# Find sum of sum of all sub-sequences

Last Updated : 07 Jul, 2022

Given an array of n integers. The task is to find the sum of each sub-sequence of the array.

Examples :

```Input : arr[] = { 6, 8, 5 }
Output : 76
All subsequence sum are:
{ 6 }, sum = 6
{ 8 }, sum = 8
{ 5 }, sum = 5
{ 6, 8 }, sum = 14
{ 6, 5 }, sum = 11
{ 8, 5 }, sum = 13
{ 6, 8, 5 }, sum = 19
Total sum = 76.

Input  : arr[] = {1, 2}
Output : 6```

Method 1 (brute force):
Generate all the sub-sequence and find the sum of each sub-sequence.

Method 2 (efficient approach):
For an array of size n, we have 2^n sub-sequences (including empty) in total. Observe, in total 2n sub-sequences, each element occurs 2n-1 times.
For example, arr[] = { 5, 6, 7 }

So, the sum of all sub-sequence will be (sum of all the elements) * 2n-1.

Below is the implementation of this approach:

## C++

 `// C++ program to find sum of all sub-sequences` `// of an array.` `#include` `using` `namespace` `std;`   `// Return sum of sum of all sub-sequence.` `int` `sum(``int` `arr[], ``int` `n)` `{` `  ``int` `ans = 0;`   `  ``// Finding sum of the array.` `  ``for` `(``int` `i = 0; i < n; i++)` `    ``ans += arr[i];`   `  ``return` `ans * ``pow``(2, n - 1);` `}`   `// Driver Code` `int` `main()` `{` `  ``int` `arr[] = { 6, 7, 8 };` `  ``int` `n = ``sizeof``(arr)/``sizeof``(arr[0]);`   `  ``cout << sum(arr, n) << endl;`   `  ``return` `0;` `} `

## Java

 `// Java program to find sum of ` `// all sub-sequences of an array.` `import` `java.io.*;` `import` `java.math.*;`   `class` `GFG {` `    `  `    ``// Return sum of sum of all sub-sequence.` `    ``static` `int` `sum(``int` `arr[], ``int` `n)` `    ``{` `    ``int` `ans = ``0``;` `    `  `    ``// Finding sum of the array.` `    ``for` `(``int` `i = ``0``; i < n; i++)` `        ``ans += arr[i];` `    `  `    ``return` `ans * (``int``)(Math.pow(``2``, n - ``1``));` `    ``}` `    `  `    ``// Driver Code` `    ``public` `static` `void` `main(String args[])` `    ``{` `    ``int` `arr[]= { ``6``, ``7``, ``8` `};` `    ``int` `n = arr.length;` `    `  `    ``System.out.println(sum(arr, n));` `    ``}` `}` `    `  `// This code is contributed by Nikita Tiwari.`

## Python3

 `# Python 3 program to find sum of ` `# all sub-sequences of an array.`     `# Return sum of sum of all sub-sequence.` `def` `sm(arr , n) :` `    ``ans ``=` `0`   `    ``# Finding sum of the array.` `    ``for` `i ``in` `range``(``0``, n) :` `        ``ans ``=` `ans ``+` `arr[i]` `    `  `    ``return` `ans ``*` `pow``(``2``, n ``-` `1``)` `    `  `    `  `# Driver Code` `arr ``=` `[ ``6``, ``7``, ``8` `]` `n``=``len``(arr)`   `print``(sm(arr, n))`     `# This code is contributed by Nikita Tiwari.`

## C#

 `// C# program to find sum of ` `// all sub-sequences of an array.` `using` `System;`   `class` `GFG` `{` `    `  `    ``// Return sum of sum of all sub-sequence.` `    ``static` `int` `sum(``int` `[]arr, ``int` `n)` `    ``{` `    ``int` `ans = 0;` `    `  `    ``// Finding sum of the array.` `    ``for` `(``int` `i = 0; i < n; i++)` `        ``ans += arr[i];` `    `  `    ``return` `ans * (``int``)(Math.Pow(2, n - 1));` `    ``}` `    `  `    ``// Driver Code` `    ``public` `static` `void` `Main()` `    ``{` `    ``int` `[]arr= { 6, 7, 8 };` `    ``int` `n = arr.Length;` `    `  `    ``Console.Write(sum(arr, n));` `    ``}` `}` `    `  `// This code is contributed by nitin mittal`

## PHP

 ``

## Javascript

 ``

Output

```84
```

Time complexity:  O(n)
Auxiliary space: O(1)

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