Queries on Number of Points Inside a Circle — LeetCode 1828 Python Solution

The problem

You are given an array points where points[i] = [xi, yi] is the coordinates of the ith point on a 2D plane. Multiple points can have the same coordinates.

Example

Input

points = [[1,3],[3,3],[5,3],[2,2]], queries = [[2,3,1],[4,3,1],[1,1,2]]

Output

[3,2,2]

Explanation

The points and circles are shown above.

Python solution

class Solution:
    def countPoints(
        self, points: List[List[int]], queries: List[List[int]]
    ) -> List[int]:
        ans = []
        for x, y, r in queries:
            cnt = 0
            for i, j in points:
                dx, dy = i - x, j - y
                cnt += dx * dx + dy * dy <= r * r
            ans.append(cnt)
        return ans

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 1828. Queries on Number of Points Inside a Circle is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math and Geometry.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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