478. Generate Random Point in a Circle

https://leetcode.com/problems/generate-random-point-in-a-circle/description/

给定圆心和半径，让以uniform distribution生成落在圆内的随机点。用拒绝采样思想，随机在以圆心为心，2r为宽的正方形采样，对落在内切圆外的重采。在C++里(double)rand() / RAND_MAX表示随机生成[0,1.0)的浮点数，所以2 * (double)rand() / RAND_MAX表示[0, 2)的随机数生成器, 让它减去1即[-1, 1)的随机数生成器，再乘以r即[-r, r)的生成器。

/*
 * @lc app=leetcode id=478 lang=cpp
 *
 * [478] Generate Random Point in a Circle
 *
 * https://leetcode.com/problems/generate-random-point-in-a-circle/description/
 *
 * algorithms
 * Medium (37.44%)
 * Likes:    109
 * Dislikes: 183
 * Total Accepted:    6.8K
 * Total Submissions: 18.2K
 * Testcase Example:  '["Solution", "randPoint", "randPoint", "randPoint"]\n[[1.0, 0.0, 0.0], [], [], []]'
 *
 * Given the radius and x-y positions of the center of a circle, write a
 * function randPoint which generates a uniform random point in the circle.
 * 
 * Note:
 * 
 * 
 * input and output values are in floating-point.
 * radius and x-y position of the center of the circle is passed into the class
 * constructor.
 * a point on the circumference of the circle is considered to be in the
 * circle.
 * randPoint returns a size 2 array containing x-position and y-position of the
 * random point, in that order.
 * 
 * 
 * 
 * Example 1:
 * 
 * 
 * Input: 
 * ["Solution","randPoint","randPoint","randPoint"]
 * [[1,0,0],[],[],[]]
 * Output:
 * [null,[-0.72939,-0.65505],[-0.78502,-0.28626],[-0.83119,-0.19803]]
 * 
 * 
 * 
 * Example 2:
 * 
 * 
 * Input: 
 * ["Solution","randPoint","randPoint","randPoint"]
 * [[10,5,-7.5],[],[],[]]
 * Output:
 * [null,[11.52438,-8.33273],[2.46992,-16.21705],[11.13430,-12.42337]]
 * 
 * 
 * Explanation of Input Syntax:
 * 
 * The input is two lists: the subroutines called and their arguments.
 * Solution's constructor has three arguments, the radius, x-position of the
 * center, and y-position of the center of the circle. randPoint has no
 * arguments. Arguments are always wrapped with a list, even if there aren't
 * any.
 * 
 * 
 */
class Solution {
public:
    double r, x_cen, y_cen;
    Solution(double radius, double x_center, double y_center) {
        r = radius;
        x_cen = x_center;
        y_cen = y_center;
    }
    
    vector<double> randPoint() {
        while (true) {
            double x = (2 * (double)rand() / RAND_MAX - 1.0) * r;
            double y = (2 * (double)rand() / RAND_MAX - 1.0) * r;
            if (x * x + y * y <= r * r) return {x_cen + x, y_cen + y}; 
        }
    }
};

/**
 * Your Solution object will be instantiated and called as such:
 * Solution* obj = new Solution(radius, x_center, y_center);
 * vector<double> param_1 = obj->randPoint();
 */