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Find the K closest points to the origin in 2D plane, given an array containing N points. You can assume K is much smaller than N and N is very large.

This is what i have so far:

   public class OriginQuestion {

     public static class Point {

     public double x;

    public double y;

 } 
  public static Point[] closestk( Point  myList[], int k ) {}
    for(int i=0;i<myList.length;i++){

    }

  }

Help appreciated

user2789485
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    I think that at the very least, you need to come up with some sort of plan for how you might accomplish this. Maybe start by thinking about how you'd do this by hand if you were given a list of points on paper? – ajb Sep 17 '13 at 23:28
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    So, basically, you have nothing. – PM 77-1 Sep 17 '13 at 23:28

2 Answers2

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This problem is a variant of the nearest neighbor search problem. The simplest solution is to compute the distance from the origin to all N points and then find the K that are nearest using for example the quickselect algorithm, giving a time and space complexity of O(n).

Joni
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This problem can be solved using heap. We can start with creating a max-heap of size k and start adding points to it. After we are done adding K points to our heap.

Now if the (K+1)th point is at distance lower than the max-heap root , we remove root and add this (K+1)th point to our max-heap.

After we are done processing all the N points, our heap will give us the solution. The worst case complexity should be N(log K) as we will do it for N numbers and log K operations are required to move a node in the heap.

kuabhina1702
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