严蔚敏数据结构习题第七章

https://www.cnblogs.com/kangjianwei101/p/5244218.html
https://wenku.baidu.com/view/a31a5ba1284ac850ad0242d8.html

1

什么是连通图，（强）连通图详解：http://c.biancheng.net/view/3405.html
https://blog.csdn.net/weixin_43843835/article/details/88381828
课本p161

7

普利姆p173 顶点–找最小边的点–把顶点加入
克鲁斯卡尔p175
https://blog.csdn.net/a2392008643/article/details/81781766

9 拓扑序列

https://blog.csdn.net/weixin_46072771/article/details/106646721

10 关键路径

https://blog.csdn.net/weixin_46072771/article/details/106673063

11 DIJKSTRA

https://blog.csdn.net/weixin_46072771/article/details/106654848

13 FLOYD

https://blog.csdn.net/weixin_46072771/article/details/106654848

22 DFS，存储

试基于图的深度优先搜索策略写一算法，判别以邻接表方式存储的有向图中是否存在由顶点vi到顶点vj的路径(i≠j)。注意：算法中涉及的图的基本操作必须在此存储结构上实现。
https://www.codeleading.com/article/32714582577/
https://www.shangmayuan.com/a/4a32db9769b94135ad0f76ae.html
ZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2hhbjI5Xw==,size_16,color_FFFFFF,t_70)

#include <stdio.h>
#include <stdlib.h>
#define INFINITY INT_MAX //最大值，正无穷
#define MaxVertexNum 20 //最大顶点数
#define DateType int
int visted[MaxVertexNum];//辅助数组
//typedef enum{DG,DN,UDG,UDN}GrapKind; //{有向图，有向网，无向图，无向网}typedef struct ArcNode//边表
{int adjvex;//顶点ArcNode* nextarc;//下一条弧int info;//权重
}ArcNode;typedef struct VNode
{DateType vertex;ArcNode* firstarc;
}VNode,AdiList[MaxVertexNum];typedef struct
{AdiList vertices;int vexnum, arcnum;
}ALGraph;int existDFS(ALGraph G, int i, int j)
{int k;ArcNode* p;if (i == j)return 1;else{//记得提前初始化visted为0visted[i] = 1;for (p = G.vertices[i].firstarc; p; p = p->nextarc){k = p->adjvex;if (!visted[k] && existDFS(G, k, j))return 1;//为什么还要visited，是因为题目要求DFS}}return 0;
}

。。。

#include <stdio.h>
#include <stdlib.h>//图的邻接表存储
#define MAX_VERTEX 20
typedef struct ArcNode
{int adjvex;//该弧所指向的顶点的位置struct ArcNode* nextarc;int* info; //该弧所相关信息的指针
};
typedef struct VNode
{int data;//顶点信息ArcNode* firstarc;
}VNode, AdjList[MAX_VERTEX];
typedef struct
{AdjList vertices;int vexnum, arcnum;//图的当前顶点数和弧数int kind;//图的种类标志
}ALGraph;int visited[MAX_VERTEX];//指示顶点是否在当前道路上
int level = 1;//递归进行的层数
int exist_path_DFS(ALGraph G, int i, int j)
{int k;ArcNode* p;if (i == j)//相同返回真return 1;//不同就标记visited[i]else{visited[i] = 1;for (p = G.vertices[i].firstarc; p != NULL; p = p->nextarc, level--;){level++;k = p->adjvex;if (!visited[k] && exist_path_DFS(G, k, j))return 1;}}if (level == 1)return 0;
}

23 BFS 深度

同7.22题要求。试基于图的广度优先搜索策略写一算法。

#include <stdio.h>
#include <stdlib.h>
#define INFINITY INT_MAX //最大值，正无穷
#define MaxVertexNum 20 //最大顶点数
#define DateType int
int visited[MaxVertexNum];//辅助数组
//typedef enum{DG,DN,UDG,UDN}GrapKind; //{有向图，有向网，无向图，无向网}typedef struct ArcNode//边表
{int adjvex;//顶点ArcNode* nextarc;//下一条弧ArcNode* info;//该弧
}ArcNode;typedef struct VNode
{DateType vertex;ArcNode* firstarc;
}VNode,AdiList[MaxVertexNum];typedef struct
{AdiList vertices;int vexnum, arcnum;
}ALGraph;//队列结点的结构
typedef struct Qnode
{int data;struct Qnode* next;
}Qnode,*QuequePrt;//链表队列结构
typedef struct
{QuequePrt front;//队头指针QuequePrt rear;
}LinkQueue;//初始化队列
void InitQueue(LinkQueue& Q)
{Q.front = Q.rear = new Qnode;//生成新的结点作为头结点，初始化队头队尾指针Q.front->next = NULL;//头结点的指针域为空
}bool EnQueue(LinkQueue& Q, int e)
{Qnode* p = new Qnode;p->data = e;Q.rear->next = p;Q.rear = p;return 1;
}bool DeQueue(LinkQueue& Q, int & e)
{Qnode* p = new Qnode;//保存头结点指针，用于释放空间p = Q.front->next;//指向队头结点e = p->data;//获取队头结点的元素的值Q.front->next = p->next;//修改头指针if (Q.rear == p)//判断删除的元素是否为最后一个元素，避免空指针异常，将队尾指针重新指向队头指针Q.rear = Q.front;Q.rear->next = Q.front->next;//最后一个结点指向首元结点delete p;return 1;
}void DeleteQueue(LinkQueue& Q)
{while (Q.front){Q.rear = Q.front->next;delete Q.front;Q.front = Q.rear;}
}//广度遍历函数
int BFS(ALGraph G, int i,int j)
{LinkQueue Q;InitQueue(Q);visited[i] = 1;EnQueue(Q, i);while (Q.front != Q.rear){int u;DeQueue(Q, u);ArcNode* p = G.vertices[u].firstarc;//获取被访问顶点的边链表的首元结点的指针while (p){int w = p->adjvex;//获取v顶点的邻接顶点if (w == j)return 1;else if (!visited[w])//判断该顶点是否被访问过{visited[w] = 1;EnQueue(Q, w);}p = p->nextarc;//指向顶点的下一个邻接点}}return 0;
}//操作函数
void BFS_Traverse(ALGraph G) {//访问标志辅助数组初始化for (int i = 0; i < G.vexnum; i++){visited[i] = false;}int i,j;printf("请输入起点和终点：");scanf("%d %d", &i, &j);BFS(G, i, j);
}

…

//复制的Status DfsReachable(ALGraph g, int i, int j){ArcNode *p;Queue Q;int e,k;InitQueue(Q);EnQueue(Q,i);while(!QueueEmpty(Q)){DeQueue(Q,e);visited[e] = TRUE;//标记被访问过的顶点p = g.vertices[e].firstarc; for(; p != NULL; p = p -> nextarc){k = p -> adjvex;//当前弧所指向顶点的位置if(k == j) return OK;else if(!visited[k])//当前顶点未被访问过EnQueue(Q,k);}}return ERROR;}

27 邻接表

https://www.freesion.com/article/64991243006/
采用邻接表存储结构，编写一个判别无向图中任意给定的两个顶点之间是否存在一条长度为k的简单路径的算法（一条路径为简单路径指的是其顶点序列中不含有重现的顶点)。

#include <stdio.h>
#include <stdlib.h>
#define INFINITY INT_MAX //最大值，正无穷
#define MaxVertexNum 20 //最大顶点数
#define DateType int
int visited[MaxVertexNum];//辅助数组
//typedef enum{DG,DN,UDG,UDN}GrapKind; //{有向图，有向网，无向图，无向网}typedef struct ArcNode//边表
{int adjvex;//顶点ArcNode* nextarc;//下一条弧ArcNode* info;//该弧
}ArcNode;typedef struct VNode
{DateType vertex;ArcNode* firstarc;
}VNode,AdiList[MaxVertexNum];typedef struct
{AdiList vertices;int vexnum, arcnum;
}ALGraph;int exist_path_len(ALGraph G, int i, int j, int k)
//判断邻接表方式存储的有向图G的顶点i到j是否存在长度为k的简单路径
{ArcNode *p;int m;if (i == j && k == 0) return 1; //找到了一条路径,且长度符合要求 else if (k > 0){visited[i] = 1;for (p = G.vertices[i].firstarc; p != NULL; p = p->nextarc){m = p->adjvex;if (!visited[m])if (exist_path_len(G, m, j, k - 1)) return 1; //剩余路径长度减一 }//for visited[i] = 0; //本题允许曾经被访问过的结点出现在另一条路径中 //这里需要把已经访问的点重新置为0，因为如果当前不存在长度为k//到达j点，那么这个点还是可以使用的，因为有可能从其他点出发//可以到达j点并且长度为k }//else return 0; //没找到
}//exist_path_lenvoid judge(ALGraph G)
{int i, j, k;//访问标志辅助数组初始化for (int i = 0; i < G.vexnum; i++){visited[i] = false;}printf("输入起点、终点和长度: ");scanf("%d %d %d", &i, &j, &k);int m=exist_path_len(G, i, j, k);if (m)printf("找到路径！");elseprintf("没有找到路径！");
}

34 拓扑

邻接矩阵：https://www.nowcoder.com/questionTerminal/c01b85c5a67a4a408bad2e95a40d3e67
邻接表：https://www.cnblogs.com/kangjianwei101/p/5296563.html
栈：https://www.cnblogs.com/kangjianwei101/p/5225684.html
试编写一个算法，给有向无环图G中每个顶点赋以一个整数序号，并满足以下条件：若从顶点i至顶点j有一条弧，则应使i<j。

#include <stdio.h>
#include <stdlib.h>
#define INFINITY INT_MAX //最大值，正无穷
#define MaxVertexNum 20 //最大顶点数
#define STACK_SIZE 20 //存储空间初始分配量
typedef int DateType;
typedef int SElemType;
int visited[MaxVertexNum];//辅助数组
//typedef enum{DG,DN,UDG,UDN}GrapKind; //{有向图，有向网，无向图，无向网}typedef struct ArcNode//边表
{int adjvex;//顶点ArcNode* nextarc;//下一条弧int info;//该弧的权重
}ArcNode;typedef struct VNode
{DateType vertex;ArcNode* firstarc;
}VNode,AdiList[MaxVertexNum];typedef struct
{AdiList vertices;int vexnum, arcnum;
}ALGraph;//栈的顺序存储表示
typedef struct
{SElemType* base;//在栈构造之前和销毁之后，base的值为NULLSElemType* top;//栈顶指针int stacksize;//当前已分配的存储空间，以元素为单位
}SqStack;void InitStack_Sq(SqStack& s)
{s.base = (SElemType*)malloc( STACK_SIZE* sizeof(SElemType));}void Push_Sq(SqStack& s, SElemType e)
{}void Pop_Sq(SqStack& s, SElemType& e)
{}int StackEmpty_Sq(SqStack& S)
{}void FindInDegree(ALGraph G, int indegree[])
//写数组，传的是首地址，所以也不用写[]
{int i, m;ArcNode* p;for (i = 1; i < G.vexnum; i++)indegree[i] = 0;for (i = 0; i < G.vexnum; i++){p = G.vertices[i].firstarc;m = G.vertices[i].vertex;while(p){indegree[m]++;p = p->nextarc;}}
}int T_34(ALGraph G, int T[])//数组Topo存储拓扑序列
{int n = G.vexnum;SqStack S;ArcNode* p;int i, k, count, indegree[MaxVertexNum];FindInDegree(G, indegree);InitStack_Sq(S);for (i = 0; i < G.vexnum; i++){if (!indegree[i])Push_Sq(S, i);}count = 0;while (!StackEmpty_Sq(S)){Pop_Sq(S, i);T[count] = i;i++;for (p = G.vertices[i].firstarc; p; p = p->nextarc){k = p->adjvex;if (!(--indegree[k]))//对i号顶点的每个邻接点的入度减一Push_Sq(S, k);}}if (count < G.vexnum)return 0;elsereturn 1;
}

42 邻接表 Dijkatra

https://blog.csdn.net/gdyhvy/article/details/107807897
以邻接表作存储结构实现求从源点到其余各顶点的最短路径的Dijkstra算法。

#include <stdio.h>
#include <stdlib.h>
#define INFINITY INT_MAX //最大值，正无穷
#define MaxVertexNum 20 //最大顶点数
#define DateType int
int visited[MaxVertexNum];//辅助数组
//typedef enum{DG,DN,UDG,UDN}GrapKind; //{有向图，有向网，无向图，无向网}typedef struct ArcNode//边表
{int adjvex;//顶点ArcNode* nextarc;//下一条弧int info;//该弧的权重
}ArcNode;typedef struct VNode
{DateType vertex;ArcNode* firstarc;
}VNode,AdiList[MaxVertexNum];typedef struct
{AdiList vertices;int vexnum, arcnum;
}ALGraph;int findMinDist(int dist[], int s[], int n)
{int min, k=0;for (int i = 0; i < n; i++){if (s[i] == 0){if (k == 0)min = dist[i];else{min = (min > dist[i]) ? dist[i] : min;}k++;}}return k;
}void ShortestPath(ALGraph G, int v0)
{int n = G.vexnum;//顶点个数int dist[MaxVertexNum], path[MaxVertexNum], s[MaxVertexNum];//初始化上面数组for (int i = 0; i < n; i++){s[i] = 0;dist[i] = INFINITY;path[i] = -1;}s[v0] = 1;//顶点放入集合S， 1代表在集合中，0代表不在集合中ArcNode* p;for (p = G.vertices[v0].firstarc; p; p = p->nextarc){int v = p->adjvex;//顶点int w = p->info;//权值path[v] = v0;dist[v] = w;}int num = 1;int min, m, k;while (num <= n)//当顶点数num小于图的顶点数{min = findMinDist(dist, s, n);//在dist中查找s[i]为0的最小值s[min] = 1;//将新生成的终点加入集合S//修改dist和pathfor (p = G.vertices[min].firstarc; p; p = p->nextarc){int v = p->adjvex;//顶点int w = p->info;//权值int sum = dist[v] + p->info;if ((s[v] == 0) && (dist[v] > sum)){dist[v] = sum;//用已经找到的最短路径修改对应的distpath[v] = min;//用已经找到的最短路径修改对应的path}}num++;}
}