Maximum Sum of Products of Two Arrays
Given two arrays A and B of positive integers of the same size N. The task is to find the maximum sum of products of their elements. Each element in A has to be multiplied with exactly one element in B or vice versa such that each element of both the arrays appears exactly once and the sum of the product obtained is maximum.
Examples:
Input : A[] = {1, 2, 3}
B[] = {4, 5, 1}
Output : 24
Explanation : Maximum sum of product is obtained by 5*3+4*2+1*1 = 24.
Input : A[] = {5, 1, 3, 4, 2}
B[] = {8, 10, 9, 7, 6}
Output : 130
Explanation : Maximum sum of product is obtained by 10*5+9*4+8*3+7*2+6*1 = 130.
The idea is to observe that product of two maximum number will contribute toward the maximum sum of the product. So the idea is to:
- Sort both the arrays.
- Traverse the arrays, and calculate the sum of products of array elements that are at the same index.
Below is the implementation of the above approach:
C++
// CPP program to calculate maximum sum// of products of two arrays#include<bits/stdc++.h>using namespace std; // Function that calculates maximum sum // of products of two arrays int maximumSOP(int *a, int *b) { // Variable to store the sum of // products of array elements int sop = 0; // length of the arrays int n = sizeof(a)/sizeof(a[0]); // Sorting both the arrays sort(a,a+n+1); sort(b,b+n+1); // Traversing both the arrays // and calculating sum of product for (int i = 0; i <=n; i++) { sop += a[i] * b[i]; } return sop; } // Driver code int main() { int A[] = { 1, 2, 3 }; int B[] = { 4, 5, 1 }; cout<<maximumSOP(A, B); return 0; }// This code is contributed by mits |
Java
// Java program to calculate maximum sum// of products of two arraysimport java.io.*;import java.util.*;public class GFG { // Function that calculates maximum sum // of products of two arrays static int maximumSOP(int[] a, int[] b) { // Variable to store the sum of // products of array elements int sop = 0; // length of the arrays int n = a.length; // Sorting both the arrays Arrays.sort(a); Arrays.sort(b); // Traversing both the arrays // and calculating sum of product for (int i = 0; i < n; i++) { sop += a[i] * b[i]; } return sop; } // Driver code public static void main(String args[]) { int[] A = { 1, 2, 3 }; int[] B = { 4, 5, 1 }; System.out.println(maximumSOP(A, B)); }} |
Python 3
# Python program to calculate# maximum sum of products of# two arrays# Function that calculates# maximum sum of products# of two arraysdef maximumSOP(a, b) : # Variable to store the sum of # products of array elements sop = 0 # length of the arrays n = len(a) # Sorting both the arrays a.sort() b.sort() # Traversing both the arrays # and calculating sum of product for i in range(n) : sop += a[i] * b[i] return sop# Driver code if __name__ == "__main__" : A = [1, 2, 3] B = [4, 5, 1] print(maximumSOP(A, B))# This code is contributed by ANKITRAI1 |
// C# program to calculate maximum sum
// of products of two arrays
using System;
class GFG
{
// Function that calculates maximum
// sum of products of two arrays
static int maximumSOP(int[] a, int[] b)
{
// Variable to store the sum of
// products of array elements
int sop = 0;
// length of the arrays
int n = a.Length;
// Sorting both the arrays
Array.Sort(a);
Array.Sort(b);
// Traversing both the arrays
// and calculating sum of product
for (int i = 0; i < n; i++)
{
sop += a[i] * b[i];
}
return sop;
}
// Driver code
public static void Main()
{
int[] A = { 1, 2, 3 };
int[] B = { 4, 5, 1 };
Console.Write(maximumSOP(A, B));
}
}
// This code is contributed
// by ChitraNayal
PHP
<?php// PHP program to calculate maximum // sum of products of two arrays// Function that calculates maximum// sum of products of two arraysfunction maximumSOP(&$a, &$b){ $sop = 0; // Sorting both the arrays sort($a); sort($b); // length of the arrays $n = sizeof($a); // Traversing both the arrays // and calculating sum of product for ($i = 0; $i < $n; $i++) { $sop = $sop + ($a[$i] * $b[$i]); } return $sop;}// Driver code$A = array(1, 2, 3 );$B = array(4, 5, 1 );echo maximumSOP($A, $B);// This code is contributed// by Shivi_Aggarwal?> |
Javascript
<script>// Javascript program to calculate maximum sum// of products of two arrays // Function that calculates maximum sum // of products of two arrays function maximumSOP(a, b) { // Variable to store the sum of // products of array elements let sop = 0; // length of the arrays let n = a.length; // Sorting both the arrays a.sort(); b.sort(); // Traversing both the arrays // and calculating sum of product for (let i = 0; i <n; i++) { sop += (a[i] * b[i]); } return sop; } // Driver code let A = [ 1, 2, 3 ]; let B = [ 4, 5, 1 ]; document.write(maximumSOP(A, B));// This code is contributed by Mayank Tyagi</script> |
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