Sum of all subsets of a set formed by first n natural numbers

10 Jun, 2022
Given a number n, we need to find the sum of all the elements from all possible subsets of a set formed by first n natural numbers.Examples :  
Input :  n = 2
Output : 6
Possible subsets are {{1}, {2}, 
{1, 2}}. Sum of elements in subsets
is 1 + 2 + 1 + 2 = 6

Input :  n = 3
Output : 24
Possible subsets are {{1}, {2}, {3}, 
{1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
Sum of subsets is : 
1 + 2 + 3 + (1 + 2) + (1 + 3) + 
(2 + 3) + (1 + 2 + 3)
 
A simple solution is to generate all subsets. For every subset, compute its sum and finally return overall sum.An efficient solution is based on the fact that every number from 1 to n appears exactly 2(n-1) times. So our required sum is (1 + 2 + 3 + ..+ n) * 2(n-1). The sum can be written as (n * (n + 1)/2) * 2(n-1) 
C++
Java
Python3
C#
PHP
Javascript
// CPP program to find sum of all subsets// of a set.#include <bits/stdc++.h>using namespace std; unsigned long long findSumSubsets(int n){    // sum of subsets is (n * (n + 1) / 2) *    // pow(2, n-1)    return (n * (n + 1) / 2) * (1 << (n - 1));} int main(){    int n = 3;    cout << findSumSubsets(n);    return 0;}
// Java program to find sum of all subsets// of a set. class GFG {    static long findSumSubsets(int n)    {        // sum of subsets is (n * (n + 1) / 2) *        // pow(2, n-1)        return (n * (n + 1) / 2) * (1 << (n - 1));    }     // Driver code    public static void main(String[] args)    {        int n = 3;        System.out.print(findSumSubsets(n));    }} // This code is contributed by Anant Agarwal.
# Python program to find# sum of all subsets# of a set. def findSumSubsets( n):     # sum of subsets    # is (n * (n + 1) / 2) *    # pow(2, n-1)    return (n * (n + 1) / 2) * (1 << (n - 1))     # Driver code    n = 3print(findSumSubsets(n)) # This code is contributed# by sunnysingh.
// C# program to find sum of all subsets// of a set.using System; class GFG {     static long findSumSubsets(int n)    {         // sum of subsets is (n * (n + 1) / 2) *        // pow(2, n-1)        return (n * (n + 1) / 2) * (1 << (n - 1));    }     // Driver code    public static void Main()    {        int n = 3;         Console.WriteLine(findSumSubsets(n));    }} // This code is contributed by vt_m.
<?php// PHP program to find sum// of all subsets of a set function findSumSubsets($n){    // sum of subsets is (n *    // (n + 1) / 2) * pow(2, n-1)    return ($n * ($n + 1) / 2) *                 (1 << ($n - 1));} // Driver Code$n = 3;echo findSumSubsets($n); // This code is contributed by ajit?>
<script> // javascript program to find sum of all subsets// of a set.  function findSumSubsets( n){    // sum of subsets is (n * (n + 1) / 2) *    // pow(2, n-1)    return (n * (n + 1) / 2) * (1 << (n - 1));}  // Driven Program     let n = 3;     document.write(findSumSubsets(n)); // This code contributed by aashish1995 </script>
Output : 
24
Time Complexity: O(1)Auxiliary Space: O(1)
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