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478. Generate Random Point in a Circle

题目

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.

题目大意

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 。

说明:

  • 输入值和输出值都将是浮点数。
  • 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。
  • 圆周上的点也认为是在圆中。
  • 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。

解题思路

  • 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。
  • 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。

代码

package leetcode import ( "math""math/rand""time" ) typeSolutionstruct { rfloat64xfloat64yfloat64 } funcConstructor(radiusfloat64, x_centerfloat64, y_centerfloat64) Solution { rand.Seed(time.Now().UnixNano()) returnSolution{radius, x_center, y_center} } func (this*Solution) RandPoint() []float64 { /* a := angle() r := this.r * math.Sqrt(rand.Float64()) x := r * math.Cos(a) + this.x y := r * math.Sin(a) + this.y return []float64{x, y}*/for { rx:=2*rand.Float64() -1.0ry:=2*rand.Float64() -1.0x:=this.r*rxy:=this.r*ryifx*x+y*y<=this.r*this.r { return []float64{x+this.x, y+this.y} } } } funcangle() float64 { returnrand.Float64() *2*math.Pi } /** * Your Solution object will be instantiated and called as such: * obj := Constructor(radius, x_center, y_center); * param_1 := obj.RandPoint(); */
close