"""
973. K Closest Points to Origin
Difficulty: Medium
https://leetcode.com/problems/k-closest-points-to-origin/

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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 <= 10^4

        • -10^4 <= xi, yi <= 10^4
"""

import heapq


class Solution:
    def kClosest(self, points: List[List[int]], k: int) -> List[List[int]]:
        minHeap = []
        for x, y in points:
            dist = (x**2) + (y**2)
            minHeap.append([dist, x, y])

        heapq.heapify(minHeap)
        res = []

        while k > 0:
            dist, x, y = heapq.heappop(minHeap)
            res.append([x, y])
            k -= 1

        return res