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 arrays import 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 arrays def 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#
// 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 arrays function 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 ?> |
24
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