1828. Queries on Number of Points Inside a Circle

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.

 

Follow up: Could you find the answer for each query in better complexity than O(n)?

Rust Solution

struct Solution;

impl Solution {
    fn count_points(points: Vec<Vec<i32>>, queries: Vec<Vec<i32>>) -> Vec<i32> {
        queries.into_iter().map(|q| query(&points, q)).collect()
    }
}

fn query(points: &[Vec<i32>], q: Vec<i32>) -> i32 {
    let r2 = q[2] * q[2];
    let mut res = 0;
    for p in points {
        let dx = p[0] - q[0];
        let dy = p[1] - q[1];
        if dx * dx + dy * dy <= r2 {
            res += 1;
        }
    }
    res
}

#[test]
fn test() {
    let points = vec_vec_i32![[1, 3], [3, 3], [5, 3], [2, 2]];
    let queries = vec_vec_i32![[2, 3, 1], [4, 3, 1], [1, 1, 2]];
    let res = vec![3, 2, 2];
    assert_eq!(Solution::count_points(points, queries), res);

    let points = vec_vec_i32![[1, 1], [2, 2], [3, 3], [4, 4], [5, 5]];
    let queries = vec_vec_i32![[1, 2, 2], [2, 2, 2], [4, 3, 2], [4, 3, 3]];
    let res = vec![2, 3, 2, 4];
    assert_eq!(Solution::count_points(points, queries), res);
}

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