Find sum of sum of all 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 = 7
{ 5 }, sum = 5
{ 6, 8 }, sum = 14
{ 6, 5 }, sum = 11
{ 8, 5 }, sum = 13
{ 6, 8, 5 }, sum = 19
Total sum = 76.

Input  : arr[] = {1, 2}
Output : 6

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.

Below is the implementation of this approach:

C++

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// C++ program to find sum of all sub-sequences
// of an array.
#include<bits/stdc++.h>
using namespace std;
  
// Return sum of sum of all sub-sequence.
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 * pow(2, n - 1);
}
  
// Driver Code
int main()
{
  int arr[] = { 6, 7, 8 };
  int n = sizeof(arr)/sizeof(arr[0]);
  
  cout << sum(arr, n) << endl;
  
  return 0;

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Java

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// Java program to find sum of 
// all sub-sequences of an array.
import java.io.*;
import java.math.*;
  
class GFG {
      
    // Return sum of sum of all sub-sequence.
    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));
    }
      
    // Driver Code
    public static void main(String args[])
    {
    int arr[]= { 6, 7, 8 };
    int n = arr.length;
      
    System.out.println(sum(arr, n));
    }
}
      
// This code is contributed by Nikita Tiwari.

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Python3

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# Python 3 program to find sum of 
# all sub-sequences of an array.
  
  
# Return sum of sum of all sub-sequence.
def sm(arr , n) :
    ans = 0
  
    # Finding sum of the array.
    for i in range(0, n) :
        ans = ans + arr[i]
      
    return ans * pow(2, n - 1)
      
      
# Driver Code
arr = [ 6, 7, 8 ]
n=len(arr)
  
print(sm(arr, n))
  
  
# This code is contributed by Nikita Tiwari.

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C#

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// C# program to find sum of 
// all sub-sequences of an array.
using System;
  
class GFG
{
      
    // Return sum of sum of all sub-sequence.
    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));
    }
      
    // Driver Code
    public static void Main()
    {
    int []arr= { 6, 7, 8 };
    int n = arr.Length;
      
    Console.Write(sum(arr, n));
    }
}
      
// This code is contributed by nitin mittal

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PHP

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<?php
// PHP program to find sum of
// all sub-sequences of an array.
  
// Return sum of sum of
// all sub-sequence.
function sum($arr, $n)
{
    $ans = 0;
  
    // Finding sum of the array.
    for ($i = 0; $i < $n; $i++)
        $ans += $arr[$i];
      
    return $ans * pow(2, $n - 1);
}
  
// Driver Code
$arr = array(6, 7, 8);
$n = sizeof($arr);
echo sum($arr, $n) ;
  
// This code is contributed by nitin mittal.
?>

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Output:

84

This article is contributed by Anuj Chauhan. 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.

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Improved By : nitin mittal



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