# Minimize the sum of squares of sum of N/2 paired formed by N numbers in C++

C++Server Side ProgrammingProgramming

## Problem statement

Given an array of n elements. The task is to create n/2 pairs in such a way that sum of squares of n/2 pairs is minimal.

## Example

If given array is −

arr[] = {5, 10, 7, 4}
then minimum sum of squares is 340 if we create pairs as (4, 10) and ( 5, 7)

## Algorithm

1. Sort the array
2. Take two variables which point to start and end index of an array
3. Calulate sum as follows:
sum = arr[start] + arr[end];
sum = sum * sum;
4. Repeate this procedure till start < end and increment minSum as follows:
While (start < end) {
sum = arr[start] + arr[end];
sum = sum * sum;
minSum += sum;
++start;
--end;
}

## Example

#include <iostream>
#include <algorithm>
#define SIZE(arr) (sizeof(arr) / sizeof(arr))
using namespace std;
int getMinSquareSum(int *arr, int n) {
sort(arr, arr + n);
int minSum = 0;
int start = 0;
int end = n - 1;
while (start < end) {
int sum = arr[start] + arr[end];
sum *= sum;
minSum += sum;
++start;
--end;
}
return minSum;
}
int main() {
int arr[] = {5, 10, 7, 4};
int res = getMinSquareSum(arr, SIZE(arr));
cout << "Minimum square sum: " << res << "\n";
return 0;
}

## Output

When you compile and execute above program. It generates following output −

Minimum square sum: 340