Minimize the Maximum Difference of Pairs - Solution & Explanation

The primary idea of this approach is to first sort the array so that elements which are closer in value are positioned adjacent to each other. This can help in reducing the maximum difference within selected pairs when paired greedily. Once sorted, the greedy approach looks to form pairs consecutively and calculate the differences. By doing so repetitively and minimizing the maximum difference, an optimal solution is achieved.

This C code uses quicksort to sort the input array, followed by a binary search to find the minimal maximum difference possible. The binary search checks for possible maximum differences by counting how many pairs can be formed with that maximum difference.

This approach also begins by sorting the input array, but tackles the problem by employing a min-heap (priority queue). The idea is to manage the smallest differences available and decide pairs greedily based on this. The heap helps efficiently remove and manage differences, ensuring that the maximum difference in the formed pairs remains minimal.

In this Python code, we sort the array and then push all possible adjacent differences into a min-heap. We then pop the smallest difference and form pairs while keeping track of used elements until the required number of pairs is formed.