generate-random-point-in-a-circle

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Algorithms

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

Implement the <code>Solution</code> class:

<ul>
	<li><code>Solution(double radius, double x_center, double y_center)</code> initializes the object with the radius of the circle <code>radius</code> and the position of the center <code>(x_center, y_center)</code>.</li>
	<li><code>randPoint()</code> 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 <code>[x, y]</code>.</li>
</ul>

&nbsp;
Example 1:

<pre>
Input
[&quot;Solution&quot;, &quot;randPoint&quot;, &quot;randPoint&quot;, &quot;randPoint&quot;]
[[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]
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>0 &lt;&nbsp;radius &lt;= 108</code></li>
	<li><code>-107 &lt;= x_center, y_center &lt;= 107</code></li>
	<li>At most <code>3 * 104</code> calls will be made to <code>randPoint</code>.</li>
</ul>

Generate Random Point in a Circle

Random Point in Non-overlapping Rectangles

random-point-in-non-overlapping-rectangles

非重叠矩形中的随机点

Geometry

Math

Rejection Sampling

Randomized

给定圆的半径和圆心的位置，实现函数 <code>randPoint</code> ，在圆中产生均匀随机点。

实现&nbsp;<code>Solution</code>&nbsp;类:

<ul>
	<li><code>Solution(double radius, double x_center, double y_center)</code>&nbsp;用圆的半径&nbsp;<code>radius</code>&nbsp;和圆心的位置<code> (x_center, y_center)</code> 初始化对象</li>
	<li><code>randPoint()</code>&nbsp;返回圆内的一个随机点。圆周上的一点被认为在圆内。答案作为数组返回 <code>[x, y]</code> 。</li>
</ul>

&nbsp;

示例 1：

<pre>
输入: 
["Solution","randPoint","randPoint","randPoint"]
[[1.0, 0.0, 0.0], [], [], []]
输出: [null, [-0.02493, -0.38077], [0.82314, 0.38945], [0.36572, 0.17248]]
解释:
Solution solution = new Solution(1.0, 0.0, 0.0);
solution.randPoint ();//返回[-0.02493，-0.38077]
solution.randPoint ();//返回[0.82314,0.38945]
solution.randPoint ();//返回[0.36572,0.17248]</pre>

&nbsp;

提示：

<ul>
	<li><code>0 &lt;&nbsp;radius &lt;= 108</code></li>
	<li><code>-107&nbsp;&lt;= x_center, y_center &lt;= 107</code></li>
	<li><code>randPoint</code> 最多被调用&nbsp;<code>3 * 104</code>&nbsp;次</li>
</ul>