From 3cd9f380071d6b38b35875fe9ffe4721b8cfe5b5 Mon Sep 17 00:00:00 2001 From: Alice-and-Bob Date: Tue, 14 Jul 2020 18:04:43 +0800 Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0=E6=95=B0=E6=8D=AE=E7=BB=93?= =?UTF-8?q?=E6=9E=84=E7=AC=AC=E4=BA=94=E7=AB=A0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- README.md | 19 +-- 数据结构/第五章 树与二叉树/二叉排序树.md | 30 ++++ 数据结构/第五章 树与二叉树/二叉树的遍历.md | 134 ++++++++++++++++++ .../第五章 树与二叉树/批注 2020-07-11 154229.png | Bin 0 -> 51721 bytes .../第五章 树与二叉树/批注 2020-07-11 171429.png | Bin 0 -> 128391 bytes .../第五章 树与二叉树/批注 2020-07-14 170228.png | Bin 0 -> 3289 bytes .../第五章 树与二叉树/批注 2020-07-14 173314.png | Bin 0 -> 152358 bytes .../第五章 树与二叉树/批注 2020-07-14 173332.png | Bin 0 -> 180121 bytes .../第五章 树与二叉树/批注 2020-07-14 173346.png | Bin 0 -> 196532 bytes .../第五章 树与二叉树/批注 2020-07-14 173401.png | Bin 0 -> 219698 bytes .../第五章 树与二叉树/批注 2020-07-14 175139.png | Bin 0 -> 10622 bytes .../第五章 树与二叉树/第五章 树与二叉树.xmind | Bin 0 -> 1363080 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2020制作,请使用等于或高于此版本的XMind打开。** + 能填多少坑取决于作者决定考哪个学校;如果决定的学校不是考408,那我只会更新那个学校的科目的总结(┓( ´∀` )┏)咕咕咕 -+ 如果对你有帮助有启发,欢迎**点个star**资瓷一下作者;同时欢迎有**对内容更好想法/懂得xmind排版**的朋友提交issue帮助这个项目更好 ++ 如果对你有帮助有启发,欢迎**点个star**资瓷一下作者;同时欢迎有**对内容更好想法/懂得xmind排版**的朋友提交issue帮助这个项目更好 + +## NOTE: ++ 不适合在XMind里表达的内容,全部写在了同文件夹里的`*.md`文件或是`*.cpp`文件;一个文件夹里应该关注的仅有`*.xmind, *.md, *.cpp`文件,其余可以不用管 > 或许你也可以参考[这个项目](https://github.com/SSHeRun/CS-Xmind-Note) @@ -26,8 +29,8 @@ + [x] [第一章 绪论](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%80%E7%AB%A0%20%E7%BB%AA%E8%AE%BA/%E7%AC%AC%E4%B8%80%E7%AB%A0%20%E7%BB%AA%E8%AE%BA.xmind) + [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 -+ [ ] 第五章 树与二叉树 ++ [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 + [ ] 第七章 查找 + [ ] 第八章 排序 @@ -36,8 +39,8 @@ ## 计算机组成原理 -## 网络安全基础与应用 -+ [x] 第一章 概论 -+ [x] 第二章 密码学 -+ [x] 第三章 应用安全 +## 网络安全基础与应用 ++ [x] [第一章 概论](https://github.com/Alice-and-Bob/CS408/blob/master/%E7%BD%91%E7%BB%9C%E5%AE%89%E5%85%A8%E5%9F%BA%E7%A1%80%E4%B8%8E%E5%BA%94%E7%94%A8/1%E3%80%81%E6%A6%82%E8%AE%BA.xmind) ++ [x] [第二章 密码学](https://github.com/Alice-and-Bob/CS408/blob/master/%E7%BD%91%E7%BB%9C%E5%AE%89%E5%85%A8%E5%9F%BA%E7%A1%80%E4%B8%8E%E5%BA%94%E7%94%A8/2%E3%80%81%E5%AF%86%E7%A0%81%E5%AD%A6.xmind) ++ [x] [第三章 应用安全](https://github.com/Alice-and-Bob/CS408/blob/master/%E7%BD%91%E7%BB%9C%E5%AE%89%E5%85%A8%E5%9F%BA%E7%A1%80%E4%B8%8E%E5%BA%94%E7%94%A8/3%E3%80%81%E7%BD%91%E7%BB%9C%E5%AE%89%E5%85%A8%E5%BA%94%E7%94%A8.xmind) + [ ] 第四章 系统安全 \ No newline at end of file diff --git a/数据结构/第五章 树与二叉树/二叉排序树.md b/数据结构/第五章 树与二叉树/二叉排序树.md new file mode 100644 index 0000000..4bc98ef --- /dev/null +++ b/数据结构/第五章 树与二叉树/二叉排序树.md @@ -0,0 +1,30 @@ +# 二叉排序树的非递归查找算法 +```cpp +BSTNode *BST_Search(BinTree T, ElemType key){ + while(T!=NULL;&&key!=T->data){ + if(key < T->data) + T = T->lchild; + else + T = T->rchild; + } + return T; +} +``` + +# 二叉排序树的插入算法 +```cpp +int BST_Insert(BiTree &T, KeyType k){ + if(T==NULL){ + T=(BiTree)malloc(sizeof(BSTNode)); + T->key=k; + T->lchild=T->rchild=NULL; + return 1; + } + else if(k==T->key) + return 0; + else if(k < T->key) + return BST_Insert(T->lchild); + else + return BST_Insert(T->rchild); +} +``` diff --git a/数据结构/第五章 树与二叉树/二叉树的遍历.md b/数据结构/第五章 树与二叉树/二叉树的遍历.md new file mode 100644 index 0000000..4d26730 --- /dev/null +++ b/数据结构/第五章 树与二叉树/二叉树的遍历.md @@ -0,0 +1,134 @@ +# 二叉树的遍历 +> 遍历的顺序是指根结点的访问次序,先序指首先访问根结点,再访问左子树,访问右子树;其他顺序遍历以此类推 +## 先序遍历 +> 若二叉树为空,什么也不做,否则: +> 1、访问根结点 +> 2、先序遍历左子树 +> 3、先序遍历右子树 +```cpp +void PreOrder(BinTree T){ + if(T!=NULL){ + visit(T); + PreOrder(T->lchild); + PreOrder(T->rchild); + } +} +``` +## 中序遍历 +> 若二叉树为空,什么也不做,否则: +> 1、中序遍历左子树 +> 2、访问根结点 +> 3、中序遍历右子树 +```cpp +void InOrder(BinTree T){ + if(T!=NULL){ + InOrder(T->lchild); + visit(T); + InOrder(T->rchild); + } +} +``` +## 后序遍历 +> 若二叉树为空,什么也不做,否则: +> 1、后序遍历左子树 +> 2、后序遍历右子树 +> 3、访问根结点 +```cpp +void PostOrder(BinTree T){ + if(T!=NULL){ + PostOrder(T->lchild); + PostOrder(T->rchild); + visit(T); + } +} +``` +## 递归、非递归算法转换 +> 以上三种遍历算法采用递归,若采用非遍历算法,须使用栈 +### 中序遍历非递归算法 +> 分析遍历过程可以得出非递归算法:①从跟结点开始,一直访问结点的左孩子,并把结点入栈,当结点没有左孩子时,弹出栈顶结点访问;②若右孩子为空,则继续执行②,若不空,则对右子树执行① + +```cpp +void InOrder2(BinTree T){ + InitStack(S); + BiTree p=T; + while(p||!IsEmpty(S)){ + if(p){ + Push(S,p); + p=p->lchild; + } + else{ + Pop(S,p); + visit(p); + p=p->rchild; + } + } +} +``` + +### 先序遍历非递归算法 + +```cpp +void PreOrder2(BinTree T){ + InitStack(S); + BiTree p=T; + while(p||!IsEmpty(S)){ + if(p){ + visit(p); + Push(S,p); + p=p->lchild; + } + else{ + Pop(S,p); + p=p->rchild; + } + } +} +``` +### 后序遍历非递归算法 +> ①沿着根结点的左孩子,把结点依次入栈,直到左孩子为空;②读栈顶元素,当其右孩子非空且未被访问过时,则对右子树执行①,否则弹出栈顶元素并访问 + +```cpp +void PostOrder(BiTree T){ + InitStack(S); + p=T; //当前访问的结点 + r=NULL; //记录最近访问的结点 + while(p||!IsEmpty(S)){ + if(p){ + push(S,p); + p=p->lchild; + } + else{ + GetTop(S,p); + if(p->rchild && p->rchild!=r){ //右子树存在且最近未被访问过 + p=p->rchild; + push(S,p); + p=p->lchild; + } + else{ + pop(S,p); + visit(p->data); + r=p; + p=NULL; + } + } + } +} +``` + +## 层次遍历 +> 层次遍历即是广度优先遍历,使用队列完成层次遍历 +```cpp +void LevelOrder(BiTree T){ + InitQueue(Q); + BiTree p; + EnQueue(Q, T); + while(!IsEmpty(Q)){ + DeQueue(Q,p); + visit(p); + if(p->lchild!=NULL) + EnQueue(Q, p->lchild); + else(p->rchild!=NULL) + EnQueue(Q, p->rchild); + } +} +``` \ No 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+ struct ThreadNode *lchild, *rchild; //左右孩子指针 + int ltag,rtag; //左右线索标志 +}ThreadNode, *ThreadTree; +``` +规定:当结点没有左孩子,其lchild指向其前驱节点;当没有右孩子,其rchild指向其后继结点 +## 二叉树中序线索化 +```cpp +void InThread(ThreadTree &p, ThreadTree &pre){ + if(p!=NULL){ + InThread(p->lchild, pre); + if(p->lchild==NULL){ + p->lchild=pre; + p->ltag=1; + } + if(pre!=NULL&&pre->rchild==NULL){ + pre->rchild=p; + pre->rtag=1; + } + pre=p; + InThread(p->rchild, pre); + } +} + +void CreateInThread(ThreadTree T){ + ThreadTree pre=NULL; + if(T!=NULL){ //非空二叉树 + InThread(T, pre); //线索化二叉树 + pre->rchild=NULL; //处理遍历的最后一个结点 + pre->rtag=1; + } +} +``` +## 中序线索二叉树的遍历 +1. 中序线索二叉树下的第一个结点 +```cpp +ThreadNode *Firstnode(ThreadNode *p){ + while(p->ltag==0) + p=p->lchild; + return p; +} +``` +2. 中序线索二叉树下某结点p的后继 +```cpp +ThreadNode *Nextnode(ThreadNode *p){ + if(p->rtag==0) //右孩子存在 + return Firstnode(p->rchild) + else + return p->rchild; +} +``` +3. 不带头结点的中序线索二叉树的中序遍历的算法 +```cpp +void Inorder(ThreadNode *T){ + for(ThreadNode *p=Firstnode(T); p!=NULL; p=Nextnode(p)){ + visit(p); + } +} +```

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