Find sum of sum of all sub-sequences
Given an array of n integers. The task is to find the sum of each 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. 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 element occurs 2n-1 times.
For example, arr[] = { 5, 6, 7 }
So, the sum of all sub-sequence will be (sum of all the elements) * 2n-1.
Below is the implementation of this approach:
C++
// 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; } |
Java
// 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. |
Python3
# 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. |
C#
// 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 |
PHP
<?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. ?> |
Javascript
<script> // JavaScript program to find sum of all sub-sequences // of an array. // Return sum of sum of all sub-sequence. function sum(arr, n) { var ans = 0; // Finding sum of the array. for ( var i = 0; i < n; i++) ans += arr[i]; return ans * Math.pow(2, n - 1); } // Driver Code var arr = [6, 7, 8]; var n = arr.length; document.write( sum(arr, n)); </script> |
Output
84
Time complexity: O(n)
Auxiliary space: O(1)