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This approach leverages the simplicity of sorting the list of points based on their distance from the origin. After sorting, the first k points will be the closest ones. The key is to use the squared Euclidean distance to avoid the computational overhead of square root operations.
Time Complexity: O(n log n) due to sorting.
Space Complexity: O(1) since the sorting is done in-place.
1using System;
2using System.Linq;
3
4public class Solution {
5 public int[][] KClosest(int[][] points, int k) {
6 return points.OrderBy(point => point[0] * point[0] + point[1] * point[1]).Take(k).ToArray();
7 }
8}
9This C# solution uses LINQ's OrderBy to sort points by squared distance, followed by Take to extract the first k elements.
The Max-Heap approach uses a priority queue to maintain the k closest points seen so far. By using a max-heap, we can efficiently insert new points and potentially evict the farthest point if it is further than any encountered point, leading to a reduced time complexity for finding the k closest points.
Time Complexity: O(n log k) since each insertion/extraction in the heap takes O(log k) time.
Space Complexity: O(k) for the heap storage.
1Using a priority queue (from a library like collections), this JavaScript solution maintains a max-heap containing the closest points, dequeuing the largest whenever k is exceeded.