# [Programming Problem] K Closest Points to Origin

Given an array of points where points[i] = [xi, yi] represents a point on the X-Y plane and an integer k, return the k closest points to the origin (0, 0).

The distance between two points on the X-Y plane is the Euclidean distance (i.e., √(x1 – x2)^2 + (y1 – y2)^2).

You may return the answer in any order. The answer is guaranteed to be unique (except for the order that it is in).

```Example 1: Input: points = [[1,3],[-2,2]], k = 1 Output: [[-2,2]] Explanation: The distance between (1, 3) and the origin is sqrt(10). The distance between (-2, 2) and the origin is sqrt(8). Since sqrt(8) < sqrt(10), (-2, 2) is closer to the origin. We only want the closest k = 1 points from the origin, so the answer is just [[-2,2]].   Example 2: Input: points = [[3,3],[5,-1],[-2,4]], k = 2 Output: [[3,3],[-2,4]] Explanation: The answer [[-2,4],[3,3]] would also be accepted.```
• Create point object that contains x, y co-ordinates and distance from origin.
• Keep adding points to max heap. Custom comparator that uses distance (inside the point object) as key.
• Make sure size of heap does not go higher than K
• In the end, the K points in the heap are your solution
• Since size of heap capped at k, Time complexity nlogK Time complexity logK
```import java.util.*;   class Point { int x; int y; double dist; public Point(int x, int y) { this.x = x; this.y = y; this.dist = Math.sqrt(Math.pow(x * 1.0, 2) + Math.pow(y * 1.0, 2)); } }   class Solution { public int[][] kClosest(int[][] points, int k) { PriorityQueue maxHeap = new PriorityQueue<Point>((x, y) -> Double.compare(y.dist, x.dist)); for (int i = 0 ; i < points.length ; i++ ) { maxHeap.offer(new Point(points[i][0], points[i][1])); if (maxHeap.size() >= k+1) maxHeap.poll(); }   int ret[][] = new int[maxHeap.size()][2]; int i = 0; while (maxHeap.size() > 0) { Point p = (Point) maxHeap.poll(); ret[i][0] = p.x; ret[i][1] = p.y; i++; }   return ret; } }```

### 18 thoughts on “[Programming Problem] K Closest Points to Origin”

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