973. K Closest Points to Origin(with. HashTable)

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 <= 104
• -104 <= xi, yi <= 104

 

code by python:

import math


class BinaryMinHeap:
    def __init__(self):
        self.items = [None]

    def __len__(self):
        return len(self.items) - 1

    def _percolate_up(self):
        cur = len(self)
        parent = cur // 2

        while parent > 0:
            if self.items[cur] < self.items[parent]:
                self.items[cur], self.items[parent] = self.items[parent], self.items[cur]

            cur = parent
            parent = cur // 2

    def _percolate_down(self, cur):
        smallest = cur
        left = 2 * cur
        right = 2 * cur + 1

        if left <= len(self) and self.items[left] < self.items[smallest]:
            smallest = left

        if right <= len(self) and self.items[right] < self.items[smallest]:
            smallest = right

        if smallest != cur:
            self.items[cur], self.items[smallest] = self.items[smallest], self.items[cur]
            self._percolate_down(smallest)

    def insert(self, dist):
        self.items.append(dist)
        self._percolate_up()

    def extract(self):
        if len(self) < 1:
            return None

        root = self.items[1]
        self.items[1] = self.items[-1]
        self.items.pop()
        self._percolate_down(1)

        return root


def cal_dist(point):
    return point[0] * point[0] + point[1] * point[1]


class Solution:
    def kClosest(self, points: List[List[int]], k: int) -> List[List[int]]:
        heap = BinaryMinHeap()
        dists = []
        for point in points:
            dist = cal_dist(point)
            heap.insert(dist)
            dists.append(dist)

        kth_dist = [heap.extract() for _ in range(k)][-1]
        return [points[idx] for idx, dist in enumerate(dists) if dist <= kth_dist]