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++
// 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 = 3print(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 setfunction 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
Time Complexity: O(1)
Auxiliary Space: O(1)
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