# Find sum of sum of all sub-sequences

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 2^{n} sub-sequences, each element occurs 2^{n-1} times.

For example, arr[] = { 5, 6, 7 }

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

Below is the implementation of this approach:

## C++

`// C++ program to find sum of all sub-sequences` `// of an array.` `#include<bits/stdc++.h>` `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

`<?php` `// PHP program to find sum of` `// all sub-sequences of an array.` `// Return sum of sum of` `// all sub-sequence.` `function` `sum(` `$arr` `, ` `$n` `)` `{` ` ` `$ans` `= 0;` ` ` `// Finding sum of the array.` ` ` `for` `(` `$i` `= 0; ` `$i` `< ` `$n` `; ` `$i` `++)` ` ` `$ans` `+= ` `$arr` `[` `$i` `];` ` ` ` ` `return` `$ans` `* pow(2, ` `$n` `- 1);` `}` `// Driver Code` `$arr` `= ` `array` `(6, 7, 8);` `$n` `= sizeof(` `$arr` `);` `echo` `sum(` `$arr` `, ` `$n` `) ;` `// This code is contributed by nitin mittal.` `?>` |

## Javascript

`<script>` `// JavaScript program to find sum of all sub-sequences` `// of an array.` `// Return sum of sum of all sub-sequence.` `function` `sum(arr, n)` `{` ` ` `var` `ans = 0;` ` ` `// Finding sum of the array.` ` ` `for` `(` `var` `i = 0; i < n; i++)` ` ` `ans += arr[i];` ` ` `return` `ans * Math.pow(2, n - 1);` `}` `// Driver Code` `var` `arr = [6, 7, 8];` `var` `n = arr.length;` `document.write( sum(arr, n));` `</script>` |

**Output: **

84

This article is contributed by **Anuj Chauhan**. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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