Sum of squares of all Subsets of given Array

13 Mar, 2022
Given an array arr[]. The value of a subset of array A is defined as the sum of squares of all the numbers in that subset. The task is to calculate the sum of values of all possible non-empty subsets of the given array. Since, the answer can be large print the val mod 1000000007.Examples:  
Input: arr[] = {3, 7} Output: 116 val({3}) = 32 = 9 val({7}) = 72 = 49 val({3, 7}) = 32 + 72 = 9 + 49 = 58 9 + 49 + 58 = 116Input: arr[] = {1, 1, 1} Output: 12  
 
Naive approach: A simple approach is to find all the subset and then square each element in that subset and add it to the result. The time complexity of this approach will be O(2N)Efficient approach: It can be observed that in all the possible subsets of the given array, every element will occur 2N – 1 times where N is the size of the array. So the contribution of any element X in the sum will be 2N – 1 * X2.Below is the implementation of the above approach:  
C++
Java
Python3
C#
Javascript
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std; const int mod = 1e9 + 7; // Function to return (2^P % mod)long long power(int p){    long long res = 1;    for (int i = 1; i <= p; ++i) {        res *= 2;        res %= mod;    }    return res % mod;} // Function to return the sum of squares of subsetslong long subset_square_sum(vector<int>& A){     int n = (int)A.size();     long long ans = 0;     // Sqauaring the elements    // and adding it to ans    for (int i : A) {        ans += (1LL * i * i) % mod;        ans %= mod;    }     return (1LL * ans * power(n - 1)) % mod;} // Driver codeint main(){    vector<int> A = { 3, 7 };     cout << subset_square_sum(A);     return 0;}
// Java implementation of the approachclass GFG{    static final int mod = (int)(1e9 + 7);         // Function to return (2^P % mod)    static long power(int p)    {        long res = 1;        for (int i = 1; i <= p; ++i)        {            res *= 2;            res %= mod;        }        return res % mod;    }         // Function to return the sum of squares of subsets    static long subset_square_sum(int A[])    {        int n = A.length;             long ans = 0;             // Sqauaring the elements        // and adding it to ans        for (int i : A)        {            ans += (1 * i * i) % mod;            ans %= mod;        }        return (1 * ans * power(n - 1)) % mod;    }         // Driver code    public static void main (String[] args)    {        int A[] = { 3, 7 };             System.out.println(subset_square_sum(A));    }} // This code is contributed by AnkitRai01
# Python3 implementation of the approachmod = 10**9 + 7 # Function to return (2^P % mod)def power(p):     res = 1    for i in range(1, p + 1):        res *= 2        res %= mod     return res % mod # Function to return the sum of# squares of subsetsdef subset_square_sum(A):     n = len(A)     ans = 0     # Squaring the elements    # and adding it to ans    for i in A:        ans += i * i % mod        ans %= mod     return ans * power(n - 1) % mod # Driver codeA = [3, 7] print(subset_square_sum(A)) # This code is contributed by Mohit Kumar
// C# implementation of the approachusing System;     class GFG{    static readonly int mod = (int)(1e9 + 7);         // Function to return (2^P % mod)    static long power(int p)    {        long res = 1;        for (int i = 1; i <= p; ++i)        {            res *= 2;            res %= mod;        }        return res % mod;    }         // Function to return the sum of squares of subsets    static long subset_square_sum(int []A)    {        int n = A.Length;             long ans = 0;             // Sqauaring the elements        // and adding it to ans        foreach (int i in A)        {            ans += (1 * i * i) % mod;            ans %= mod;        }        return (1 * ans * power(n - 1)) % mod;    }         // Driver code    public static void Main (String[] args)    {        int []A = { 3, 7 };             Console.WriteLine(subset_square_sum(A));    }}     // This code is contributed by 29AjayKumar
<script>// Javascript implementation of the approach const mod = 1000000000 + 7; // Function to return (2^P % mod)function power(p){    let res = 1;    for (let i = 1; i <= p; ++i) {        res *= 2;        res %= mod;    }    return res % mod;} // Function to return the sum of squares of subsetsfunction subset_square_sum(A){     let n = A.length;     let ans = 0;     // Sqauaring the elements    // and adding it to ans    for (let i = 0; i < n; i++) {        ans += (A[i] * A[i]) % mod;        ans %= mod;    }     return (ans * power(n - 1)) % mod;} // Driver code    let A = [ 3, 7 ];     document.write(subset_square_sum(A));</script>
116
 
Time Complexity: O(N)
Auxiliary Space: O(1) 
mohit kumar 29
ankthon
29AjayKumar
subham348
subhammahato348
subset
Arrays
Mathematical
Arrays
Mathematical
subset
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.
Maximum and minimum of an array using minimum number of comparisons
Top 50 Array Coding Problems for Interviews
Multidimensional Arrays in Java
Stack Data Structure (Introduction and Program)
Linear Search
Set in C++ Standard Template Library (STL)
Write a program to print all permutations of a given string
C++ Data Types
Merge two sorted arrays
Operators in C / C++