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z=84BGEF$=PSdl|8cI3W>`I4T~XoXZo`JbY(t8MM~slL@X%2W?*_Hpt$O3}H}c@p2b z9{ZyHZYfg#u{3-z#Vr=Iq3R2Stk~bQ`uu$CfAUwe5TpG}?{!t*%)&o#b))LCPtb4^ zrrE^uHryJ-=F{OlF0NjnLs-nclC6^&E*0r#K%4f8e++l`8}`h)rOe)$g1488zSxpW z6uNU^!LaV>jAv$MpCzRt@A*yKL~UT{az;1>ejl3=DuzB z*@ndwkM(dd%%)#*`G*USaFD#>ypHO(WkBw5mpcPSa-847>~VlVMRQQTe)4szk+Dyi z2FH6ogm8}xvil8Qk@EfDm;92qy-k8<5l$xb@6$(OZ^(OmUrt9Mu}jOG!RzF^&-Jax>QtxSQmb>~0ZH&{cPq(WMBwuIBewiu>pO*4)L z;FQ!_7yp+S!)1OM7pey_wrR$t%`-2$*tWd`rb&`oT=waT3Er*PtL$efDoj%~zAJ3J z{D6mFGpi9$9m1`>JPE9r;cw~%irMT}YXcNLCeLJyRk1Wys0l2X24Q?Ed!;8ni?MHY z3@a8UXJ@rfMkca>ymo#;i=GIlo=-y!ec%Y{2W}mz zpS^f^%^?-agskT>ic@xAF-*$wM6D6hFl4N7*42#LL=6gap;RePY0}_xdotZ0uZK0~ z$nDD*oqcIw*R1Yrf~Ic{wG|J@B~Yl-W 不会,以下为解答 + +1. 求最小合并次数类似于求最小带权路径长度,则联想到哈夫曼树。那么每次选择表集合中长度最小的两个表进行合并 +第一次 合并A、B +第二次 合并AB和C +第三次 合并D、E +第四次 合并ABC和DE +第五次 合并ABCDE和F + +**合并两个有序表的最坏情况需要比较m+n-1次** +则 +按合并顺序可以算出每次需要比较的次数 + +2. 合并表长不同的顺序表时,最坏情况下的比较次数依赖于合并的次序,则每次选择表长最短的两个表合并,可以获得最坏情况下的最小比较次数 + +> 原以为要考具体的元素级别的合并算法,结果是考表与表的合并…… +> 能获得启发就是:**合并两个有序表的最坏情况需要比较m+n-1次** + +# 习题5.4 +## T4 2016 +1. `(k-1)*n+1` +2. $$ + \begin{aligned} + n_{max} &= \frac{1-k^h}{1-k} \\ + n_{min} &= k+\frac{1-k^{h-1}}{1-k} + \end{aligned} + $$ + +# 习题5.3 +## T19 2014 +1. 采用深度优先的递归遍历搜索,记录递归层数,当访问到叶结点时把当前层数乘以叶结点权值,最后全部叶结点的带权路径长度值相加 +2. ```cpp + typedef struct BiTreeNode{ + struct BiTreeNode *left; + int weight; + struct BiTreeNode *right; + }BiTreeNode, *BiTree; + ``` +3. ```cpp + i=1; //递归层数 + WPL=0; //带权路径长度 + void GetWPL(BiTree *p){ + if(p->left==NULL && p->right==NULL){ //叶结点 + i--; + WPL+=i*p->weight; + return ; + } + else{ + if(p->left!=NULL&&p->right==NULL){ + i++; + GetWPL(p->left); + } + else(p->left==NULL&&p->right!=NULL){ + i++; + GetWPL(p->right); + } + } + } + ``` +## T20 2017 +1. 中序遍历二叉树,在递归访问某结点的左孩子之前输出一个左括号,在递归访问右孩子之后输出一个右括号 +2. ```cpp + void func(BTree p){ + if(p!=NULL){ + cout<<'('; + func(p->left); + visit(p); + func(p->right); + cout<<')'; + } + } + ``` diff --git a/数据结构/第五章 树与二叉树/第五章 树与二叉树.xmind b/数据结构/第五章 树与二叉树/第五章 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MaxVertexNum 100 +typedef char VertexType; +typedef int EdgeType; +typedef struct{ + VertexType Vex[MaxVertexNum]; + EdgeType Edge[MaxVertexNum][MaxVertexNum]; + int vexnum, arcnum; //图的当前顶点数和弧数 +}MGraph; +``` + +![](1.png) + +## 邻接表法 +邻接表是指对每一个顶点建立一个单链表,第i个单链表中的结点代表了依附于顶点i的边(无向图),或是代表了以i为弧尾的边(有向图) + +```cpp +#define MaxVertexNum 100 +typedef struct ArcNode{ //边表结点 + int adjvex; //该弧指向的顶点的位置 + struct ArcNode *next; + //InfoType info; 边权值 +}ArcNode; +typedef struct VNode{ //顶点表结点 + VertexType data; + ArcNode *first; +}VNode, AdjList[MaxVertexNum]; +typedef struct{ + AdjList vertices; //邻接表 + int vexnum,arcnum; //图的顶点数和弧数 +}ALGraph; +``` + +![](2.1.png) +![](2.2.png) + +## 十字链表法 +> 用于有向图 + +弧结点有5个域: +* tailvex, headvex指向弧头结点和弧尾结点 +* hlink指向弧头相同的下一条弧 +* tlink指向弧尾相同的下一条弧 +* info包括了弧的相关信息 + +顶点结点有3个域: +* data存放顶点有关信息 +* firstin和firstout指向以该节点为弧头或弧尾的第一个弧结点 + +![](3.png) + +## 邻接多重表 +> 用于无向图 + +与十字链表类似,每个边和顶点都有顶点 + +边结点: +* Mark标记是否被搜索过 +* ivex指向该边依附的i结点位置 +* jvex指向该边依附的j结点位置 +* ilink指向下一条依附于i结点的边 +* jlink指向下一条依附于j结点的边 +* info表示边信息 + +顶点结点: +* data代表顶点信息 +* firstedge指向第一条依附于该顶点的边 + +![](4.png) + +# 图的基本操作 +- Adjacent(G, x, y) + - 判断图G是否存在边(x,y)或 +- Neighbors(G, x) + - 列出G中与结点x邻接的边 +- InsertVertex(G, x) + - 在G中插入顶点x +- DeleteVertex(G, x) + - 在G中删除顶点x +- AddEdge(G, x, y) + - 若G中不存在边(x,y)或,则添加该边 +- RemoveEdge(G, x, y) + - 若G中存在边(x,y)或,则删除该边 +- FirstNeighbor(G, x) + - 求G中顶点x的第一个邻接点,返回顶点号;出现错误则返回-1 +- NextNeighbor(G, x, y) + - 设y为x的一个邻接点,返回除y的下一个邻接点号;其他情况返回-1 +- Get_edge_value(G, x, y) + - 返回边(x,y)或的权值 +- Set_edge_value(G, x, y, v) + - 设置边(x,y)或的权值为v \ 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/第六章 图/图的遍历.md new file mode 100644 index 0000000..9273673 --- /dev/null +++ b/数据结构/第六章 图/图的遍历.md @@ -0,0 +1,84 @@ +# 广度优先搜索 +1. **基本思想**:从一个选定的顶点v出发,依次访问v的邻接结点,再从这些结点出发,去访问与他们邻接且没有被访问过的结点,重复这个过程直到图中所有的结点都被访问过 + +2. 伪代码: +```cpp +bool visited[MAX_VERTEX_NUM]; //标记数组 +void BFSTraverse(Graph G){ + for(i=0;i=0; w=NextNeighbor(G,v,w)){ + //检测v的所有邻接点 + if(!visited[w]){ //对每一个v的未曾访问过的邻接点w + visit(w); //访问 + visited[w]=TRUE;//标记 + EnQueue(Q,w); //入队 + } + } + } +} +``` +3. 性质分析: + - 复杂度分析: + - **时间复杂度** : $O(|V|^2)$ + - **空间复杂度** : $O(|V|)$ + - BFS是树的层次遍历的扩充 + + + +# 深度优先搜索 +1. **基本思想**:从一个顶点v出发,访问其邻接且未访问过的任意一个w1,继续访问w1的邻接点中的任意一个w2,如此下去直到无法继续,回退到最近访问过的结点,若它还有未访问过的邻接结点,则对其使用深搜。 + +2. 伪代码: +```cpp +bool visited[MAX_VERTEX_NUM]; //新建标记数组 +void DFSTraverse(Graph G){ + for(v=0;v=0;w=NextNeighbor(G,v,w)){ + //对于v的每一个邻接结点w + if(!visited[w]){ + DFS(G,w); + } + } +} +``` + +3. 性质分析: + - 复杂度分析: + - **时间复杂度** : + - 邻接矩阵表达: $O(|V|^2)$ + - 邻接表表达:$O(|V|+|E|)$ + - **空间复杂度** : $O(|V|)$ + - DFS是树的先序遍历的扩展 + +> 图、树、森林的等效遍历方式 +> | 树 | 森林 | 二叉树 | 图 | +> | :-: | :-: | :-: | :-: | +> | 先根遍历 | 先序遍历 | 先序遍历 | DFS | +> | 后根遍历 | 中序遍历 | 中序遍历 | x | +> | 层次遍历 | x | 层次遍历 | BFS | \ No newline at end of file diff --git a/数据结构/第六章 图/批注 2020-07-23 163518.png b/数据结构/第六章 图/批注 2020-07-23 163518.png new file mode 100644 index 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