Sum of all subsequences of an array

Given an array of n integers. Find the sum of all possible subarrays.

Examples :

Input : arr[] = { 1, 2 }
Output : 6
All possible subarrays are {}, {1}, {2} 
and { 1, 2 }

Input : arr[] = { 1, 2, 3 }
Output : 24

We have already discussed two different solutions in below post.
Sum of all Subarrays | Set 1

In this post a different solution is discussed. Let us take a closer look at the problem and try to find a pattern

Let a[] = { 1, 2, 3 }

All subarrays are {}, {1}, {2}, {3}, {1, 2}, 
                     {1, 3}, {2, 3}, {1, 2, 3}

So sum of subarrays are 0 + 1 + 2 + 3 + 3 + 
                             4 + 5 + 8 = 24

Here we can observe that in sum every elements 
occurs 4 times. Or in general every element 
will occur 2^(n-1) times. And we can also 
observe that sum of array elements is 6. So
final result will be 6*4.

In general we can find sum of all subarrays by adding all elements of array multiplied by 2^(n-1) where n is number of elements in array.

C++

// CPP program to find sum of
// all subarrays of array
#include <bits/stdc++.h>
using namespace std;

// To find sum of all subarrya
int findSum(int arr[], int n)
{
    // Sum all array elements
    int sum = 0;
    for (int i = 0; i < n; i++)
        sum += arr[i];

    // Result is sum * 2^(n-1)
    return sum * (1 << (n - 1));
}

// Driver program to test findSum()
int main()
{
    int arr[] = { 1, 2 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << findSum(arr, n);
    return 0;
}

Java

// Java program to find sum of
// all subarrays of array

public class Main {
    // To find sum of all subarrya
    static int findSum(int arr[], int n)
    {
        // Sum all array elements
        int sum = 0;
        for (int i = 0; i < n; i++)
            sum += arr[i];

        // Result is sum * 2^(n-1)
        return sum * (1 << (n - 1));
    }

    // Driver program to test findSum()
    public static void main(String[] args)
    {
        int arr[] = { 1, 2 };
        int n = arr.length;
        System.out.print(findSum(arr, n));
    }
}

Python

# Python program to find sum of
# all subarrays of array

# To find sum of all subarrya
def findSum(arr, n):

    # Sum all array elements
    sum = 0
    for i in range(n):
        sum += arr[i]

    # Result is sum * 2^(n-1)
    return sum * (1 << (n - 1))

# Driver program to test findSum()
arr = [1, 2]
n = len(arr)
print findSum(arr, n)

# This code is submitted by Sachin Bisht

C#

// C# program to find sum of
// all subarrays of array
using System;

class GFG
{

// To find sum of all subarrya
static int findSum(int []arr, int n)
{
    // Sum all array elements
    int sum = 0;
    for (int i = 0; i < n; i++)
        sum += arr[i];

    // Result is sum * 2^(n-1)
    return sum * (1 << (n - 1));
}

// Driver Code
static public void Main ()
{
    int []arr = { 1, 2 };
    int n = arr.Length;
    Console.WriteLine(findSum(arr, n));
}
}

// This code is contributed by ajit

PHP

<?php
// PHP program to find sum of
// all subarrays of array

// To find sum of all subarrays

function findSum($arr, $n)
{
    // Sum all array elements
    $sum = 0;
    for ($i = 0; $i < $n; $i++)
        $sum += $arr[$i];

    // Result is sum * 2^(n-1)
    return $sum * (1 << ($n - 1));
}

// Driver Code
$arr = array( 1, 2 );
$n = sizeof($arr);

echo findSum($arr, $n);

// This code is contributed by ajit
?>

Output :

6

This article is contributed by nuclode. 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.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.