Skip to content
Related Articles

Related Articles

Save Article
Improve Article
Save Article
Like Article

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

  • Difficulty Level : Medium
  • Last Updated : 19 Mar, 2021

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)

 

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

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++




// 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




// 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.

Python3




# 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 = 3
print(findSumSubsets(n))
 
# This code is contributed
# by sunnysingh.

C#




// 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
// 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
?>

Javascript




<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

This article is contributed by Raj Kumar. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 




My Personal Notes arrow_drop_up
Recommended Articles
Page :