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This approach utilizes sorting and a min-heap (or priority queue) to efficiently manage and retrieve the k-th smallest distance. The key steps are:
nums. This simplifies the process of finding the distances as all distance calculations will involve consecutive elements.Time Complexity: O(n^2 log n) due to the double loop and heap operations.
Space Complexity: O(n^2) for storing all possible distances in the heap.
1#include <vector>
2#include <queue>
3#include <algorithm>
4
5int findKthSmallestPairDistance(std::vector<int>& nums, int k) {
6 std::sort(nums.begin(), nums.end());
7 std::priority_queue<int, std::vector<int>, std::greater<int>> minHeap;
8 for (int i = 0; i < nums.size() - 1; ++i) {
9 for(int j = i + 1; j < nums.size(); ++j) {
10 minHeap.push(std::abs(nums[j] - nums[i]));
11 }
12 }
13 for (int i = 0; i < k - 1; ++i) {
14 minHeap.pop();
15 }
16 return minHeap.top();
17}The code begins by sorting nums to facilitate easier comparison of distances. A min-heap is employed to efficiently extract the k smallest elements after pushing all pair distances into it. This minimizes unnecessary storage usage while maintaining time efficiency.
This more efficient approach combines binary search with a two-pointer technique. The principal idea is to use binary search over distance values to pinpoint the k-th smallest distance. It involves:
nums.Time Complexity: O(n log n + n log(maxDistance))
Space Complexity: O(1) as no additional space beyond fixed variables is used.
1import java.
This Java solution identifies the k-th smallest distance through binary search coupled with a counting mechanism, using a two-pointer approach. It narrows the search space based on how many pairs are under a proposed distance.