# Subset array sum by generating all the subsets

Given an array of size N and a sum, the task is to check whether some array elements can be added to sum to N .

Note: At least one element should be included to form the sum.(i.e. sum cant be zero)

Examples:

```Input: array = -1, 2, 4, 121, N = 5
Output: YES
The array elements 2, 4, -1 can be added to sum to N

Input: array = 1, 3, 7, 121, N = 5
Output:NO
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The idea is to generate all subsets using Generate all subsequences of array and correspondingly check if any subsequence has the sum equal to the given sum.

Below is the implementation of above approach:

## CPP

 `// C++ implementation of the above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Find way to sum to N using array elements atmost once ` `void` `find(``int` `arr[], ``int` `length, ``int` `s) ` `{ ` `    ``// loop for all 2^n combinations ` `    ``for` `(``int` `i = 1; i < (``pow``(2, length)); i++) { ` ` `  `        ``// sum of a combination ` `        ``int` `sum = 0; ` ` `  `        ``for` `(``int` `j = 0; j < length; j++) ` ` `  `            ``// if the bit is 1 then add the element ` `            ``if` `(((i >> j) & 1)) ` `                ``sum += arr[j]; ` ` `  `        ``// if the sum is equal to given sum print yes ` `        ``if` `(sum == s) { ` `            ``cout << ``"YES"` `<< endl; ` `            ``return``; ` `        ``} ` `    ``} ` ` `  `    ``// else print no ` `    ``cout << ``"NO"` `<< endl; ` `} ` ` `  `// driver code ` `int` `main() ` `{ ` `    ``int` `sum = 5; ` `    ``int` `array[] = { -1, 2, 4, 121 }; ` `    ``int` `length = ``sizeof``(array) / ``sizeof``(``int``); ` ` `  `    ``// find whether it is possible to sum to n ` `    ``find(array, length, sum); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the above approach ` `class` `GFG ` `{ ` `     `  `        ``// Find way to sum to N using array elements atmost once ` `        ``static` `void` `find(``int` `[] arr, ``int` `length, ``int` `s) ` `        ``{ ` `            ``// loop for all 2^n combinations ` `            ``for` `(``int` `i = ``1``; i <= (Math.pow(``2``, length)); i++) { ` `         `  `                ``// sum of a combination ` `                ``int` `sum = ``0``; ` `         `  `                ``for` `(``int` `j = ``0``; j < length; j++) ` `         `  `                    ``// if the bit is 1 then add the element ` `                    ``if` `(((i >> j) & ``1``) % ``2` `== ``1``) ` `                        ``sum += arr[j]; ` `         `  `                ``// if the sum is equal to given sum print yes ` `                ``if` `(sum == s) { ` `                    ``System.out.println(``"YES"``); ` `                    ``return``; ` `                ``} ` `            ``} ` `         `  `            ``// else print no ` `            ``System.out.println(``"NO"``); ` `        ``} ` `         `  `        ``// driver code ` `        ``public` `static` `void` `main(String[] args) ` `        ``{ ` `            ``int` `sum = ``5``; ` `            ``int` `[]array = { -``1``, ``2``, ``4``, ``121` `}; ` `            ``int` `length = array.length; ` `         `  `            ``// find whether it is possible to sum to n ` `            ``find(array, length, sum); ` `         `  `        ``} ` ` `  `} ` ` `  `// This code is contributed by ihritik `

## Python3

 `# Python3 implementation ` `from` `itertools ``import` `combinations ` ` `  `def` `find(lst, n): ` `    ``print``(``'YES'` `if` `[``1` `for` `r ``in` `range``(``1``, ``len``(lst) ``+` `1``)  ` `                      ``for` `subset ``in` `combinations(lst, r)  ` `                      ``if` `sum``(subset) ``=``=`   `n] ``else` `'NO'``) ` ` `  `find([``-``1``, ``2``, ``4``, ``121``], ``5``) ` ` `  `#This code is contributed by signi dimitri `

## C#

 `     `  `// C# implementation of the above approach ` `using` `System; ` `public` `class` `GFG ` `{ ` `      `  `        ``// Find way to sum to N using array elements atmost once ` `        ``static` `void` `find(``int` `[] arr, ``int` `length, ``int` `s) ` `        ``{ ` `            ``// loop for all 2^n combinations ` `            ``for` `(``int` `i = 1; i <= (Math.Pow(2, length)); i++) { ` `          `  `                ``// sum of a combination ` `                ``int` `sum = 0; ` `          `  `                ``for` `(``int` `j = 0; j < length; j++) ` `          `  `                    ``// if the bit is 1 then add the element ` `                    ``if` `(((i >> j) & 1) % 2 == 1) ` `                        ``sum += arr[j]; ` `          `  `                ``// if the sum is equal to given sum print yes ` `                ``if` `(sum == s) { ` `                    ``Console.Write(``"YES"``); ` `                    ``return``; ` `                ``} ` `            ``} ` `          `  `            ``// else print no ` `            ``Console.Write(``"NO"``); ` `        ``} ` `          `  `        ``// driver code ` `        ``public` `static` `void` `Main() ` `        ``{ ` `            ``int` `sum = 5; ` `            ``int` `[]array = { -1, 2, 4, 121 }; ` `            ``int` `length = array.Length; ` `          `  `            ``// find whether it is possible to sum to n ` `            ``find(array, length, sum); ` `          `  `        ``} ` `  `  `} ` ` `  `// This code is contributed by PrinciRaj19992 `

## PHP

 `> ``\$j``) & 1)) ` `                ``\$sum` `+= ``\$arr``[``\$j``]; ` ` `  `        ``// if the sum is equal to given sum print yes ` `        ``if` `(``\$sum` `== ``\$s``)  ` `        ``{ ` `            ``echo` `"YES"``,``"\n"``; ` `            ``return``; ` `        ``} ` `    ``} ` ` `  `    ``// else print no ` `    ``echo` `"NO"``,``"\n"``; ` `} ` ` `  `    ``// Driver code ` `    ``\$sum` `= 5; ` `    ``\$array` `= ``array``(-1, 2, 4, 121 ); ` `    ``\$length` `= sizeof(``\$array``) / sizeof(``\$array``); ` ` `  `    ``// find whether it is possible to sum to n ` `    ``find(``\$array``, ``\$length``, ``\$sum``); ` ` `  ` `  `// This code is contributed by ajit. ` `?> `

Output:

```YES
```

Note: This program would not run for the large size of the array. My Personal Notes arrow_drop_up Third year Department of Information Technology Jadavpur University

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