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Minimum sum of product of elements of pairs of the given array
• Last Updated : 24 Feb, 2021

Given an array arr[] of even number of element N in it. The task is to form N/2 pairs such that sum of product of elements in those pairs is minimum.
Examples

Input: arr[] = { 1, 6, 3, 1, 7, 8 }
Output: 270
Explanation:
The pair formed are {1, 1}, {3, 6}, {7, 8}
Product of sum of these pairs = 2 * 9 * 15 = 270
Input: arr[] = {2, 3, 90, 12}
Output: 510
Explanation:
Pairs should be created in this way {2, 3}, {12, 90}
Product of sum of these pairs = 5*112 = 510

Approach:

• Sort the elements in the given array arr[].
• Make pairs of first two-element, then next two-element and so on.
• Calculate the sum of product of corresponding pairs formed.

Below is the implementation of the above approach:

## CPP

 `// C++ program to find the minimum``// product of sum of pair of element``// in array arr[]``#include "bits/stdc++.h"``using` `namespace` `std;` `// Function to find the minimum``// product``int` `minimumProduct(``int``* arr, ``int` `n)``{` `    ``// Sort the array using STL``    ``// sort() function``    ``sort(arr, arr + n);` `    ``// Intialise product to 1``    ``int` `product = 1;` `    ``for` `(``int` `i = 0; i < n; i += 2) {` `        ``// Find product of sum of``        ``// all pairs``        ``product *= (arr[i] + arr[i + 1]);``    ``}` `    ``// Return the product``    ``return` `product;``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 1, 6, 3, 1, 7, 8 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``// Function call to find product``    ``cout << minimumProduct(arr, n) << endl;``    ``return` `0;``}`

## Java

 `// Java program to find the minimum``// product of sum of pair of element``// in array arr[]``import` `java.util.*;` `class` `GFG{`` ` `// Function to find the minimum``// product``static` `int` `minimumProduct(``int``[] arr, ``int` `n)``{`` ` `    ``// Sort the array using STL``    ``// sort() function``    ``Arrays.sort(arr);`` ` `    ``// Intialise product to 1``    ``int` `product = ``1``;`` ` `    ``for` `(``int` `i = ``0``; i < n; i += ``2``) {`` ` `        ``// Find product of sum of``        ``// all pairs``        ``product *= (arr[i] + arr[i + ``1``]);``    ``}`` ` `    ``// Return the product``    ``return` `product;``}`` ` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``1``, ``6``, ``3``, ``1``, ``7``, ``8` `};``    ``int` `n = arr.length;`` ` `    ``// Function call to find product``    ``System.out.print(minimumProduct(arr, n) +``"\n"``);``}``}` `// This code is contributed by sapnasingh4991`

## Python3

 `# Python3 program to find the minimum``# product of sum of pair of element``# in array arr[]` `# Function to find the minimum``# product``def` `minimumProduct(arr, n):` `    ``# Sort the array using STL``    ``# sort() function``    ``arr ``=` `sorted``(arr)` `    ``# Intialise product to 1``    ``product ``=` `1` `    ``for` `i ``in` `range``(``0``, n, ``2``):` `        ``# Find product of sum of``        ``# all pairs``        ``product ``*``=` `(arr[i] ``+` `arr[i ``+` `1``])` `    ``# Return the product``    ``return` `product` `# Driver code` `arr ``=` `[``1``, ``6``, ``3``, ``1``, ``7``, ``8``]``n ``=` `len``(arr)` `# Function call to find product``print``(minimumProduct(arr, n))` `# This code is contributed by mohit kumar 29`

## C#

 `// C# program to find the minimum``// product of sum of pair of element``// in array arr[]``using` `System;` `class` `GFG {` `    ``// Function to find the minimum``    ``// product``    ``static` `int` `minimumProduct(``int``[] arr, ``int` `n)``    ``{``    ` `        ``// Sort the array``        ``// sort() function``        ``Array.Sort(arr);``    ` `        ``// Intialise product to 1``        ``int` `product = 1;``    ` `        ``for` `(``int` `i = 0; i < n; i += 2) {``    ` `            ``// Find product of sum of``            ``// all pairs``            ``product *= (arr[i] + arr[i + 1]);``        ``}``    ` `        ``// Return the product``        ``return` `product;``    ``}``    ` `    ``// Driver code``    ``static` `void` `Main()``    ``{``        ``int``[] arr = ``new` `int``[] { 1, 6, 3, 1, 7, 8 };``        ``int` `n = arr.Length;``    ` `        ``// Function call to find product``        ``Console.Write(minimumProduct(arr, n));``    ``}``}` `// This code is contributed by shubhamsingh10`

## Javascript

 ``
Output:
`270`

Time Complexity: O(N*log N)

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