https://leetcode.com/problems/k-closest-points-to-origin
Since the k smallest elements don’t need to be sorted, we can find kth smallest with quickselect and return the smaller partition including it. This achieves linear time on average, so should be faster than doing heapq.nsmallest.
Algorithm
from typing import List
from random import randint
# Time: O(n) average O(n^2) with very unlucky pivots
# Space: O(1)
class Solution:
def kClosest(self, points: List[List[int]], k: int) -> List[List[int]]:
quickselect(points, 0, len(points)-1, k)
return points[:k]
def quickselect(points: List[List[int]], left, right, k: int):
if left == right:
return
pivot = partition(points, left, right)
if pivot == k-1:
return
if pivot < k-1:
return quickselect(points, pivot+1, right, k)
return quickselect(points, left, pivot-1, k)
def partition(points: List[List[int]], left, right: int) -> int:
if left == right:
return left
pivot = randint(left, right)
pivot_dist = distance(points[pivot])
points[pivot], points[right] = points[right], points[pivot]
for i in range(left, right):
if distance(points[i]) <= pivot_dist:
points[i], points[left] = points[left], points[i]
left += 1
points[left], points[right] = points[right], points[left]
return left
def distance(point: List[int]) -> int:
return point[0]*point[0] + point[1]*point[1]
# ## Edge Case!
# Use `<=` in the partition comparison! There's a test case with all equal points.
# If you use `<`, the algorithm will never finish because it will keep swapping the pivot
# with itself.
#
# ## Test with this
#
# ```python
# print(Solution().kClosest([[1,3],[-2,2]], 1))
# print(Solution().kClosest([[3,3],[5,-1],[-2,4]], 2))
# print(Solution().kClosest([[1,1],[9,-9],[1,1]], 2))
# print(Solution().kClosest([[-5,4],[-6,-5],[4,6]], 2))
# print(Solution().kClosest([[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10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,[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000],[10000,10000]], 10000))
# ```
# You can also heapify a list of tuples: `(euclidean_distance, point)` and then pop `k` points!
#
# - Building the list of tuples: `O(n)`
# - Heapifying it: `O(n)`
# - Popping `k` points: `O(k*logn)`
#
# This is a 4-line solution! But it's not `O(n)` time.
# import heapq
# class Solution:
# # Time: O(n + k*logn)
# # Space: O(n)
# def kClosest(self, points: List[List[int]], k: int) -> List[List[int]]:
# h = [(point[0]*point[0] + point[1]*point[1], point) for point in points]
# heapq.heapify(h)
return [heapq.heappop(h)[1] for _ in range(k)]