478. Generate Random Point in a Circle

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Problem

Given the radius and the position of the center of a circle, implement the function randPoint which generates a uniform random point inside the circle.

Implement the Solution class:

• Solution(double radius, double x_center, double y_center) initializes the object with the radius of the circle radius and the position of the center (x_center, y_center).
• randPoint() returns a random point inside the circle. A point on the circumference of the circle is considered to be in the circle. The answer is returned as an array [x, y].

Example 1:

Input
["Solution", "randPoint", "randPoint", "randPoint"]
[[1.0, 0.0, 0.0], [], [], []]
Output
[null, [-0.02493, -0.38077], [0.82314, 0.38945], [0.36572, 0.17248]]

Explanation
Solution solution = new Solution(1.0, 0.0, 0.0);
solution.randPoint(); // return [-0.02493, -0.38077]
solution.randPoint(); // return [0.82314, 0.38945]
solution.randPoint(); // return [0.36572, 0.17248]

Constraints:

• 0 < radius <= 10^8
• -10^7 <= x_center, y_center <= 10^7
• At most 3 * 10^4 calls will be made to randPoint.

Code

class Solution {
    double a;
    double b;
    double r;
    Random rand = null;
    
    public Solution(double radius, double x_center, double y_center) {
        a = x_center;
        b = y_center;
        r = radius;
        rand = new Random();
    }
    
    public double[] randPoint() {
        double x = getRandom(r, a);
        double y = getRandom(r, b);

        while(getDist(x, y) > r * r) {
            x = getRandom(r, a);
            y = getRandom(r, b);
        }

        return new double[]{x, y};

    }

    private double getDist(double x, double y){
        return (x - a) * (x - a) + (y - b) * (y - b);
    }

    private double getRandom(double r, double num){
        return num - r + Math.random() * (2 * r);
    }
}