K Closest Points to Origin

Problem

https://leetcode.com/problems/k-closest-points-to-origin/

Given an array of points where points[i] = [x_i, y_i] 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., sqrt(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<= x_i, y_i<= 10⁴

Pattern

Heap, Sorting

Approaches

Heap

Code

import heapq


def kClosest(points: list[list[int]], k: int) -> list[list[int]]:
    """Return the *k* closest points to the origin."""
    heap = [(x**2 + y**2, x, y) for x, y in points]
    heapq.heapify(heap)
    return [[x, y] for _, x, y in heapq.nsmallest(k, heap)]

Test

>>> from k_closest_points_to_origin__heap import kClosest
>>> kClosest([[1, 3], [-2, 2]], 1)
[[-2, 2]]
>>> sorted(kClosest([[3, 3], [5, -1], [-2, 4]], 2))
[[-2, 4], [3, 3]]

k_closest_points_to_origin__heap.kClosest(points: list[list[int]], k: int) → list[list[int]]

Return the k closest points to the origin.