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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.
1function minimizeMaxDifference(nums, p) {
2 nums.sort((a, b) => a - b);
3 let left = 0;
4 let right = nums[nums.length - 1] - nums[0];
5 while (left < right) {
6 let mid = Math.floor((left + right) / 2);
7 let count = 0;
8 for (let i = 1; i < nums.length && count < p; ++i) {
9 if (nums[i] - nums[i - 1] <= mid) {
10 count++;
11 i++; // Skip the next index to ensure each number is used at most once
12 }
13 }
14 if (count >= p) right = mid;
15 else left = mid + 1;
16 }
17 return left;
18}
19
20let nums = [10, 1, 2, 7, 1, 3];
21let p = 2;
22console.log(minimizeMaxDifference(nums, p));This JavaScript solution adopts a similar sorting strategy and binary search methodology to ascertain the minimum possible value for maximal differences during pairing.
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.
1from heapq import heappush, heappop
2
3
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.