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# Sum of subsets of all the subsets of an array | O(3^N)

• Difficulty Level : Medium
• Last Updated : 10 Jun, 2022

Given an array arr[] of length N, the task is to find the overall sum of subsets of all the subsets of the array.
Examples:

Input: arr[] = {1, 1}
Output:
All possible subsets:
a) {} : 0
All the possible subsets of this subset
will be {}, Sum = 0
b) {1} : 1
All the possible subsets of this subset
will be {} and {1}, Sum = 0 + 1 = 1
c) {1} : 1
All the possible subsets of this subset
will be {} and {1}, Sum = 0 + 1 = 1
d) {1, 1} : 4
All the possible subsets of this subset
will be {}, {1}, {1} and {1, 1}, Sum = 0 + 1 + 1 + 2 = 4
Thus, ans = 0 + 1 + 1 + 4 = 6
Input: arr[] = {1, 4, 2, 12}
Output: 513

Approach: In this article, an approach with O(3N) time complexity to solve the given problem will be discussed.
First, generate all the possible subsets of the array. There will be 2N subsets in total. Then for each subset, find the sum of all of its subset.
Now, let’s understand the time-complexity of this solution.
There are NCk subsets of length K and time to find the subsets of an array of length K is 2K
Total time = (NC1 * 21) + (NC2 * 22) + … + (NCk * K) = 3K
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to sum of all subsets of a``// given array``void` `subsetSum(vector<``int``>& c, ``int` `i,``               ``int``& ans, ``int` `curr)``{``    ``// Base case``    ``if` `(i == c.size()) {``        ``ans += curr;``        ``return``;``    ``}` `    ``// Recursively calling subsetSum``    ``subsetSum(c, i + 1, ans, curr + c[i]);``    ``subsetSum(c, i + 1, ans, curr);``}` `// Function to generate the subsets``void` `subsetGen(``int``* arr, ``int` `i, ``int` `n,``               ``int``& ans, vector<``int``>& c)``{``    ``// Base-case``    ``if` `(i == n) {` `        ``// Finding the sum of all the subsets``        ``// of the generated subset``        ``subsetSum(c, 0, ans, 0);``        ``return``;``    ``}` `    ``// Recursively accepting and rejecting``    ``// the current number``    ``subsetGen(arr, i + 1, n, ans, c);``    ``c.push_back(arr[i]);``    ``subsetGen(arr, i + 1, n, ans, c);``    ``c.pop_back();``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 1, 1 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``);` `    ``// To store the final ans``    ``int` `ans = 0;``    ``vector<``int``> c;` `    ``subsetGen(arr, 0, n, ans, c);``    ``cout << ans;` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.util.*;` `class` `GFG``{``    ``static` `Vector c = ``new` `Vector<>();` `    ``// To store the final ans``    ``static` `int` `ans = ``0``;` `    ``// Function to sum of all subsets of a``    ``// given array``    ``static` `void` `subsetSum(``int` `i, ``int` `curr)``    ``{` `        ``// Base case``        ``if` `(i == c.size())``        ``{``            ``ans += curr;``            ``return``;``        ``}` `        ``// Recursively calling subsetSum``        ``subsetSum(i + ``1``, curr + c.elementAt(i));``        ``subsetSum(i + ``1``, curr);``    ``}` `    ``// Function to generate the subsets``    ``static` `void` `subsetGen(``int``[] arr, ``int` `i, ``int` `n)``    ``{` `        ``// Base-case``        ``if` `(i == n)``        ``{` `            ``// Finding the sum of all the subsets``            ``// of the generated subset``            ``subsetSum(``0``, ``0``);``            ``return``;``        ``}` `        ``// Recursively accepting and rejecting``        ``// the current number``        ``subsetGen(arr, i + ``1``, n);``        ``c.add(arr[i]);``        ``subsetGen(arr, i + ``1``, n);``        ``c.remove(c.size() - ``1``);``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int``[] arr = { ``1``, ``1` `};``        ``int` `n = arr.length;` `        ``subsetGen(arr, ``0``, n);``        ``System.out.println(ans);``    ``}``}` `// This code is contributed by``// sanjeev2552`

## Python3

 `# Python3 implementation of the approach` `# Function to sum of all subsets``# of a given array``c ``=` `[]``ans ``=` `0` `def` `subsetSum(i, curr):``    ``global` `ans, c``    ` `    ``# Base case``    ``if` `(i ``=``=` `len``(c)):``        ``ans ``+``=` `curr``        ``return` `    ``# Recursively calling subsetSum``    ``subsetSum(i ``+` `1``, curr ``+` `c[i])``    ``subsetSum(i ``+` `1``, curr)` `# Function to generate the subsets``def` `subsetGen(arr, i, n):``    ``global` `ans, c``    ` `    ``# Base-case``    ``if` `(i ``=``=` `n):` `        ``# Finding the sum of all the subsets``        ``# of the generated subset``        ``subsetSum(``0``, ``0``)``        ``return` `    ``# Recursively accepting and rejecting``    ``# the current number``    ``subsetGen(arr, i ``+` `1``, n)``    ``c.append(arr[i])``    ``subsetGen(arr, i ``+` `1``, n)``    ``del` `c[``-``1``]` `# Driver code``arr ``=` `[``1``, ``1``]``n ``=` `len``(arr)` `subsetGen(arr, ``0``, n)` `print``(ans)` `# This code is contributed by Mohit Kumar`

## C#

 `// C# implementation of the approach``using` `System;``using` `System.Collections.Generic;` `class` `GFG``{``    ``static` `List<``int``> c = ``new` `List<``int``>();` `    ``// To store the readonly ans``    ``static` `int` `ans = 0;` `    ``// Function to sum of all subsets of a``    ``// given array``    ``static` `void` `subsetSum(``int` `i, ``int` `curr)``    ``{` `        ``// Base case``        ``if` `(i == c.Count)``        ``{``            ``ans += curr;``            ``return``;``        ``}` `        ``// Recursively calling subsetSum``        ``subsetSum(i + 1, curr + c[i]);``        ``subsetSum(i + 1, curr);``    ``}` `    ``// Function to generate the subsets``    ``static` `void` `subsetGen(``int``[] arr, ``int` `i, ``int` `n)``    ``{` `        ``// Base-case``        ``if` `(i == n)``        ``{` `            ``// Finding the sum of all the subsets``            ``// of the generated subset``            ``subsetSum(0, 0);``            ``return``;``        ``}` `        ``// Recursively accepting and rejecting``        ``// the current number``        ``subsetGen(arr, i + 1, n);``        ``c.Add(arr[i]);``        ``subsetGen(arr, i + 1, n);``        ``c.RemoveAt(c.Count - 1);``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``int``[] arr = { 1, 1 };``        ``int` `n = arr.Length;` `        ``subsetGen(arr, 0, n);``        ``Console.WriteLine(ans);``    ``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

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Output:

`6`

Time Complexity: O(n * 2n ), to generate all the subsets where n is the size of the given array
Auxiliary Space: O(n), to store the final answer

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