DSA TrainerK Closest Points to Origin
Given an array of points on a 2D plane, return the k points closest to the origin (0, 0). Distance is Euclidean. The answer can be in any order.
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Problem
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).
Input
An array of `points` where `points[i] = [xi, yi]`, and an integer `k`.
Output
The k points closest to the origin.
Examples
Input: points = [[1,3],[-2,2]], k = 1
Output: [[-2,2]]
Distance² from origin: [1,3] → 10, [-2,2] → 8. Closest is [-2,2].
Input: points = [[3,3],[5,-1],[-2,4]], k = 2
Output: [[3,3],[-2,4]]
The brute-force approach
Sort all points by distance from origin and return the first k.
points.sort(key=lambda p: p[0]**2 + p[1]**2)
return points[:k]O(n log n) — sorting the full array even if k is much smaller than n.
Spotting the pattern
This is a Heap / Priority Queue problem. The key question to ask yourself:
To keep only the k closest points seen so far, you need to quickly find and remove the farthest. Which data structure finds the maximum in O(1) and removes it in O(log k)?
Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.
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