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103 lines
3.2 KiB
Markdown
103 lines
3.2 KiB
Markdown
# [478. Generate Random Point in a Circle](https://leetcode.com/problems/generate-random-point-in-a-circle/)
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## 题目
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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.
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Note:
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1. input and output values are in [floating-point](https://www.webopedia.com/TERM/F/floating_point_number.html).
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2. radius and x-y position of the center of the circle is passed into the class constructor.
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3. a point on the circumference of the circle is considered to be in the circle.
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4. `randPoint` returns a size 2 array containing x-position and y-position of the random point, in that order.
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**Example 1:**
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```
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Input:
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["Solution","randPoint","randPoint","randPoint"]
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[[1,0,0],[],[],[]]
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Output: [null,[-0.72939,-0.65505],[-0.78502,-0.28626],[-0.83119,-0.19803]]
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```
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**Example 2:**
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```
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Input:
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["Solution","randPoint","randPoint","randPoint"]
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[[10,5,-7.5],[],[],[]]
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Output: [null,[11.52438,-8.33273],[2.46992,-16.21705],[11.13430,-12.42337]]
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```
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**Explanation of Input Syntax:**
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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.
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## 题目大意
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给定圆的半径和圆心的 x、y 坐标，写一个在圆中产生均匀随机点的函数 randPoint 。
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说明:
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- 输入值和输出值都将是浮点数。
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- 圆的半径和圆心的 x、y 坐标将作为参数传递给类的构造函数。
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- 圆周上的点也认为是在圆中。
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- randPoint 返回一个包含随机点的x坐标和y坐标的大小为2的数组。
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## 解题思路
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- 随机产生一个圆内的点，这个点一定满足定义 `(x-a)^2+(y-b)^2 ≤ R^2`，其中 `(a,b)` 是圆的圆心坐标，`R` 是半径。
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- 先假设圆心坐标在 (0,0)，这样方便计算，最终输出坐标的时候整体加上圆心的偏移量即可。`rand.Float64()` 产生一个 `[0.0,1.0)` 区间的浮点数。`-R ≤ 2 * R * rand() - R < R`，利用随机产生坐标点的横纵坐标 `(x,y)` 与半径 R 的关系，如果 `x^2 + y^2 ≤ R^2`，那么说明产生的点在圆内。最终输出的时候要记得加上圆心坐标的偏移值。
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## 代码
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```go
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package leetcode
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import (
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"math"
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"math/rand"
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"time"
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)
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type Solution struct {
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r float64
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x float64
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y float64
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}
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func Constructor(radius float64, x_center float64, y_center float64) Solution {
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rand.Seed(time.Now().UnixNano())
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return Solution{radius, x_center, y_center}
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}
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func (this *Solution) RandPoint() []float64 {
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/*
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a := angle()
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r := this.r * math.Sqrt(rand.Float64())
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x := r * math.Cos(a) + this.x
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y := r * math.Sin(a) + this.y
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return []float64{x, y}*/
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for {
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rx := 2*rand.Float64() - 1.0
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ry := 2*rand.Float64() - 1.0
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x := this.r * rx
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y := this.r * ry
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if x*x+y*y <= this.r*this.r {
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return []float64{x + this.x, y + this.y}
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}
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}
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}
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func angle() float64 {
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return rand.Float64() * 2 * math.Pi
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}
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/**
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* Your Solution object will be instantiated and called as such:
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* obj := Constructor(radius, x_center, y_center);
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* param_1 := obj.RandPoint();
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*/
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``` |