Practice/Meta/Leetcode 478. Generate Random Point in a Circle

Leetcode 478. Generate Random Point in a Circle

CodingMust

Problem

Design a class that generates uniformly distributed random points within a rectangular region. You need to implement a constructor that accepts the rectangle's dimensions and position, and a method that returns random points.

The constructor takes four parameters:

• width: the width of the rectangle (positive float)
• height: the height of the rectangle (positive float)
• x_min: the x-coordinate of the bottom-left corner
• y_min: the y-coordinate of the bottom-left corner

Implement the randPoint() method that returns a random point [x, y] uniformly distributed within the rectangle (including the boundary).

Requirements

1. The RectangleSampler class must store the rectangle's dimensions and position
2. The randPoint() method must return a list/array of two floats representing [x, y] coordinates
3. Points must be uniformly distributed across the entire rectangular area
4. The sampling should include boundary points (edges of the rectangle)
5. Each call to randPoint() should be independent and return a new random point

Constraints

• 0 < width ≤ 10^8
• 0 < height ≤ 10^8
• -10^7 ≤ x_min, y_min ≤ 10^7
• At most 3 * 10^4 calls will be made to randPoint()
• All test cases will have valid rectangle dimensions

Examples

Example 1:

` Input: RectangleSampler(5.0, 3.0, 0.0, 0.0) randPoint() randPoint() randPoint()

Output: [2.4153, 1.8945] [4.7832, 0.2341] [1.0923, 2.9987]

Explanation: A rectangle with width 5, height 3, positioned at origin (0,0). All returned points have x in range [0, 5] and y in range [0, 3]. `

Example 2:

` Input: RectangleSampler(10.0, 10.0, -5.0, -5.0) randPoint() randPoint()

Output: [-2.3451, 3.8762] [4.1234, -1.9876]

Explanation: A square centered around the origin. Points have x and y coordinates in range [-5, 5]. `

Example 3:

` Input: RectangleSampler(1.0, 100.0, 0.0, 0.0) randPoint()

Output: [0.8234, 67.4523]

Explanation: A tall narrow rectangle. The x-coordinate is in [0, 1] and y-coordinate is in [0, 100]. `