k-closest-points-to-origin

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Description

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

Solution(Python)

class Solution:
    def kClosest(self, points: List[List[int]], k: int) -> List[List[int]]:
        # Sort the list with a custom comparator function
        points.sort(key=self.squared_distance)

        # Return the first k elements of the sorted list
        return points[:k]

    def squared_distance(self, point: List[int]) -> int:
        """Calculate and return the squared Euclidean distance."""
        return point[0] ** 2 + point[1] ** 2