From 038ac66f21ec7638cf32bc959fcc5715dd86ead1 Mon Sep 17 00:00:00 2001 From: Alice-and-Bob Date: Thu, 6 Aug 2020 22:18:36 +0800 Subject: [PATCH] =?UTF-8?q?=E4=BF=AE=E6=94=B9=E4=BA=86=E9=A1=B9=E7=9B=AE?= =?UTF-8?q?=E7=BB=93=E6=9E=84?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- README.md | 4 +- .../批注 2020-03-25 224043.png | Bin .../{第一章 绪论 => 第1章 绪论}/第一章 绪论.xmind | Bin .../{第二章 线性表 => 第2章 线性表}/单链表.cpp | 0 .../批注 2020-03-26 232754.png | Bin .../批注 2020-03-27 122454.png | Bin .../批注 2020-03-27 124407.png | Bin .../批注 2020-03-27 124636.png | Bin .../第二章 线性表.xmind | Bin .../{第二章 线性表 => 第2章 线性表}/链表习题.cpp | 0 .../{第二章 线性表 => 第2章 线性表}/顺序表.cpp | 0 .../顺序表习题.cpp | 0 .../ayUzRCUwQSU.png | Bin .../批注 2020-07-09 173827.png | Bin .../批注 2020-07-09 174359.png | Bin .../批注 2020-07-09 174925.png | Bin .../{第三章 栈和队列 => 第3章 栈和队列}/栈.md | 0 .../第三章 栈与队列.xmind | Bin .../{第三章 栈和队列 => 第3章 栈和队列}/队列.md | 0 .../v2-67dd66b86323d3d08f976589cf712a1a_1440w.png | Bin 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第6章 应用层}/第六章 应用层.xmind (100%) diff --git a/README.md b/README.md index b4131e0..033d967 100644 --- a/README.md +++ b/README.md @@ -30,8 +30,8 @@ + [x] [第二章 线性表](https://github.com/Alice-and-Bob/CS408/blob/master/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84/%E7%AC%AC%E4%BA%8C%E7%AB%A0%20%E7%BA%BF%E6%80%A7%E8%A1%A8/%E7%AC%AC%E4%BA%8C%E7%AB%A0%20%E7%BA%BF%E6%80%A7%E8%A1%A8.xmind) + [x] [第三章 栈和队列](https://github.com/Alice-and-Bob/CS408/blob/master/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84/%E7%AC%AC%E4%B8%89%E7%AB%A0%20%E6%A0%88%E5%92%8C%E9%98%9F%E5%88%97/%E7%AC%AC%E4%B8%89%E7%AB%A0%20%E6%A0%88%E4%B8%8E%E9%98%9F%E5%88%97.xmind) + [x] [第四章 串](https://github.com/Alice-and-Bob/CS408/blob/master/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84/%E7%AC%AC%E5%9B%9B%E7%AB%A0%20%E4%B8%B2/%E7%AC%AC%E5%9B%9B%E7%AB%A0%20%E4%B8%B2.xmind) -+ [x] 第五章 树与二叉树 -+ [ ] 第六章 图 ++ [x] [第五章 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+![](https://images2018.cnblogs.com/blog/1309518/201808/1309518-20180817112621902-186744050.png) +![](https://images2018.cnblogs.com/blog/1309518/201808/1309518-20180817112643333-1291619542.png) +![](https://img2018.cnblogs.com/i-beta/1309518/202002/1309518-20200226135124598-1168867260.png) + +初始状态:V是所有顶点的集合,即V={A,B,C,D,E,F,G};U和T都是空! + +- 第1步:将顶点A加入到U中。 + 此时,U={A}。 + +- 第2步:将顶点B加入到U中。 + 上一步操作之后,U={A}, V-U={B,C,D,E,F,G}; + 因此,边(A,B)的权值最小。将顶点B添加到U中;此时,U={A,B}。 + +- 第3步:将顶点F加入到U中。 + 上一步操作之后,U={A,B}, V-U={C,D,E,F,G}; + 因此,边(B,F)的权值最小。将顶点F添加到U中;此时,U={A,B,F}。 + +- 第4步:将顶点E加入到U中。 + 上一步操作之后,U={A,B,F}, V-U={C,D,E,G}; + 因此,边(F,E)的权值最小。将顶点E添加到U中;此时,U={A,B,F,E}。 + +- 第5步:将顶点D加入到U中。 + 上一步操作之后,U={A,B,F,E}, V-U={C,D,G}; + 因此,边(E,D)的权值最小。将顶点D添加到U中;此时,U={A,B,F,E,D}。 + +- 第6步:将顶点C加入到U中。 + 上一步操作之后,U={A,B,F,E,D}, V-U={C,G}; + 因此,边(D,C)的权值最小。将顶点C添加到U中;此时,U={A,B,F,E,D,C}。 + +- 第7步:将顶点G加入到U中。 + 上一步操作之后,U={A,B,F,E,D,C}, V-U={G}; + 因此,边(E,G)的权值最小。将顶点G添加到U中;此时,U=V。 + +此时,最小生成树构造完成!它包括的顶点依次是:A B F E D C G。 +> 注意每一次从U和V集合中选一个权值最小的边,对应的顶点加入U中,直到V中没有元素 + +## 克鲁斯卡尔算法 +算法思想: +1. 将所有边的边权从小到大依次排列,并且均标为未选; +2. 选择最小的未选边; +3. 如果该边与前面所选的边无法构成回路,则选中该边,并标为已选;如果该边与前面所选的边构成了回路,则不选该边,并标为已选; +4. 重复(2)(3),直到所有点之间都有边相连; +> 过程容易理解,只需要注意选边的时候不能成环,如果有成环则跳过该边; + +# 最短路径 +## 迪杰斯特拉算法 +> 求解**带权有向图G中**某一顶点到其他各个顶点的最短路径 + +- 概述: +![](dj1.png) + +- 实例: +![](dj2.png) +![](dj3.png) + +> 结合实例容易理解算法过程,需要注意的是初始化和算法每一次前进一步都需要更新当前到未确定的各个顶点的最短距离,这是因为可能存在拐弯之后的权值相加仍小于原值的情况。 +> +> 注意算法只能求解**权值为正数**的带权有向图 + +## 弗洛伊德算法 +- 算法思想: +![](fl1.png) +- 实例: +![](fl2.png) +![](fl3.png) + +# 拓扑排序 +- AOV网:有向无环图,边的指向代表了事件发生的前后顺序 +- 拓扑排序:将AOV网以一个一维序列形式表达,这个序列满足 + - 每个顶点出现且仅出现一次 + - 若A排在B前面,则在AOV网中不存在B到A的路径,即A必须先于B发生 +- 算法: +![](a.png) + +# 关键路径 +- AOE网:在AOV网的基础上,添加了边权值,代表了完成活动的开销(需要的时间等) \ No newline at end of file diff --git a/数据结构/第六章 图/图的遍历.md b/数据结构/第6章 图/图的遍历.md similarity index 100% rename from 数据结构/第六章 图/图的遍历.md rename to 数据结构/第6章 图/图的遍历.md diff --git a/数据结构/第六章 图/批注 2020-07-23 163518.png b/数据结构/第6章 图/批注 2020-07-23 163518.png similarity 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