suff[:k-1])
ans+=sum(A)
print(ans)
``` | instruction | 0 | 19,516 | 12 | 39,032 |
Yes | output | 1 | 19,516 | 12 | 39,033 |
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 a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8
Submitted Solution:
```
n, k = map(int, input().split())
a = list(map(int, input().split()))
p = [0]
for i in a[ : : -1]:
p.append(p[-1] + i)
p = p[ : : -1]
ans = p[0]
ans += sum(sorted(p[1: -1], reverse = True)[ : k - 1])
print(ans)
``` | instruction | 0 | 19,517 | 12 | 39,034 |
Yes | output | 1 | 19,517 | 12 | 39,035 |
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 a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8
Submitted Solution:
```
n,k=[int(x) for x in input().split()]
a=[int(x) for x in input().split()]
a.reverse()
b=[]
answer=0
counter=0
for item in a:
counter+=item
b.append(counter)
y=n-k
index=-1
counter=0
for j in range(k,0,-1):
x=index+1
maxim=-10**10
index=0
if j==1:
maxim=b[-1]
else:
for i in range(x,y+1):
if b[i]>maxim:
maxim=b[i]
index=i
answer+=(maxim-counter)*j
counter=maxim
y+=1
print(answer)
``` | instruction | 0 | 19,518 | 12 | 39,036 |
No | output | 1 | 19,518 | 12 | 39,037 |
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 a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8
Submitted Solution:
```
import sys
#Library Info(ACL for Python/Pypy) -> https://github.com/not522/ac-library-python
def input():
return sys.stdin.readline().rstrip()
DXY = [(0, -1), (1, 0), (0, 1), (-1, 0)] # L,D,R,Uの順番
def main():
n, k = map(int, input().split())
a = [0] + list(map(int, input().split()))
for i in range(1, n + 1):
a[i] += a[i - 1]
ans = k * a[n]
a.pop();a.sort()
for i in range(k - 1):
ans -= a[i]
print(ans)
return 0
if __name__ == "__main__":
main()
``` | instruction | 0 | 19,519 | 12 | 39,038 |
No | output | 1 | 19,519 | 12 | 39,039 |
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 a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8
Submitted Solution:
```
import math
n,k=[int(x) for x in input().split()]
a=[int(x) for x in input().split()]
b=[]
a.reverse()
counter=0
for item in a:
counter+=item
b.append(counter)
b.sort(reverse=True)
print(sum(b[:k-1])+sum(a))
``` | instruction | 0 | 19,520 | 12 | 39,040 |
No | output | 1 | 19,520 | 12 | 39,041 |
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 a_1, a_2, ..., a_n and an integer k.
You are asked to divide this array into k non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let f(i) be the index of subarray the i-th element belongs to. Subarrays are numbered from left to right and from 1 to k.
Let the cost of division be equal to ∑_{i=1}^{n} (a_i ⋅ f(i)). For example, if a = [1, -2, -3, 4, -5, 6, -7] and we divide it into 3 subbarays in the following way: [1, -2, -3], [4, -5], [6, -7], then the cost of division is equal to 1 ⋅ 1 - 2 ⋅ 1 - 3 ⋅ 1 + 4 ⋅ 2 - 5 ⋅ 2 + 6 ⋅ 3 - 7 ⋅ 3 = -9.
Calculate the maximum cost you can obtain by dividing the array a into k non-empty consecutive subarrays.
Input
The first line contains two integers n and k (1 ≤ k ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ..., a_n ( |a_i| ≤ 10^6).
Output
Print the maximum cost you can obtain by dividing the array a into k nonempty consecutive subarrays.
Examples
Input
5 2
-1 -2 5 -4 8
Output
15
Input
7 6
-3 0 -1 -2 -2 -4 -1
Output
-45
Input
4 1
3 -1 6 0
Output
8
Submitted Solution:
```
#########################################################################################################\
#########################################################################################################
###################################The_Apurv_Rathore#####################################################
#########################################################################################################
#########################################################################################################
import sys,os,io
from sys import stdin
from math import log, gcd, ceil
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop
from bisect import bisect_left , bisect_right
import math
alphabets = list('abcdefghijklmnopqrstuvwxyz')
def ncr(n, r, p):
num = den = 1
for i in range(r):
num = (num * (n - i)) % p
den = (den * (i + 1)) % p
return (num * pow(den,
p - 2, p)) % p
def primeFactors(n):
l = []
while n % 2 == 0:
l.append(2)
n = n / 2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
l.append(int(i))
n = n / i
if n > 2:
l.append(n)
return list(set(l))
def power(x, y, p) :
res = 1
x = x % p
if (x == 0) :
return 0
while (y > 0) :
if ((y & 1) == 1) :
res = (res * x) % p
y = y >> 1 # y = y/2
x = (x * x) % p
return res
def SieveOfEratosthenes(n):
prime = [True for i in range(n+1)]
p = 2
while (p * p <= n):
if (prime[p] == True):
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
return prime
def countdig(n):
c = 0
while (n > 0):
n //= 10
c += 1
return c
def si():
return input()
def prefix_sum(arr):
r = [0] * (len(arr)+1)
for i, el in enumerate(arr):
r[i+1] = r[i] + el
return r
def divideCeil(n,x):
if (n%x==0):
return n//x
return n//x+1
def ii():
return int(input())
def li():
return list(map(int,input().split()))
def ws(s): sys.stdout.write(s + '\n')
def wi(n): sys.stdout.write(str(n) + '\n')
def wia(a): sys.stdout.write(''.join([str(x) for x in a]) + '\n')
#__________________________TEMPLATE__________________OVER_______________________________________________________
if(os.path.exists('input.txt')):
sys.stdin = open("input.txt","r") ; sys.stdout = open("output.txt","w")
else:
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
t = 1
# t = int(input())
for _ in range(t):
n,k = li()
a =li()
suf = []
if k==1:
print(sum(a))
continue
s = 0
for i in range(n-1,-1,-1):
s+=a[i]
suf.append(s)
cur = -100000000000000
ind = -1
suf = suf[::-1]
for i in range(n-k-1,n):
if suf[i]>cur:
cur = suf[i]
ind = i
ans = suf[ind]*k
# print("suf",suf)
# print(ind)
# print(ans)
c = k-1
for i in range(ind-1,-1,-1):
ans+=a[i]*c
c-=1
c = max(c,1)
print(ans)
# ind = -1
# suf.reverse()
# for i in range(n-k):
# if (suf[i]>cur):
# cur = suf[i]
# ind = i
# print(ind,suf[ind])
# #print(suf)
# ans = 0
# ans+=suf[ind]*k
# c = k-1
# #print(ans)
# ind = n - ind-1
# for i in range(ind-1,-1,-1):
# if (c==1):
# break
# ans+=c*a[i]
# #print("c*a[i]",c*a[i])
# c-=1
# #print(ans)
# ans+=sum(a[:i+1])
# print(ans)
``` | instruction | 0 | 19,521 | 12 | 39,042 |
No | output | 1 | 19,521 | 12 | 39,043 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3 | instruction | 0 | 19,625 | 12 | 39,250 |
Tags: data structures, divide and conquer, dp, greedy
Correct Solution:
```
import sys
input = sys.stdin.readline
sys.setrecursionlimit(5010)
n=int(input())
A=list(map(int,input().split()))
DICT=dict()
def dfs(x,y):
if x==y:
return []
MIN=min(A[x:y])
for i in range(x,y):
A[i]-=MIN
ANS=[]
NOW=x
for i in range(x,y):
if A[i]==0:
if NOW!=i:
ANS.append((NOW,i))
NOW=i+1
if NOW!=y:
ANS.append((NOW,y))
DICT[(x,y)]=(ANS,MIN)
return ANS
Q=[(0,n)]
TOP=[]
while Q:
x,y=Q.pop()
TOP.append((x,y))
Q+=dfs(x,y)
ANSDICT=dict()
for x,y in TOP[::-1]:
A=y-x
B=DICT[x,y][1]
for z,w in DICT[x,y][0]:
B+=ANSDICT[z,w]
ANSDICT[x,y]=min(A,B)
print(ANSDICT[0,n])
``` | output | 1 | 19,625 | 12 | 39,251 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3 | instruction | 0 | 19,626 | 12 | 39,252 |
Tags: data structures, divide and conquer, dp, greedy
Correct Solution:
```
import os
import sys
from io import BytesIO, IOBase
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------------------
def RL(): return map(int, sys.stdin.readline().rstrip().split())
def RLL(): return list(map(int, sys.stdin.readline().rstrip().split()))
def N(): return int(input())
def print_list(l):
print(' '.join(map(str,l)))
import sys
sys.setrecursionlimit(5010)
# import heapq as hq
# from collections import deque as dq
# from collections import Counter
# from math import ceil,floor,sqrt
# import bisect as bs
# from collections import defaultdict as dc
n = N()
a = RLL()
def clear(l,r,last):
if l==r:
return 0
res = r-l
m = min(a[l:r])
tmp = m - last
s = l
for i in range(l,r):
if a[i]==m:
tmp+=clear(s,i,m)
s = i+1
tmp+=clear(s,r,m)
return min(res,tmp)
s = 0
ans = 0
for i in range(n):
if a[i]==0:
ans+=clear(s,i,0)
s = i+1
ans+=clear(s,n,0)
print(ans)
``` | output | 1 | 19,626 | 12 | 39,253 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3 | instruction | 0 | 19,627 | 12 | 39,254 |
Tags: data structures, divide and conquer, dp, greedy
Correct Solution:
```
n = int(input()) + 1
l = list(map(int, input().split())) + [0]
out = 0
q = []
for v in l:
if v == 0:
dp = []
n = len(q)
for i in range(n):
curr = q[i] + i
smol = q[i]
for j in range(i - 1, -1, -1):
smol = min(q[j], smol)
diff = q[i] - smol
curr = min(curr, diff + dp[j] + i - j - 1)
dp.append(curr)
real = [n - i + dp[i] - 1 for i in range(n)] + [n]
out += min(real)
q = []
else:
q.append(v)
print(out)
``` | output | 1 | 19,627 | 12 | 39,255 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3 | instruction | 0 | 19,628 | 12 | 39,256 |
Tags: data structures, divide and conquer, dp, greedy
Correct Solution:
```
from sys import stdin
n = int(stdin.readline())
a = list(map(int,stdin.readline().split()))
a = [0] + a
ans = n
dp = [float("inf")] * (n+1)
dp[0] = 0
for i in range(1,n+1):
nmin = float("inf")
for j in range(i-1,-1,-1):
if a[j] <= nmin:
dp[i] = min(dp[i] , dp[j] + max(0,a[i]-a[j]) + (i-j-1) )
nmin = min(nmin,a[j])
#print (dp)
for i in range(n+1):
ans = min(ans , dp[i] + n-i)
print (ans)
``` | output | 1 | 19,628 | 12 | 39,257 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3 | instruction | 0 | 19,629 | 12 | 39,258 |
Tags: data structures, divide and conquer, dp, greedy
Correct Solution:
```
import sys, math
import io, os
# data = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
from bisect import bisect_left as bl, bisect_right as br, insort
# from heapq import heapify, heappush, heappop
from collections import defaultdict as dd, deque, Counter
# from itertools import permutations,combinations
def data(): return sys.stdin.readline().strip()
def mdata(): return list(map(int, data().split()))
def outl(var): sys.stdout.write(' '.join(map(str, var)) + '\n')
def out(var): sys.stdout.write(str(var) + '\n')
from decimal import Decimal
# from fractions import Fraction
# sys.setrecursionlimit(100000)
INF = float('inf')
mod = int(1e9) + 7
from types import GeneratorType
def bootstrap(f, stack=[]):
def wrappedfunc(*args, **kwargs):
if stack:
return f(*args, **kwargs)
else:
to = f(*args, **kwargs)
while True:
if type(to) is GeneratorType:
stack.append(to)
to = next(to)
else:
stack.pop()
if not stack:
break
to = stack[-1].send(to)
return to
return wrappedfunc
@bootstrap
def cal(l,r,val):
if r-l<0:
yield 0
return
min1=min(a[l:r+1])
ans=min1-val
k=l-1
for i in range(l,r+1):
if a[i]==min1:
ans+=yield cal(k+1,i-1,min1)
k=i
ans+= yield cal(k+1,r,min1)
yield min(r-l+1,ans)
n=int(data())
a=mdata()
out(cal(0,n-1,0))
``` | output | 1 | 19,629 | 12 | 39,259 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3 | instruction | 0 | 19,630 | 12 | 39,260 |
Tags: data structures, divide and conquer, dp, greedy
Correct Solution:
```
from bisect import *
from collections import *
from math import gcd,ceil,sqrt,floor,inf
from heapq import *
from itertools import *
from operator import add,mul,sub,xor,truediv,floordiv
from functools import *
#------------------------------------------------------------------------
import os
import sys
from io import BytesIO, IOBase
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
#------------------------------------------------------------------------
def RL(): return map(int, sys.stdin.readline().rstrip().split())
def RLL(): return list(map(int, sys.stdin.readline().rstrip().split()))
def N(): return int(input())
#------------------------------------------------------------------------
from types import GeneratorType
def bootstrap(f, stack=[]):
def wrappedfunc(*args, **kwargs):
if stack:
return f(*args, **kwargs)
else:
to = f(*args, **kwargs)
while True:
if type(to) is GeneratorType:
stack.append(to)
to = next(to)
else:
stack.pop()
if not stack:
break
to = stack[-1].send(to)
return to
return wrappedfunc
farr=[1]
ifa=[]
def fact(x,mod=0):
if mod:
while x>=len(farr):
farr.append(farr[-1]*len(farr)%mod)
else:
while x>=len(farr):
farr.append(farr[-1]*len(farr))
return farr[x]
def ifact(x,mod):
global ifa
ifa.append(pow(farr[-1],mod-2,mod))
for i in range(x,0,-1):
ifa.append(ifa[-1]*i%mod)
ifa=ifa[::-1]
def per(i,j,mod=0):
if i<j: return 0
if not mod:
return fact(i)//fact(i-j)
return farr[i]*ifa[i-j]%mod
def com(i,j,mod=0):
if i<j: return 0
if not mod:
return per(i,j)//fact(j)
return per(i,j,mod)*ifa[j]%mod
def catalan(n):
return com(2*n,n)//(n+1)
def linc(f,t,l,r):
while l<r:
mid=(l+r)//2
if t>f(mid):
l=mid+1
else:
r=mid
return l
def rinc(f,t,l,r):
while l<r:
mid=(l+r+1)//2
if t<f(mid):
r=mid-1
else:
l=mid
return l
def ldec(f,t,l,r):
while l<r:
mid=(l+r)//2
if t<f(mid):
l=mid+1
else:
r=mid
return l
def rdec(f,t,l,r):
while l<r:
mid=(l+r+1)//2
if t>f(mid):
r=mid-1
else:
l=mid
return l
def isprime(n):
for i in range(2,int(n**0.5)+1):
if n%i==0:
return False
return True
def binfun(x):
c=0
for w in arr:
c+=ceil(w/x)
return c
def lowbit(n):
return n&-n
def inverse(a,m):
a%=m
if a<=1: return a
return ((1-inverse(m,a)*m)//a)%m
class BIT:
def __init__(self,arr):
self.arr=arr
self.n=len(arr)-1
def update(self,x,v):
while x<=self.n:
self.arr[x]+=v
x+=x&-x
def query(self,x):
ans=0
while x:
ans+=self.arr[x]
x&=x-1
return ans
'''
class SMT:
def __init__(self,arr):
self.n=len(arr)-1
self.arr=[0]*(self.n<<2)
self.lazy=[0]*(self.n<<2)
def Build(l,r,rt):
if l==r:
self.arr[rt]=arr[l]
return
m=(l+r)>>1
Build(l,m,rt<<1)
Build(m+1,r,rt<<1|1)
self.pushup(rt)
Build(1,self.n,1)
def pushup(self,rt):
self.arr[rt]=self.arr[rt<<1]+self.arr[rt<<1|1]
def pushdown(self,rt,ln,rn):#lr,rn表区间数字数
if self.lazy[rt]:
self.lazy[rt<<1]+=self.lazy[rt]
self.lazy[rt<<1|1]=self.lazy[rt]
self.arr[rt<<1]+=self.lazy[rt]*ln
self.arr[rt<<1|1]+=self.lazy[rt]*rn
self.lazy[rt]=0
def update(self,L,R,c,l=1,r=None,rt=1):#L,R表示操作区间
if r==None: r=self.n
if L<=l and r<=R:
self.arr[rt]+=c*(r-l+1)
self.lazy[rt]+=c
return
m=(l+r)>>1
self.pushdown(rt,m-l+1,r-m)
if L<=m: self.update(L,R,c,l,m,rt<<1)
if R>m: self.update(L,R,c,m+1,r,rt<<1|1)
self.pushup(rt)
def query(self,L,R,l=1,r=None,rt=1):
if r==None: r=self.n
#print(L,R,l,r,rt)
if L<=l and R>=r:
return self.arr[rt]
m=(l+r)>>1
self.pushdown(rt,m-l+1,r-m)
ans=0
if L<=m: ans+=self.query(L,R,l,m,rt<<1)
if R>m: ans+=self.query(L,R,m+1,r,rt<<1|1)
return ans
'''
class DSU:#容量+路径压缩
def __init__(self,n):
self.c=[-1]*n
def same(self,x,y):
return self.find(x)==self.find(y)
def find(self,x):
if self.c[x]<0:
return x
self.c[x]=self.find(self.c[x])
return self.c[x]
def union(self,u,v):
u,v=self.find(u),self.find(v)
if u==v:
return False
if self.c[u]<self.c[v]:
u,v=v,u
self.c[u]+=self.c[v]
self.c[v]=u
return True
def size(self,x): return -self.c[self.find(x)]
class UFS:#秩+路径
def __init__(self,n):
self.parent=[i for i in range(n)]
self.ranks=[0]*n
def find(self,x):
if x!=self.parent[x]:
self.parent[x]=self.find(self.parent[x])
return self.parent[x]
def union(self,u,v):
pu,pv=self.find(u),self.find(v)
if pu==pv:
return False
if self.ranks[pu]>=self.ranks[pv]:
self.parent[pv]=pu
if self.ranks[pv]==self.ranks[pu]:
self.ranks[pu]+=1
else:
self.parent[pu]=pv
def Prime(n):
c=0
prime=[]
flag=[0]*(n+1)
for i in range(2,n+1):
if not flag[i]:
prime.append(i)
c+=1
for j in range(c):
if i*prime[j]>n: break
flag[i*prime[j]]=prime[j]
if i%prime[j]==0: break
return prime
def dij(s,graph):
d={}
d[s]=0
heap=[(0,s)]
seen=set()
while heap:
dis,u=heappop(heap)
if u in seen:
continue
for v in graph[u]:
if v not in d or d[v]>d[u]+graph[u][v]:
d[v]=d[u]+graph[u][v]
heappush(heap,(d[v],v))
return d
def GP(it): return [(ch,len(list(g))) for ch,g in groupby(it)]
class DLN:
def __init__(self,val):
self.val=val
self.pre=None
self.next=None
t=1
for i in range(t):
n=N()
a=RLL()
dp=[[n]*(n+2) for i in range(n)]
for i in range(min(a[0],n),-1,-1):
dp[0][i]=min(dp[0][i+1],i+(a[0]>i))
#print(dp[0])
for i in range(1,n):
for j in range(min(n,a[i]),-1,-1):
dp[i][j]=min(dp[i][j+1],dp[i-1][j]+(a[i]>j))
if j>a[i-1]:
dp[i][j]=min(dp[i][j],dp[i-1][a[i-1]]+j-a[i-1]+(a[i]>j))
print(min(dp[-1]))
'''
sys.setrecursionlimit(200000)
import threading
threading.stack_size(10**8)
t=threading.Thread(target=main)
t.start()
t.join()
'''
``` | output | 1 | 19,630 | 12 | 39,261 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3 | instruction | 0 | 19,631 | 12 | 39,262 |
Tags: data structures, divide and conquer, dp, greedy
Correct Solution:
```
#from collections import defaultdict
#
#tests = int(input())
#for t in range(tests):
from collections import Counter
from sys import stdin, stdout
def input():
return stdin.readline().strip()
def bootstrap(f, stack=[]):
from collections import defaultdict
from types import GeneratorType
def wrappedfunc(*args, **kwargs):
if stack:
return f(*args, **kwargs)
else:
to = f(*args, **kwargs)
while True:
if type(to) is GeneratorType:
stack.append(to)
to = next(to)
else:
stack.pop()
if not stack:
break
to = stack[-1].send(to)
return to
return wrappedfunc
n = int(input())
ls = list(map(int, input().split()))
res = 0
@bootstrap
def ops(start, end, curr_val):
if start == end:
yield 1
if end < start:
yield 0
curr_min = None
ls_min = []
for i in range(start, end+1):
if curr_min is None or ls[i] < curr_min:
curr_min = ls[i]
ls_min = [i]
elif ls[i] == curr_min:
ls_min.append(i)
res_1 = end-start+1
res_2 = curr_min - curr_val
curr_idx = start
for idx in ls_min:
res_2 += yield ops(curr_idx, idx-1, curr_min)
curr_idx = idx + 1
res_2 += yield ops(curr_idx, end, curr_min)
yield min(res_1, res_2)
if sum(ls) != 0:
print(ops(0, n-1, 0))
else:
print(0)
``` | output | 1 | 19,631 | 12 | 39,263 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3 | instruction | 0 | 19,632 | 12 | 39,264 |
Tags: data structures, divide and conquer, dp, greedy
Correct Solution:
```
import sys
def minp():
return sys.stdin.readline().strip()
def mint():
return int(minp())
def mints():
return map(int, minp().split())
def check(s, n, v):
for i in range(n):
if s[i:i+n].count(v) == 0:
return False
return True
def solve():
n = mint()
a = list(mints())
a.append(0)
dp = [int(1e18)]*(n+2)
dp[0] = 0
for i in range(1,n+2):
d = int(1e18)
s = 0
z = a[i-1]
for j in range(i-2, -2, -1):
if a[j] < z:
z = a[j]
d = min(d, s + max(a[j] - z, 0) + dp[j+1])
s += 1
dp[i] = d
print(dp[n+1])
solve()
``` | output | 1 | 19,632 | 12 | 39,265 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3
Submitted Solution:
```
import sys
import threading
input=sys.stdin.readline
sys.setrecursionlimit(10**9)
threading.stack_size(16*2048*2048)
n=int(input())
a=[int(i) for i in input().split() if i!='\n']
a.insert(0,0)
a.append(0)
def solve(l,r):
if l>r:
return(0)
#"outside" is the minimum number obtained in the previous iteration
#which we have to subtract from all the elements in this segment
outside=max(a[l-1],a[r+1])
mina=min(a[l:r+1])
min_index=a.index(mina,l,r+1)
return(min(r-l+1,solve(l,min_index-1)+solve(min_index+1,r)+mina-outside))
ans=solve(1,n)
sys.stdout.write(str(ans)+'\n')
``` | instruction | 0 | 19,633 | 12 | 39,266 |
Yes | output | 1 | 19,633 | 12 | 39,267 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3
Submitted Solution:
```
import sys
def solve(l,r):
if l>=r:
return 0
x = a.index(min(a[l:r]),l,r)
mn = min(a[l:r])
i,j = 0,0
if(l-1>=0):
i = a[l-1]
if(r<n):
j = a[r]
out = max(i,j)
return min(r-l,mn + solve(l,x) + solve(x+1,r) - out)
sys.setrecursionlimit(10000)
n = int(input())
a = list(map(int,input().split()))
print(solve(0,n))
``` | instruction | 0 | 19,634 | 12 | 39,268 |
Yes | output | 1 | 19,634 | 12 | 39,269 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3
Submitted Solution:
```
import sys
sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]
def cal(l,r,h=0):
if l>=r:return 0
mn=mni=inf
for i in range(l,r):
if aa[i]<mn:
mn=aa[i]
mni=i
return min(cal(l,mni,mn)+cal(mni+1,r,mn)+mn-h,r-l)
inf=10**16
n=II()
aa=LI()
print(cal(0,n))
``` | instruction | 0 | 19,635 | 12 | 39,270 |
Yes | output | 1 | 19,635 | 12 | 39,271 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3
Submitted Solution:
```
import sys
sys.setrecursionlimit(10000)
n = int(input())
a = list(map(int, input().split()))
def f(l, r, h):
if l >= r:
return 0
x = a.index(min(a[l:r]), l, r)
return min(r - l, a[x] - h + f(l, x, a[x]) + f(x + 1, r, a[x]))
print(f(0, n, 0))
``` | instruction | 0 | 19,636 | 12 | 39,272 |
Yes | output | 1 | 19,636 | 12 | 39,273 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3
Submitted Solution:
```
List = []
history = []
x = int(input())
for i in input().split():
List.append(int(i))
print(List)
sum = 0
for i in List:
if not(i in history):
x = List.count(i)
sum += (x-1)
history.append(i)
print(sum)
``` | instruction | 0 | 19,637 | 12 | 39,274 |
No | output | 1 | 19,637 | 12 | 39,275 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3
Submitted Solution:
```
n = int(input())
a = "".join(input().split())
s = [i for i in a.split("0") if i!=""]
ans = 0
for i in s:
j = 0
maxi = 0
p = set()
while(j<len(i)):
while(j<len(i)-1 and i[j]!="1" and int(i[j])>int(i[j+1])):
p.add(int(i[j]))
j+=1
if(len(p)!=0):
ans += min(len(p),max(p))
p = set()
while (j < len(i) - 1 and i[j] != "1" and int(i[j]) > int(i[j + 1])):
p.add(int(i[j]))
j += 1
if (len(p)!=0):
ans += min(len(p),max(p))
j+=1
ans += 1
print(min(ans,n))
``` | instruction | 0 | 19,638 | 12 | 39,276 |
No | output | 1 | 19,638 | 12 | 39,277 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3
Submitted Solution:
```
n = int(input())
a = [0]+list(map(int,input().split()))+[0]
def dfs(l,r,base):
if r-l <= 1:
return 0
mn = float("INF")
for i in range(l+1,r-1):
mn = min(mn,a[i]-base)
count = r-l-1
if r-l-1 > mn:
k = l
now = mn
for i in range(l+1,r-1):
if a[i]-base == mn:
now += dfs(k,i,mn+base)
k = i
if k != r-2:
now += dfs(k,r,mn+base)
count = min(r-l-1,now)
return count
print(dfs(0,n+2,0))
``` | instruction | 0 | 19,639 | 12 | 39,278 |
No | output | 1 | 19,639 | 12 | 39,279 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a multiset containing several integers. Initially, it contains a_1 elements equal to 1, a_2 elements equal to 2, ..., a_n elements equal to n.
You may apply two types of operations:
* choose two integers l and r (l ≤ r), then remove one occurrence of l, one occurrence of l + 1, ..., one occurrence of r from the multiset. This operation can be applied only if each number from l to r occurs at least once in the multiset;
* choose two integers i and x (x ≥ 1), then remove x occurrences of i from the multiset. This operation can be applied only if the multiset contains at least x occurrences of i.
What is the minimum number of operations required to delete all elements from the multiset?
Input
The first line contains one integer n (1 ≤ n ≤ 5000).
The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
Output
Print one integer — the minimum number of operations required to delete all elements from the multiset.
Examples
Input
4
1 4 1 1
Output
2
Input
5
1 0 1 0 1
Output
3
Submitted Solution:
```
import sys
def minp():
return sys.stdin.readline().strip()
def mint():
return int(minp())
def mints():
return map(int, minp().split())
def check(s, n, v):
for i in range(n):
if s[i:i+n].count(v) == 0:
return False
return True
def solve():
n = mint()
a = list(mints())
a.append(0)
dp = [int(1e18)]*(n+2)
dp[0] = 0
for i in range(1,n+2):
d = int(1e18)
s = 0
z = a[i-1]
dpcan = int(1e9+1)
for j in range(i-2, -1, -2):
if a[j] < z:
z = a[i]
dpcan = z
if a[j] <= dpcan:
d = min(d, s + max(a[j] - z, 0) + dp[j+1])
s += (a[j] > z)
dp[i] = d
#print(dp)
print(dp[n+1])
solve()
``` | instruction | 0 | 19,640 | 12 | 39,280 |
No | output | 1 | 19,640 | 12 | 39,281 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two arrays a and b, each consisting of n positive integers, and an integer x. Please determine if one can rearrange the elements of b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n).
Input
The first line of input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. t blocks follow, each describing an individual test case.
The first line of each test case contains two integers n and x (1 ≤ n ≤ 50; 1 ≤ x ≤ 1000) — the length of arrays a and b, and the parameter x, described in the problem statement.
The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_1 ≤ a_2 ≤ ... ≤ a_n ≤ x) — the elements of array a in non-descending order.
The third line of each test case contains n integers b_1, b_2, …, b_n (1 ≤ b_1 ≤ b_2 ≤ ... ≤ b_n ≤ x) — the elements of array b in non-descending order.
Test cases are separated by a blank line.
Output
For each test case print Yes if one can rearrange the corresponding array b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n) or No otherwise.
Each character can be printed in any case.
Example
Input
4
3 4
1 2 3
1 1 2
2 6
1 4
2 5
4 4
1 2 3 4
1 2 3 4
1 5
5
5
Output
Yes
Yes
No
No
Note
In the first test case, one can rearrange b so it'll look like [1, 2, 1]. In this case, 1 + 1 ≤ 4; 2 + 2 ≤ 4; 3 + 1 ≤ 4.
In the second test case, one can set b to [5, 2], then 1 + 5 ≤ 6; 4 + 2 ≤ 6.
In the third test case, no matter how one shuffles array b, a_4 + b_4 = 4 + b_4 > 4.
In the fourth test case, there is only one rearrangement of array b and it doesn't satisfy the condition since 5 + 5 > 5. | instruction | 0 | 19,641 | 12 | 39,282 |
Tags: greedy, sortings
Correct Solution:
```
from sys import stdin, stdout
import heapq
import cProfile
from collections import Counter, defaultdict, deque
from functools import reduce
import math
import threading
import sys
import time
def get_int(): return int(stdin.readline().strip())
def get_tuple(): return map(int, stdin.readline().split())
def get_list(): return list(map(int, stdin.readline().split()))
def solve(t,T):
n,x = get_tuple()
a = get_list()
b = get_list()
if t!=T:
_ = input()
a.sort()
b.sort(reverse=True)
visited = [False]*n
ans = "YES"
for i in range(n):
flag = False
for i in range(n):
if not visited[i] and a[i]+b[i]<=x:
visited[i] = True
flag = True
break
if not flag:
ans = "NO"
print(ans)
def main(i,t):
solve(i,t)
TestCases = True
if TestCases:
t = get_int()
for i in range(t):
main(i+1,t)
else:
main()
``` | output | 1 | 19,641 | 12 | 39,283 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two arrays a and b, each consisting of n positive integers, and an integer x. Please determine if one can rearrange the elements of b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n).
Input
The first line of input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. t blocks follow, each describing an individual test case.
The first line of each test case contains two integers n and x (1 ≤ n ≤ 50; 1 ≤ x ≤ 1000) — the length of arrays a and b, and the parameter x, described in the problem statement.
The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_1 ≤ a_2 ≤ ... ≤ a_n ≤ x) — the elements of array a in non-descending order.
The third line of each test case contains n integers b_1, b_2, …, b_n (1 ≤ b_1 ≤ b_2 ≤ ... ≤ b_n ≤ x) — the elements of array b in non-descending order.
Test cases are separated by a blank line.
Output
For each test case print Yes if one can rearrange the corresponding array b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n) or No otherwise.
Each character can be printed in any case.
Example
Input
4
3 4
1 2 3
1 1 2
2 6
1 4
2 5
4 4
1 2 3 4
1 2 3 4
1 5
5
5
Output
Yes
Yes
No
No
Note
In the first test case, one can rearrange b so it'll look like [1, 2, 1]. In this case, 1 + 1 ≤ 4; 2 + 2 ≤ 4; 3 + 1 ≤ 4.
In the second test case, one can set b to [5, 2], then 1 + 5 ≤ 6; 4 + 2 ≤ 6.
In the third test case, no matter how one shuffles array b, a_4 + b_4 = 4 + b_4 > 4.
In the fourth test case, there is only one rearrangement of array b and it doesn't satisfy the condition since 5 + 5 > 5. | instruction | 0 | 19,642 | 12 | 39,284 |
Tags: greedy, sortings
Correct Solution:
```
t = int(input())
while(t!=0):
a, b = map(int,input().split())
c = list( map(int,input().split()))
d = list(map(int,input().split()))
c.reverse()
d.sort()
j = 0
for _ in range (a):
if(c[_]+d[_] > b):
j = 1
if j == 1:
print ("NO")
else :
print ("YES")
t = t-1
if t>0:
c = input()
``` | output | 1 | 19,642 | 12 | 39,285 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two arrays a and b, each consisting of n positive integers, and an integer x. Please determine if one can rearrange the elements of b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n).
Input
The first line of input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. t blocks follow, each describing an individual test case.
The first line of each test case contains two integers n and x (1 ≤ n ≤ 50; 1 ≤ x ≤ 1000) — the length of arrays a and b, and the parameter x, described in the problem statement.
The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_1 ≤ a_2 ≤ ... ≤ a_n ≤ x) — the elements of array a in non-descending order.
The third line of each test case contains n integers b_1, b_2, …, b_n (1 ≤ b_1 ≤ b_2 ≤ ... ≤ b_n ≤ x) — the elements of array b in non-descending order.
Test cases are separated by a blank line.
Output
For each test case print Yes if one can rearrange the corresponding array b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n) or No otherwise.
Each character can be printed in any case.
Example
Input
4
3 4
1 2 3
1 1 2
2 6
1 4
2 5
4 4
1 2 3 4
1 2 3 4
1 5
5
5
Output
Yes
Yes
No
No
Note
In the first test case, one can rearrange b so it'll look like [1, 2, 1]. In this case, 1 + 1 ≤ 4; 2 + 2 ≤ 4; 3 + 1 ≤ 4.
In the second test case, one can set b to [5, 2], then 1 + 5 ≤ 6; 4 + 2 ≤ 6.
In the third test case, no matter how one shuffles array b, a_4 + b_4 = 4 + b_4 > 4.
In the fourth test case, there is only one rearrangement of array b and it doesn't satisfy the condition since 5 + 5 > 5. | instruction | 0 | 19,643 | 12 | 39,286 |
Tags: greedy, sortings
Correct Solution:
```
import sys
input = sys.stdin.readline
tests=int(input())
# x,y,z=map(int,input().split())
for test in range(tests):
n,x = map (int,input().split())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
for step in range(n):
if a[step]+b[-(step+1)]>x:
print("No")
break
else:
print("Yes")
blankrad = input()
``` | output | 1 | 19,643 | 12 | 39,287 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two arrays a and b, each consisting of n positive integers, and an integer x. Please determine if one can rearrange the elements of b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n).
Input
The first line of input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. t blocks follow, each describing an individual test case.
The first line of each test case contains two integers n and x (1 ≤ n ≤ 50; 1 ≤ x ≤ 1000) — the length of arrays a and b, and the parameter x, described in the problem statement.
The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_1 ≤ a_2 ≤ ... ≤ a_n ≤ x) — the elements of array a in non-descending order.
The third line of each test case contains n integers b_1, b_2, …, b_n (1 ≤ b_1 ≤ b_2 ≤ ... ≤ b_n ≤ x) — the elements of array b in non-descending order.
Test cases are separated by a blank line.
Output
For each test case print Yes if one can rearrange the corresponding array b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n) or No otherwise.
Each character can be printed in any case.
Example
Input
4
3 4
1 2 3
1 1 2
2 6
1 4
2 5
4 4
1 2 3 4
1 2 3 4
1 5
5
5
Output
Yes
Yes
No
No
Note
In the first test case, one can rearrange b so it'll look like [1, 2, 1]. In this case, 1 + 1 ≤ 4; 2 + 2 ≤ 4; 3 + 1 ≤ 4.
In the second test case, one can set b to [5, 2], then 1 + 5 ≤ 6; 4 + 2 ≤ 6.
In the third test case, no matter how one shuffles array b, a_4 + b_4 = 4 + b_4 > 4.
In the fourth test case, there is only one rearrangement of array b and it doesn't satisfy the condition since 5 + 5 > 5. | instruction | 0 | 19,644 | 12 | 39,288 |
Tags: greedy, sortings
Correct Solution:
```
t = int(input())
for i in range(t):
ans = 1
if i > 0: line = input()
n, x = map(int, input().split())
a = sorted(list(map(int, input().split())))
b = sorted(list(map(int, input().split())), reverse=True)
for j in range(n):
if a[j]+b[j]>x:
ans = 0
break
if ans == 1:
print("Yes")
else:
print("No")
``` | output | 1 | 19,644 | 12 | 39,289 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two arrays a and b, each consisting of n positive integers, and an integer x. Please determine if one can rearrange the elements of b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n).
Input
The first line of input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. t blocks follow, each describing an individual test case.
The first line of each test case contains two integers n and x (1 ≤ n ≤ 50; 1 ≤ x ≤ 1000) — the length of arrays a and b, and the parameter x, described in the problem statement.
The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_1 ≤ a_2 ≤ ... ≤ a_n ≤ x) — the elements of array a in non-descending order.
The third line of each test case contains n integers b_1, b_2, …, b_n (1 ≤ b_1 ≤ b_2 ≤ ... ≤ b_n ≤ x) — the elements of array b in non-descending order.
Test cases are separated by a blank line.
Output
For each test case print Yes if one can rearrange the corresponding array b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n) or No otherwise.
Each character can be printed in any case.
Example
Input
4
3 4
1 2 3
1 1 2
2 6
1 4
2 5
4 4
1 2 3 4
1 2 3 4
1 5
5
5
Output
Yes
Yes
No
No
Note
In the first test case, one can rearrange b so it'll look like [1, 2, 1]. In this case, 1 + 1 ≤ 4; 2 + 2 ≤ 4; 3 + 1 ≤ 4.
In the second test case, one can set b to [5, 2], then 1 + 5 ≤ 6; 4 + 2 ≤ 6.
In the third test case, no matter how one shuffles array b, a_4 + b_4 = 4 + b_4 > 4.
In the fourth test case, there is only one rearrangement of array b and it doesn't satisfy the condition since 5 + 5 > 5. | instruction | 0 | 19,645 | 12 | 39,290 |
Tags: greedy, sortings
Correct Solution:
```
for _ in range(int(input())):
n,x=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
b.reverse()
i=0
broke=False
while i<n:
if a[i]+b[i]>x:
print('NO')
broke=True
break
i+=1
if not broke:
print('YES')
try:
blank=input()
except:
pass
``` | output | 1 | 19,645 | 12 | 39,291 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two arrays a and b, each consisting of n positive integers, and an integer x. Please determine if one can rearrange the elements of b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n).
Input
The first line of input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. t blocks follow, each describing an individual test case.
The first line of each test case contains two integers n and x (1 ≤ n ≤ 50; 1 ≤ x ≤ 1000) — the length of arrays a and b, and the parameter x, described in the problem statement.
The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_1 ≤ a_2 ≤ ... ≤ a_n ≤ x) — the elements of array a in non-descending order.
The third line of each test case contains n integers b_1, b_2, …, b_n (1 ≤ b_1 ≤ b_2 ≤ ... ≤ b_n ≤ x) — the elements of array b in non-descending order.
Test cases are separated by a blank line.
Output
For each test case print Yes if one can rearrange the corresponding array b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n) or No otherwise.
Each character can be printed in any case.
Example
Input
4
3 4
1 2 3
1 1 2
2 6
1 4
2 5
4 4
1 2 3 4
1 2 3 4
1 5
5
5
Output
Yes
Yes
No
No
Note
In the first test case, one can rearrange b so it'll look like [1, 2, 1]. In this case, 1 + 1 ≤ 4; 2 + 2 ≤ 4; 3 + 1 ≤ 4.
In the second test case, one can set b to [5, 2], then 1 + 5 ≤ 6; 4 + 2 ≤ 6.
In the third test case, no matter how one shuffles array b, a_4 + b_4 = 4 + b_4 > 4.
In the fourth test case, there is only one rearrangement of array b and it doesn't satisfy the condition since 5 + 5 > 5. | instruction | 0 | 19,646 | 12 | 39,292 |
Tags: greedy, sortings
Correct Solution:
```
def solve(a,b,n,x):
for i in range(n):
if a[i] + b[i] > x:
return False
return True
for _ in range(2*int(input())):
try:
n,x = map(int,input().split())
A = list(map(int,input().split()))
B = list(map(int,input().split()))
A.sort()
B.sort(reverse = True)
if solve(A,B,n,x):
print("YES")
else:
print("NO")
except:
continue
``` | output | 1 | 19,646 | 12 | 39,293 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given two arrays a and b, each consisting of n positive integers, and an integer x. Please determine if one can rearrange the elements of b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n).
Input
The first line of input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. t blocks follow, each describing an individual test case.
The first line of each test case contains two integers n and x (1 ≤ n ≤ 50; 1 ≤ x ≤ 1000) — the length of arrays a and b, and the parameter x, described in the problem statement.
The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_1 ≤ a_2 ≤ ... ≤ a_n ≤ x) — the elements of array a in non-descending order.
The third line of each test case contains n integers b_1, b_2, …, b_n (1 ≤ b_1 ≤ b_2 ≤ ... ≤ b_n ≤ x) — the elements of array b in non-descending order.
Test cases are separated by a blank line.
Output
For each test case print Yes if one can rearrange the corresponding array b so that a_i + b_i ≤ x holds for each i (1 ≤ i ≤ n) or No otherwise.
Each character can be printed in any case.
Example
Input
4
3 4
1 2 3
1 1 2
2 6
1 4
2 5
4 4
1 2 3 4
1 2 3 4
1 5
5
5
Output
Yes
Yes
No
No
Note
In the first test case, one can rearrange b so it'll look like [1, 2, 1]. In this case, 1 + 1 ≤ 4; 2 + 2 ≤ 4; 3 + 1 ≤ 4.
In the second test case, one can set b to [5, 2], then 1 + 5 ≤ 6; 4 + 2 ≤ 6.
In the third test case, no matter how one shuffles array b, a_4 + b_4 = 4 + b_4 > 4.
In the fourth test case, there is only one rearrangement of array b and it doesn't satisfy the condition since 5 + 5 > 5. | instruction | 0 | 19,647 | 12 | 39,294 |
Tags: greedy, sortings
Correct Solution:
```
p=int(input())
for ctr in range(p):
n,k=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
if ctr!=p-1:
input()
a.sort()
b.sort(reverse=1)
for i in range(n):
if a[i]+b[i]>k:
print("No")
break
else:
print("Yes")
``` | output | 1 | 19,647 | 12 | 39,295 |
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