K Closest Points to Origin

Medium~20 min

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: sqrt(x^2 + y^2).

You may return the answer in any order. The answer is guaranteed to be unique (except for the order that it is in).

Examples

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 point, so the answer is [[-2, 2]].

Example 2

Input: points = [[3,3],[5,-1],[-2,4]], k = 2

Output: [[3,3],[-2,4]]

Explanation: Distances: (3,3) → sqrt(18), (5,-1) → sqrt(26), (-2,4) → sqrt(20). The 2 closest are (3,3) and (-2,4). The output order does not matter.

Constraints

1 <= k <= points.length <= 10^4
-10^4 <= xi, yi <= 10^4
Expected time complexity: O(n log k)

Code

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Output

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