1828

1828. Queries on Number of Points Inside a Circle (Medium)

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.

You are also given an array queries where queries[j] = [xj, yj, rj] describes a circle centered at (xj, yj) with a radius of rj.

For each query queries[j], compute the number of points inside the jth circle. Points on the border of the circle are considered inside.

Return an array answer, where answer[j] is the answer to the jth query.

 

Example 1:

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.
queries[0] is the green circle, queries[1] is the red circle, and queries[2] is the blue circle.

Example 2:

Input: points = [[1,1],[2,2],[3,3],[4,4],[5,5]], queries = [[1,2,2],[2,2,2],[4,3,2],[4,3,3]]
Output: [2,3,2,4]
Explanation: The points and circles are shown above.
queries[0] is green, queries[1] is red, queries[2] is blue, and queries[3] is purple.

 

Constraints:

• 1 <= points.length <= 500
• points[i].length == 2
• 0 <= x​​​​​​i, y​​​​​​i <= 500
• 1 <= queries.length <= 500
• queries[j].length == 3
• 0 <= xj, yj <= 500
• 1 <= rj <= 500
• All coordinates are integers.

Related Topics:
Math

Solution 1. Brute force

// OJ: https://leetcode.com/problems/queries-on-number-of-points-inside-a-circle/
// Author: github.com/lzl124631x
// Time: O(PQ)
// Space: O(1)
class Solution {
public:
    vector<int> countPoints(vector<vector<int>>& P, vector<vector<int>>& Q) {
        vector<int> ans;
        for (auto &q : Q) {
            int cnt = 0;
            for (auto &p : P) {
                if (pow(q[0] - p[0], 2) + pow(q[1] - p[1], 2) <= pow(q[2], 2)) ++cnt;
            }
            ans.push_back(cnt);
        }
        return ans;
    }
};