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

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[0]))
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