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Solution: Queries on Number of Points Inside a Circle

Explore how to efficiently determine the number of points inside or on the edge of circles using sorting and binary search techniques. Understand the application of geometry formulas and algorithm optimization for coding interview problems focused on spatial data queries.

Statement

Given an array of points, where each point is represented as points[i]=[xi,yi]\text = [x_i, y_i], which are the coordinates of the ithi^{th} point on an X-Y plane where some points may have identical coordinates. Additionally, given an array of queries, where each queries[j] =[xj,yj,rj]\text = [x_j, y_j, r_j]represents a circle centered at the point [xj,yj][x_j, y_j] with a radius rjr_j.

For each query, your task is to determine how many points lie within or on the boundary of the specified circle. The function should return an array answer, where answer[j] holds the number of points inside the jthj^{th} circle.

Note: Points on the circle’s edge should also be counted inside the circle.

Constraints:

  • 11 \leq points.length 100\leq 100

  • points[i].length ==2== 2 ...