[LeetCode] 973. K Closest Points to Origin

Posted 2020-11-26 aaronliu1991

最接近原点的K个点。题意是给一些点的坐标（以二维数组表示）和一个数字K。求距离最靠近原点的前K个点。例子，

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]]
(The answer [[-2,4],[3,3]] would also be accepted.)

求前K个XX的问题，十有八九可以用heap/priority queue解决，这个题也不例外。我这里给出pq的解法，将每个坐标与原点的距离加入pq。求距离就是初中数学的勾股定理。

时间O(nlogk)

空间O(n)

Java实现

 1 class Solution {
 2     public int[][] kClosest(int[][] points, int K) {
 3         PriorityQueue<int[]> pq = new PriorityQueue<>(K,
 4                 (o1, o2) -> o1[0] * o1[0] + o1[1] * o1[1] - o2[0] * o2[0] - o2[1] * o2[1]);
 5         for (int[] point : points) {
 6             pq.add(point);
 7         }
 8         int[][] res = new int[K][2];
 9         for (int i = 0; i < K; i++) {
10             res[i] = pq.poll();
11         }
12         return res;
13     }
14 }