# 478. Generate Random Point in a Circle

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:

1. input and output values are in floating-point.
2. radius and x-y position of the center of the circle is passed into the class constructor.
3. a point on the circumference of the circle is considered to be in the circle.
4. 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:
Solution(double radius, double x_center, double y_center) {
r = radius; centerX = x_center; centerY = y_center;
}

vector<double> randPoint() {
double theta = 2 * M_PI * ((double)rand() / RAND_MAX);
double len = sqrt((double)rand() / RAND_MAX) * r;
return {centerX + len * cos(theta), centerY + len * sin(theta)};
}

private:
double r, centerX, centerY;
};

class Solution {
public:
Solution(double radius, double x_center, double y_center) {
r = radius; centerX = x_center; centerY = 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 {centerX + x, centerY + y};
}
}

private:
double r, centerX, centerY;
};

Github 同步地址：

https://github.com/grandyang/leetcode/issues/478

Implement Rand10() Using Rand7()

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

https://leetcode.com/problems/generate-random-point-in-a-circle/discuss/154405/C%2B%2B-solution-polar-coordinates

https://leetcode.com/problems/generate-random-point-in-a-circle/discuss/169518/C%2B%2B-AC-solution-using-rejection-sampling

https://leetcode.com/problems/generate-random-point-in-a-circle/discuss/155650/Explanation-with-Graphs-why-using-Math.sqrt()

LeetCode All in One 题目讲解汇总(持续更新中…)

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