Find sum of sum of all subsequences

https://www.geeksforgeeks.org/find-sum-sum-sub-sequences/

Given an array of n integers. The task is to find the sum of sum of each of sub-sequence of the array.

Examples :

Input : arr[] = { 6, 8, 5 }
Output : 76
All subsequence sum are:
{ 6 }, sum = 6
{ 8 }, sum = 8
{ 5 }, sum = 5
{ 6, 8 }, sum = 14
{ 6, 5 }, sum = 11
{ 8, 5 }, sum = 13
{ 6, 8, 5 }, sum = 19
Total sum = 76.

Method 1 (brute force):
Generate all the sub-sequence and find the sum of each sub-sequence.

Method 2 (efficient approach):
For an array of size n, we have 2^n sub-sequences (including empty) in total. Observe, in total 2n sub-sequences, each elements occurs 2n-1 times.
For example, arr[] = { 5, 6, 7 }

So, sum of sum of all sub-sequence will be (sum of all the elements) * 2n-1.

    static int sum(int arr[], int n)

    {

    int ans = 0;

      

    // Finding sum of the array.

    for (int i = 0; i < n; i++)

        ans += arr[i];

      

    return ans * (int)(Math.pow(2, n - 1));

    }