CentOS7 系统配置国内 yum 源和epel源

本文介绍如何在CentOS7系统中配置使用国内的YUM源,包括网易和阿里的开源镜像,以及EPEL源的安装与配置过程。

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1.首先进入/etc/yum.repos.d/ 目录下,新建一个repo_bak目录,用于保存系统中原来的repo文件

[root@bogon ~]# cd /etc/yum.repos.d/
[root@bogon yum.repos.d]# mkdir repo_bak
[root@bogon yum.repos.d]# mv *.repo repo_bak/

2.在CentOS中配置使用网易和阿里的开源镜像

到网易和阿里开源镜像站点下载系统对应版本的repo文件

[root@bogon yum.repos.d]# wget http://mirrors.aliyun.com/repo/Centos-7.repo

[root@bogon yum.repos.d]# wget http://mirrors.163.com/.help/CentOS7-Base-163.repo

[root@bogon yum.repos.d]# ls
Centos-7.repo CentOS-Base-163.repo repo.bak
或者手动下载repo文件并上传到/etc/yum.repos.d/目录

网易开源镜像站:http://mirrors.163.com/.help/centos.html
阿里开源镜像站:https://opsx.alibaba.com/mirror?lang=zh-cn

3.清除系统yum缓存并生成新的yum缓存

[root@bogon yum.repos.d]# ls # 列出/etc/yum.repos.d/目录下的文件
Centos-7.repo CentOS-Base-163.repo repo.bak

[root@bogon yum.repos.d]# yum clean all # 清除系统所有的yum缓存
Loaded plugins: fastestmirror, langpacks
Repository base is listed more than once in the configuration
Repository updates is listed more than once in the configuration
Repository extras is listed more than once in the configuration
Repository centosplus is listed more than once in the configuration
Cleaning repos: base extras updates
Cleaning up everything
Cleaning up list of fastest mirrors

[root@bogon yum.repos.d]# yum makecache # 生成yum缓存
Loaded plugins: fastestmirror, langpacks
Repository base is listed more than once in the configuration
Repository updates is listed more than once in the configuration
Repository extras is listed more than once in the configuration
Repository centosplus is listed more than once in the configuration
base | 3.6 kB 00:00:00
extras | 3.4 kB 00:00:00
updates | 3.4 kB 00:00:00
(1/12): base/7/x86_64/filelists_db | 6.7 MB 00:00:02
(2/12): base/7/x86_64/group_gz | 156 kB 00:00:02
(3/12): base/7/x86_64/other_db | 2.5 MB 00:00:01
(4/12): base/7/x86_64/primary_db | 5.7 MB 00:00:02
(5/12): extras/7/x86_64/prestodelta | 51 kB 00:00:01
(6/12): extras/7/x86_64/filelists_db | 494 kB 00:00:02
(7/12): extras/7/x86_64/other_db | 86 kB 00:00:00
(8/12): extras/7/x86_64/primary_db | 130 kB 00:00:01
(9/12): updates/7/x86_64/prestodelta | 406 kB 00:00:01
(10/12): updates/7/x86_64/filelists_db | 2.1 MB 00:00:01
(11/12): updates/7/x86_64/other_db | 354 kB 00:00:00
(12/12): updates/7/x86_64/primary_db | 3.6 MB 00:00:01
Determining fastest mirrors
Metadata Cache Created

4.安装epel源

[root@bogon yum.repos.d]# yum list | grep epel-release
Repository base is listed more than once in the configuration
Repository updates is listed more than once in the configuration
Repository extras is listed more than once in the configuration
Repository centosplus is listed more than once in the configuration
epel-release.noarch 7-9 extras

[root@bogon yum.repos.d]# yum install -y epel-release
Loaded plugins: fastestmirror, langpacks
Repository base is listed more than once in the configuration
Repository updates is listed more than once in the configuration
Repository extras is listed more than once in the configuration
Repository centosplus is listed more than once in the configuration
Loading mirror speeds from cached hostfile
Resolving Dependencies
–> Running transaction check
—> Package epel-release.noarch 0:7-9 will be installed
–> Finished Dependency Resolution

Dependencies Resolved

Package Arch Version Repository Size

Installing:
epel-release noarch 7-9 extras 14 k

Transaction Summary

Install 1 Package

Total download size: 14 k
Installed size: 24 k
Downloading packages:
epel-release-7-9.noarch.rpm | 14 kB 00:00:00
Running transaction check
Running transaction test
Transaction test succeeded
Running transaction
Installing : epel-release-7-9.noarch 1/1
Verifying : epel-release-7-9.noarch 1/1

Installed:
epel-release.noarch 0:7-9

Complete!
[root@bogon yum.repos.d]# ls # epel源安装成功,比原来多了一个epel.repo和epel-testing.repo文件
Centos-7.repo CentOS-Base-163.repo epel.repo epel-testing.repo repo.bak

5.使用阿里开源镜像提供的epel源

[root@bogon yum.repos.d]# wget -O /etc/yum.repos.d/epel-7.repo http://mirrors.aliyun.com/repo/epel-7.repo # 下载阿里开源镜像的epel源文件
–2018-03-08 20:22:14-- http://mirrors.aliyun.com/repo/epel-7.repo
Resolving mirrors.aliyun.com (mirrors.aliyun.com)… 183.2.199.237, 113.96.109.95, 113.96.109.93, …
Connecting to mirrors.aliyun.com (mirrors.aliyun.com)|183.2.199.237|:80… connected.
HTTP request sent, awaiting response… 200 OK
Length: 1084 (1.1K) [application/octet-stream]
Saving to: ‘/etc/yum.repos.d/epel-7.repo’

100%[==============================================>] 1,084 --.-K/s in 0s

2018-03-08 20:22:14 (130 MB/s) - ‘/etc/yum.repos.d/epel-7.repo’ saved [1084/1084]

[root@bogon yum.repos.d]# ls
CentOS7-Base-163.repo Centos-7.repo epel-7.repo epel.repo epel-testing.repo repo_bak

6.再次清除系统yum缓存,并重新生成新的yum缓存

[root@bogon yum.repos.d]# yum clean all
Loaded plugins: fastestmirror, langpacks
Repository base is listed more than once in the configuration
Repository updates is listed more than once in the configuration
Repository extras is listed more than once in the configuration
Repository centosplus is listed more than once in the configuration
Repository epel is listed more than once in the configuration
Repository epel-debuginfo is listed more than once in the configuration
Repository epel-source is listed more than once in the configuration
Cleaning repos: base epel extras updates
Cleaning up everything
Cleaning up list of fastest mirrors

[root@bogon yum.repos.d]# yum makecache
Loaded plugins: fastestmirror, langpacks
Repository base is listed more than once in the configuration
Repository updates is listed more than once in the configuration
Repository extras is listed more than once in the configuration
Repository centosplus is listed more than once in the configuration
Repository epel is listed more than once in the configuration
Repository epel-debuginfo is listed more than once in the configuration
Repository epel-source is listed more than once in the configuration
base | 3.6 kB 00:00:00
epel | 4.7 kB 00:00:00
extras | 3.4 kB 00:00:00
updates | 3.4 kB 00:00:00
(1/18): base/7/x86_64/group_gz | 156 kB 00:00:01
(2/18): base/7/x86_64/filelists_db | 6.7 MB 00:00:07
(3/18): base/7/x86_64/primary_db | 5.7 MB 00:00:06
(4/18): epel/x86_64/group_gz | 266 kB 00:00:01
(5/18): epel/x86_64/updateinfo | 899 kB 00:00:02
(6/18): epel/x86_64/prestodelta | 7.1 kB 00:00:00
(7/18): base/7/x86_64/other_db | 2.5 MB 00:00:05
(8/18): epel/x86_64/primary_db | 6.3 MB 00:00:04
(9/18): extras/7/x86_64/filelists_db | 636 kB 00:00:00
(10/18): extras/7/x86_64/primary_db | 166 kB 00:00:00
(11/18): extras/7/x86_64/other_db | 108 kB 00:00:00
(12/18): extras/7/x86_64/prestodelta | 102 kB 00:00:01
(13/18): epel/x86_64/other_db | 3.0 MB 00:00:01
(14/18): epel/x86_64/filelists_db | 10 MB 00:00:09
(15/18): updates/7/x86_64/filelists_db | 3.5 MB 00:00:02
(16/18): updates/7/x86_64/prestodelta | 771 kB 00:00:02
(17/18): updates/7/x86_64/other_db | 621 kB 00:00:00
(18/18): updates/7/x86_64/primary_db | 6.0 MB 00:00:03
Determining fastest mirrors

7.查看系统可用的yum源和所有的yum源

[root@bogon yum.repos.d]# yum repolist enabled
Loaded plugins: fastestmirror, langpacks
Repository base is listed more than once in the configuration
Repository updates is listed more than once in the configuration
Repository extras is listed more than once in the configuration
Repository centosplus is listed more than once in the configuration
Repository epel is listed more than once in the configuration
Repository epel-debuginfo is listed more than once in the configuration
Repository epel-source is listed more than once in the configuration
Loading mirror speeds from cached hostfile

  • epel: mirrors.aliyun.com
    repo id repo name status
    base/7/x86_64 CentOS-7 - Base - 163.com 9,591
    epel/x86_64 Extra Packages for Enterprise Linux 7 - x86_64 12,382
    extras/7/x86_64 CentOS-7 - Extras - 163.com 390
    updates/7/x86_64 CentOS-7 - Updates - 163.com 1,941
    repolist: 24,304

[root@bogon yum.repos.d]# yum repolist all
Loaded plugins: fastestmirror, langpacks
Repository base is listed more than once in the configuration
Repository updates is listed more than once in the configuration
Repository extras is listed more than once in the configuration
Repository centosplus is listed more than once in the configuration
Repository epel is listed more than once in the configuration
Repository epel-debuginfo is listed more than once in the configuration
Repository epel-source is listed more than once in the configuration
Loading mirror speeds from cached hostfile

  • epel: mirrors.aliyun.com
    repo id repo name status
    base/7/x86_64 CentOS-7 - Base - 163.com enabled: 9,591
    centosplus/7/x86_64 CentOS-7 - Plus - 163.com disabled
    contrib/7/x86_64 CentOS-7 - Contrib - mirrors.aliyun.com disabled
    epel/x86_64 Extra Packages for Enterprise Linux 7 - x86_64 enabled: 12,382
    epel-debuginfo/x86_64 Extra Packages for Enterprise Linux 7 - x86_64 - Debug disabled
    epel-source Extra Packages for Enterprise Linux 7 - x86_64 - Source disabled
    epel-testing/x86_64 Extra Packages for Enterprise Linux 7 - Testing - x86_64 disabled
    epel-testing-debuginfo/x86_64 Extra Packages for Enterprise Linux 7 - Testing - x86_64 - Debug disabled
    epel-testing-source/x86_64 Extra Packages for Enterprise Linux 7 - Testing - x86_64 - Source disabled
    extras/7/x86_64 CentOS-7 - Extras - 163.com enabled: 390
    updates/7/x86_64 CentOS-7 - Updates - 163.com enabled: 1,941
    repolist: 24,304


转发:https://www.cnblogs.com/renpingsheng/p/7845096.html

<think>好的,我需要处理用户关于数学逻辑的问题,特别是汉诺塔、替换函数和奥数中的排列组合。首先,我需要明确用户的具体需求,可能他们想了解这些概念的基础知识、应用场景或者解题技巧。 首先,汉诺塔是一个经典递归问题,应该从问题描述、递归解法、时间复杂度和实际应用等方面来介绍。要确保解释清晰,步骤详细,可能还需要举例说明。例如,三个盘子的移动步骤,以及如何推广到n个盘子。 接下来是替换函数,这个术语在数学中有不同的含义,可能用户指的是函数替换或者变量替换。需要确认常见的替换函数类型,比如代数替换、三角替换或者在递归中的替换应用。可能需要解释替换函数在解决方程、积分或递归关系中的作用,并举出具体例子,如使用替换法求解递推关系式。 然后是奥数中的排列组合,这部分需要涵盖排列组合的基本定义、计算公式,以及常见题型,比如排列数、组合数的计算,排列组合在实际问题中的应用(如分组问题、路径问题)。同时,可能需要提到奥数中常见的难题类型,例如包含限制条件的排列组合,或者需要使用容斥原理的情况。 用户之前询问过C++的十进制问题,这次转向数学逻辑,可能他们在学习编程算法时遇到这些数学概念,需要理解其理论基础。因此,回答需要兼顾数学原理和实际应用,特别是编程相关的部分,比如递归在汉诺塔问题中的实现,或者排列组合在算法设计中的应用。 需要检查是否有混淆的概念,例如替换函数是否指代特定的数学概念,或者用户可能有其他意图。由于用户提到的三个主题跨度较大,需要分别处理每个部分,同时指出它们之间的联系,比如汉诺塔问题中的递归排列组合中的递推关系。 另外,要确保语言简洁明了,结构清晰,分点说明,方便用户逐步理解。可能需要使用示例和公式来增强解释,比如排列组合的公式$P(n,k)$和$C(n,k)$,以及汉诺塔的移动次数公式$2^n - 1$。同时,注意使用正确的LaTeX格式,行内公式用$...$,独立公式用$$...$$。 最后,总结部分需要强调这些数学逻辑概念在编程和算法中的重要性,帮助用户建立理论实践的联系。可能需要提醒用户在实际应用中注意的常见错误,例如递归的终止条件或排列组合中的重复计数问题。</think>以下是关于数学逻辑中汉诺塔、替换函数、奥数排列组合的详细解析: --- ### 一、汉诺塔问题(Tower of Hanoi) #### 1. **问题定义** - **目标**:将$n$个圆盘从A柱移动到C柱,每次只能移动一个盘,且大盘不能压在小盘上 - **核心逻辑**:递归思想分治策略 #### 2. **递归解法** ```python def hanoi(n, source, target, auxiliary): if n == 1: print(f"从 {source} 移动盘1到 {target}") else: hanoi(n-1, source, auxiliary, target) # 前n-1盘移到辅助柱 print(f"从 {source} 移动盘{n}到 {target}") hanoi(n-1, auxiliary, target, source) # 辅助柱上的盘移到目标 ``` **时间复杂度**:$O(2^n)$(移动次数为$2^n -1$) #### 3. **数学规律** - 最少移动次数公式:$T(n) = 2T(n-1) +1 \Rightarrow T(n)=2^n -1$ - 实际应用:理解递归栈、内存管理模型 --- ### 二、替换函数(Substitution Function) #### 1. **基本概念** - **代数替换**:用新变量代替复杂表达式,例如: $$ \int x\sqrt{x+1}dx \xrightarrow{u=x+1} \int (u-1)\sqrt{u}du $$ - **递归替换**:解决递推关系的核心方法(如求解$T(n)=2T(n/2)+n$) #### 2. **典型应用场景** - **微分方程**:变量代换简化方程形式 - **算法分析**:主定理的推导基础 - **组合优化**:状态替换降低问题维度 --- ### 三、奥数中的排列组合 #### 1. **核心公式** - **排列数**(考虑顺序): $$ P(n,k) = \frac{n!}{(n-k)!} $$ - **组合数**(不考虑顺序): $$ C(n,k) = \frac{n!}{k!(n-k)!} $$ #### 2. **奥数经典题型** | 类型 | 示例问题 | 解题关键 | |-------------------|-----------------------------------|------------------------------| | 限制排列 | 甲乙不能相邻的排队方式数 | 插空法或减法原理 | | 分组问题 | 10人分成3/3/4组的方案数 | 消除重复计数(除以组间阶乘) | | 路径计数 | 网格中不穿越对角线的路径数 | 卡特兰数应用 | #### 3. **高阶技巧** - **容斥原理**:处理多重限制条件 $$ |A \cup B| = |A| + |B| - |A \cap B| $$ - **生成函数**:将组合问题转化为多项式运算 - **递推关系**:建立状态转移方程(如斐波那契数列推广) --- ### 四、数学逻辑的编程映射 1. **汉诺塔递归实现**: - 函数调用栈模拟圆盘移动过程 - 理解递归树结构对算法优化至关重要 2. **排列组合的算法应用**: - **全排列生成**:回溯法(时间复杂度$O(n!)$) - **组合选择**:位运算技巧(如二进制枚举) --- ### 总结建议 1. **汉诺塔**:重点理解递归思维模式,可尝试非递归实现(栈模拟) 2. **替换函数**:掌握变量替换的灵活性,注意替换后的定义域变化 3. **排列组合**:熟练使用公式的同时,注重实际建模能力训练 这些数学逻辑工具在算法设计(如动态规划、回溯算法)、密码学(置换网络设计)、编译原理(语法分析)等领域均有重要应用。建议通过LeetCode等平台练习相关算法题巩固理解。
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