算法设计与分析复习06：随机化算法

傷城~ 2024-03-30 13:33 62阅读 0赞

> 作者：非妃是公主  
> 专栏：《算法》  
> **个性签：顺境不惰，逆境不馁，以心制境，万事可成。——曾国藩**
> 
> ![在这里插入图片描述][7cea80270e124c7faeb5f6b5fd8ac41a.jpeg]
> 
> ### 专栏系列文章 ###
> 
> [算法设计与分析复习01：主方法求递归算法时间复杂度][01]
> 
> [算法设计与分析复习02：分而治之算法][02]
> 
> [算法设计与分析复习03：动态规划算法][03]  
> [算法设计与分析复习04：贪心算法][04]
> 
> [算法设计与分析复习05：回溯及分支限界][05]
> 
> [算法设计与分析复习06：随机化算法][06]
> 
> [算法设计与分析复习07：样题][07]
> 
> #### 文章目录 ####
> 
>  *   *  专栏系列文章
>      *  复习重点
>      *  随机化算法
>      *   *  舍伍德算法：线性时间选择、快速排序
>          *   *  线性时间选择
>              *  快速排序
>          *  拉斯维加斯算法：N后问题
>          *  蒙特卡洛算法：求PI值

### 复习重点 ###

![在这里插入图片描述][16ee73d314d24fd7a218b4b65604a9f6.png]

### 随机化算法 ###

![在这里插入图片描述][8b797becd9c5445dbee2b200795e08ae.png]  
![在这里插入图片描述][f99ec43545f443e08f841384c651367a.png]

#### 舍伍德算法：线性时间选择、快速排序 ####

##### 线性时间选择 #####

![在这里插入图片描述][bf7ff1ed33cc43d49ad428554b005e58.png]  
![在这里插入图片描述][476285043d4945eebb8a1a439b1b0718.png]

##### 快速排序 #####

![在这里插入图片描述][e749209b286f4b23beb841a6e6b5c337.png]  
![在这里插入图片描述][c53b8fc793c84d269dce9ed3e90d03f9.png]  
![在这里插入图片描述][8c8fb828e96046fab5f85bc6d74752a7.png]

#### 拉斯维加斯算法：N后问题 ####

![在这里插入图片描述][4998cbcb41194d878350fbb4a21a60d5.png]  
![在这里插入图片描述][33350ff82e004ed9ac69e8a556a8ec90.png]  
![在这里插入图片描述][ff7b70121490468281ea4e60693be696.png]  
![在这里插入图片描述][04d1d3abd3394e9292aa2b537565d025.png]  
![在这里插入图片描述][1a2e584d57f04d1da1be5665c4517cfa.png]  
![在这里插入图片描述][226c4800d6ad46bfa93aa7f33695ae92.png]  
另一种解决方案：  
![在这里插入图片描述][3c69b7fd257545d49eeedeb3b4c39832.png]

#### 蒙特卡洛算法：求PI值 ####

![在这里插入图片描述][f05cd7c72cf14c00a3e8e5109736b747.png]  
![在这里插入图片描述][2475a8bd2ff24be1b41c39258a3eb401.png]  
![在这里插入图片描述][9baa23ee84b4403895eb2fba47f3a8ab.png]  
![在这里插入图片描述][94fa09d08822468781bc482f83a88fde.png]  
![在这里插入图片描述][aed83b6594e54abcb54a3a155267c7e3.png]  
![在这里插入图片描述][59eb2b2791d64947870fe09f2faca44a.png]

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[01]: https://blog.csdn.net/myf_666/article/details/128509102
[02]: https://blog.csdn.net/myf_666/article/details/128509126
[03]: https://blog.csdn.net/myf_666/article/details/128509143
[04]: https://blog.csdn.net/myf_666/article/details/128509159
[05]: https://blog.csdn.net/myf_666/article/details/128509168
[06]: https://blog.csdn.net/myf_666/article/details/128509174
[07]: https://blog.csdn.net/myf_666/article/details/128509183
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