# Minimum sum of product of elements of pairs of the given array

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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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:

 // 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[0]);        // Function call to find product     cout << minimumProduct(arr, n) << endl;     return 0; }

 // 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 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# 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

Output:
270

Time Complexity: O(N*log N)

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