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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.
Time Complexity: O(n log n), dominated by the sorting step.
Space Complexity: O(1), if we ignore the space used by the sorting algorithm.
1using System;
2using System.Linq;
3
4public class MinMaxDifference {
5 public int MinimizeMaxDifference(int[] nums, int p) {
6 Array.Sort(nums);
7 int left = 0, right = nums[nums.Length - 1] - nums[0];
8 while (left < right) {
9 int mid = (left + right) / 2;
10 int count = 0;
11 for (int i = 1; i < nums.Length && count < p; ++i) {
12 if (nums[i] - nums[i - 1] <= mid) {
13 count++;
14 i++; // Ensure each number is used at most once
15 }
16 }
17 if (count >= p) right = mid;
18 else left = mid + 1;
19 }
20 return left;
21 }
22
23 public static void Main() {
24 int[] nums = {10, 1, 2, 7, 1, 3};
25 int p = 2;
26 MinMaxDifference mmd = new MinMaxDifference();
27 Console.WriteLine(mmd.MinimizeMaxDifference(nums, p));
28 }
29}The C# version utilizes the System library to apply a similar approach to sort and iterate using binary search to identify the minimum maximum difference by counting feasible pairs.
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.
Time Complexity: O(n log n) due to the heap operations.
Space Complexity: O(n) for holding the differences.
1import java.util.PriorityQueue;
2
This Java implementation uses a priority queue to actively manage and utilize the smallest available differences in the sorted array to form the pairs, similar to the approach presented in Python.