973.K-Closest-Points-to-Origin

973. K Closest Points to Origin

题目地址

https://leetcode.com/problems/k-closest-points-to-origin/

题目描述

We have a list of points on the plane.  Find the K closest points to the origin (0, 0).

(Here, the distance between two points on a plane is the Euclidean distance.)

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

Note:
1 <= K <= points.length <= 10000
-10000 < points[i][0] < 10000
-10000 < points[i][1] < 10000

代码

Approach #1 Sort

Time: O(NlogN) && Space: O(N)

class Solution {
  public int[][] kClosest(int[][] points, int K) {
    int N = points.length;
    int[] dists = new int[N];
    for (int i = 0; i < N; ++i)
      dists[i] = dist(points[i]);

    Arrays.sort(dists);
    int distK = dists[K-1];

    int[][] ans = new int[K][2];
    int t = 0;
    for (int i = 0; i < N; ++i)
       if (dist(points[i]) <= distK)
          ans[t++] = points[i];
    return ans;
  }

  public int dist(int[] point) {
      return point[0] * point[0] + point[1] * point[1];
  }
}

Approach #2 Divide and Conquer

Time: O(NlogN) && Space: O(N)

class Solution {
  int[][] points;

  public int[][] kClosest(int[][] points, int K) {
    this.points = points;
    int n = points.length;

    divideConquer(0, n-1, K);

    return Arrays.copyOfRange(points, 0, K); 
  }

  public void divideConquer(int start, int end, int K) {
    if (start >= end)   return;

    int mid = partion(start, end);
    if (mid < K) {
        divideConquer(mid + 1, end, K);
    } else if (mid > K) {
        divideConquer(start, mid - 1, K);
    } 
  }

  public int partion(int lo, int hi) {
    int pivot = dist(hi);
    int s = lo;
    for (int i = lo; i < hi; i++) {
        if (dist(i) < pivot) {
            swap(i, s);
            s++;
        }
    }

    swap(hi, s);

    return s;
  }


  private void swap(int i, int j) {
    int[] temp = points[i];
    points[i] = points[j];
    points[j] = temp;
  }


  public int dist(int i) {
    return points[i][0] * points[i][0] + points[i][1] * points[i][1];
  }

}