973. 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.

Constraints:

  • 1 <= k <= points.length <= 104
  • -104 < xi, yi < 104

Solution1:

class Solution(object):
     def kClosest(self, points, K):
        return heapq.nsmallest(K, points, lambda (x, y): x * x + y * y)
        

Solution2:

Python sorting by distance


Hint:

Recall the definition of Euclidean distance.

Launch customized sorting to sort points by distance to origin.


Illustration and Visualization:

image

Implementation by sorting with distance:

class Solution:
    def kClosest(self, points, K):
        
        # sort by the distance to origin, in ascending order
        points.sort( key = lambda point: (point[0]**2 + point[1]**2) )
        
        return points[:K]

Implementation by heap sort with distance:

class Solution:
    def kClosest(self, points, K):
        
                
        # sort by the distance to origin, in ascending order
        k_closet = heapq.nsmallest( K, points, key = lambda point: point[0]**2 + point[1]**2  )
        
        return k_closet

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