K Closest Points to Origin

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Your question is K Closest Points to Origin. Start with the requirements on the right.

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Problem

In a Meta-style ranking or retrieval pipeline, you may need to quickly keep only the nearest candidate embeddings or coordinates. Given a list of points on a 2D plane, return the k points closest to the origin (0, 0).

The distance between a point (x, y) and the origin is sqrt(x^2 + y^2). For efficiency, compare points using squared distance x^2 + y^2 instead of computing square roots. You may return the answer in any order.

Formal Specification

Input:
- points: a list of 2-element lists, where each element is [x, y]
- k: an integer
Output:
- A list containing exactly k points from points with the smallest distances to the origin

Constraints

1 <= len(points) <= 10^4
-10^4 <= x, y <= 10^4
1 <= k <= len(points)
Each point contains exactly two integers

Function Signature

def k_closest_points(points, k):

Your solutionPython 3

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