Sum of the sums of all possible subsets

Given an array a of size N. The task is to find the sum of the sums of all possible subsets.

Examples:

Input: a[] = {3, 7}
Output: 20
The subsets are: {3} {7} {3, 7}
{3, 7} = 10
{3} = 3
{7} = 7
10 + 3 + 7 = 20



Input: a[] = {10, 16, 14, 9}
Output: 392

Naive Approach: A naive approach is to find all the subsets using power set and then summate all the possible subsets to get the answer.

Time Complexity: O(2N)

Efficient Approach: An efficient approach is to solve the problem using observation. If we write all the subsequences, a common point of observation is that each number appears 2(N – 1) times in a subset and hence will lead to the 2(N-1) as the contribution to the sum. Iterate through the array and add (arr[i] * 2N-1) to the answer.

Below is the implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to find the sum of
// the addition of all possible subsets.
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the sum
// of sum of all the subset
int sumOfSubset(int a[], int n)
{
    int times = pow(2, n - 1);
  
    int sum = 0;
  
    for (int i = 0; i < n; i++) {
        sum = sum + (a[i] * times);
    }
  
    return sum;
}
  
// Driver Code
int main()
{
    int a[] = { 3, 7 };
    int n = sizeof(a) / sizeof(a[0]);
    cout << sumOfSubset(a, n);
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to find the sum of
// the addition of all possible subsets.
class GFG
{
      
// Function to find the sum
// of sum of all the subset
static int sumOfSubset(int []a, int n)
{
    int times = (int)Math.pow(2, n - 1);
  
    int sum = 0;
  
    for (int i = 0; i < n; i++) 
    {
        sum = sum + (a[i] * times);
    }
  
    return sum;
}
  
// Driver Code
public static void main(String[] args)
{
    int []a = { 3, 7 };
    int n = a.length;
    System.out.println(sumOfSubset(a, n));
}
}
  
// This code is contributed by 29AjayKumar

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 program to find the Sum of
# the addition of all possible subsets.
  
# Function to find the sum
# of sum of all the subset
def SumOfSubset(a, n):
  
    times = pow(2, n - 1)
  
    Sum = 0
  
    for i in range(n):
        Sum = Sum + (a[i] * times)
  
    return Sum
  
# Driver Code
a = [3, 7]
n = len(a)
print(SumOfSubset(a, n))
  
# This code is contributed by Mohit Kumar

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to find the sum of
// the addition of all possible subsets.
using System;
  
class GFG
{
      
// Function to find the sum
// of sum of all the subset
static int sumOfSubset(int []a, int n)
{
    int times = (int)Math.Pow(2, n - 1);
  
    int sum = 0;
  
    for (int i = 0; i < n; i++) 
    {
        sum = sum + (a[i] * times);
    }
  
    return sum;
}
  
// Driver Code
public static void Main()
{
    int []a = { 3, 7 };
    int n = a.Length;
    Console.Write(sumOfSubset(a, n));
}
}
  
// This code is contributed by Nidhi

chevron_right


Output:

20

Time Complexity: O(N)
Space Complexity: O(1)

Note: If N is large, the answer can overflow, thereby use larger data-type.



My Personal Notes arrow_drop_up

Striver(underscore)79 at Codechef and codeforces D

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 Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.





Article Tags :
Practice Tags :


2


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.