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

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);

    // Initialise 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

// 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);

    // Initialise 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)

    # Initialise 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);

        // Initialise 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

<script>
// Javascript program to find the minimum
// product of sum of pair of element
// in array arr[]

// Function to find the minimum
// product
function minimumProduct(arr, n)
{

    // Sort the array using STL
    // sort() function
    arr.sort();

    // Initialise product to 1
    let product = 1;

    for (let 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
    let arr = [ 1, 6, 3, 1, 7, 8 ];
    let n = arr.length;

    // Function call to find product
    document.write(minimumProduct(arr, n) + "<br>");

// This code is contributed by Mayank Tyagi

</script>

Output:

270

Time Complexity: O(N*log N) the inbuilt sort function takes N log N time to complete all operations, hence the overall time taken by the algorithm is N log N
Auxiliary Space: O(1) since no extra array is used so the space taken by the algorithm is constant