# Find if there is any subset of size K with 0 sum in an array of -1 and +1

• Difficulty Level : Easy
• Last Updated : 03 Jun, 2021

Given an integer K and an array arr containing only 1 and -1, the task is to find if there is any subset of size K sum of whose elements is 0.
Examples:

Input: arr[] = {1, -1, 1}, K = 2
Output: Yes
{1, -1} is a valid subset
Input: arr[] = {1, 1, -1, -1, 1}, K = 5
Output: No

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Approach:

• In order for the sum to be 0, there has to be equal number of 1 and -1 in the subset.
• If K is odd then no subset will satisfy the given condition.
• Else if K is even then we need to choose exactly (K / 2) 1’s and (K / 2) -1’s in order to form the subset so that the sum of all of it’s elements is 0
• So, if K is even and number of 1’s ≥ K / 2 and number of -1’s ≥ K / 2 then print Yes else print No.

Below is the implementation of the above approach:

## C++

 `// C++ program to find if there is a subset of size``// k with sum 0 in an array of -1 and +1``#include ``using` `namespace` `std;` `// Function to return the number of 1's in the array``int` `countOnes(``int` `n, ``int` `a[])``{``    ``int` `i, count = 0;``    ``for` `(i = 0; i < n; i++)``        ``if` `(a[i] == 1)``            ``count++;``    ``return` `count;``}` `bool` `isSubset(``int` `arr[], ``int` `n, ``int` `k)``{``    ``int` `countPos1 = countOnes(n, arr);``    ``int` `countNeg1 = n - countPos1;` `    ``// If K is even and there are``    ``// at least K/2 1's and -1's``    ``return` `(k % 2 == 0 && countPos1 >= k / 2 &&``                          ``countNeg1 >= k / 2);``}` `// Driver Program to test above function``int` `main()``{``    ``int` `a[] = { 1, 1, -1, -1, 1 };``    ``int` `n = ``sizeof``(a) / ``sizeof``(a);``    ``int` `k = 5;``    ``if` `(isSubset(a, n, k))``      ``cout << ``"Yes"``;``    ``else``      ``cout << ``"No"``;``    ``return` `0;``}`

## Java

 `// Java program to find if there is a subset of size``// k with sum 0 in an array of -1 and +1` `import` `java.io.*;` `class` `GFG {``   `  `// Function to return the number of 1's in the array``static` `int` `countOnes(``int` `n, ``int` `a[])``{``    ``int` `i, count = ``0``;``    ``for` `(i = ``0``; i < n; i++)``        ``if` `(a[i] == ``1``)``            ``count++;``    ``return` `count;``}` `static` `boolean` `isSubset(``int` `arr[], ``int` `n, ``int` `k)``{``    ``int` `countPos1 = countOnes(n, arr);``    ``int` `countNeg1 = n - countPos1;` `    ``// If K is even and there are``    ``// at least K/2 1's and -1's``    ``return` `(k % ``2` `== ``0` `&& countPos1 >= k / ``2` `&&``                        ``countNeg1 >= k / ``2``);``}` `// Driver Program to test above function``public` `static` `void` `main (String[] args) {``        ``int` `[]a = { ``1``, ``1``, -``1``, -``1``, ``1` `};``    ``int` `n = a.length;``    ``int` `k = ``5``;``    ``if` `(isSubset(a, n, k))``     ``System.out.println( ``"Yes"``);``    ``else``    ``System.out.println( ``"No"``);``    ``}``}``// This code is contributed by shs`

## Python3

 `# Python3 program to find if there is``# a subset of size k with sum 0 in an``# array of -1 and +1` `# Function to return the number of``# 1's in the array``def` `countOnes(n, a):` `    ``count ``=` `0``    ``for` `i ``in` `range``(``0``, n):``        ``if` `a[i] ``=``=` `1``:``            ``count ``+``=` `1``    ``return` `count` `def` `isSubset(arr, n, k):` `    ``countPos1 ``=` `countOnes(n, arr)``    ``countNeg1 ``=` `n ``-` `countPos1` `    ``# If K is even and there are``    ``# at least K/2 1's and -1's``    ``return` `(k ``%` `2` `=``=` `0` `and` `countPos1 >``=` `k ``/``/` `2` `and``                           ``countNeg1 >``=` `k ``/``/` `2``)` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:` `    ``a ``=` `[``1``, ``1``, ``-``1``, ``-``1``, ``1``]``    ``n ``=` `len``(a)``    ``k ``=` `5``    ` `    ``if` `isSubset(a, n, k) ``=``=` `True``:``        ``print``(``"Yes"``)``    ``else``:``        ``print``(``"No"``)``    ` `# This code is contributed``# by Rituraj Jain`

## C#

 `// C# program to find if there is``// a subset of size k with sum 0``// in an array of -1 and +1``using` `System;` `class` `GFG``{` `// Function to return the number``// of 1's in the array``static` `int` `countOnes(``int` `n, ``int` `[]a)``{``    ``int` `i, count = 0;``    ``for` `(i = 0; i < n; i++)``        ``if` `(a[i] == 1)``            ``count++;``    ``return` `count;``}` `static` `bool` `isSubset(``int` `[]arr,``                     ``int` `n, ``int` `k)``{``    ``int` `countPos1 = countOnes(n, arr);``    ``int` `countNeg1 = n - countPos1;` `    ``// If K is even and there are``    ``// at least K/2 1's and -1's``    ``return` `(k % 2 == 0 && countPos1 >= k / 2 &&``                          ``countNeg1 >= k / 2);``}` `// Driver Code``public` `static` `void` `Main ()``{``    ``int` `[]a = { 1, 1, -1, -1, 1 };``    ``int` `n = a.Length;``    ``int` `k = 5;``    ``if` `(isSubset(a, n, k))``        ``Console.WriteLine( ``"Yes"``);``    ``else``        ``Console.WriteLine( ``"No"``);``}``}` `// This code is contributed by shs`

## PHP

 `= ``\$k` `/ 2 &&``                           ``\$countNeg1` `>= ``\$k` `/ 2);``}` `// Driver Code``\$a` `= ``array``(1, 1, -1, -1, 1);``\$n` `= sizeof(``\$a``);``\$k` `= 5;` `if` `(isSubset(``\$a``, ``\$n``, ``\$k``))``    ``echo` `"Yes"``;``else``    ``echo` `"No"``;` `// This code is contributed``// by Akanksha Rai``?>`

## Javascript

 ``
Output:
`No`

Time Complexity: O(n)

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