太原理工数据结构实验报告 实验三 图

实验报告课程名称：数据结构B实验项目：图实验地点：实验楼110专业班级：计科1301班学号：********** 学生姓名：**指导教师：**2015年1 月1 日一、实验目的和要求熟悉图的存储结构，掌握有关算法的实现，了解图在计算机科学及其他工程技术中的应用。

二、实验内容和原理1.采用邻接表存储结构，编写一个求无向图的连通分量个数的算法。

2.试基于图的深度优先搜索策略编写一程序，判别以邻接表方式存储的有向图中是否存在有顶点V i到V j顶点的路径(i≠j)。

3.在上述例题中，如改用邻接表的方式存储图，试编一程序实现上述算法。

顶点表nodelist的每个元素包含四个字段：其中mark mark字段为false，每访问过一个顶点，则mark字段置为true。

info为顶点值，pre为访问路径上该顶点的前驱顶点的序号，out指向该顶点的出边表。

三、主要仪器设备1.设备: PC微机;2.实验环境: windows操作系统；VC++6.0,四、实验结果与分析（必填）（1）程序代码：//————————*********用邻接矩阵实现#include <stdio.h>#define OK 1#define ORROR 0#define max 10 // a function to build adjacency matrix of a graphtypedef int Status;void buildadjm(int adj[][max], int n){int i,j;for(i=0;i<n;i++)for(j=0;j<n;j++){printf("enter 1 if there is an edge from %d to %d, otherwise enter 0 \n",i,j);scanf("%d",&adj[i][j]);}}// a function to visit the nodes in a depth-first ordervoid dfs(int x,int visited[],int adj[][max],char adjc[], int n){int j;visited[x] = 1;printf("%c结点被访问\n",adjc[x]);for(j=0;j<n;j++)if(adj[x][j] ==1 && visited[j] ==0)dfs(j,visited,adj,adjc, n);}void buildadjm_1(int adj[][max], char adjc[], int n){int visited[max];int i;printf("\n请输入你要建立图的结点数(<= %d)\n",max);scanf("%d",&n);buildadjm(adj,n);for(i=0; i<n; i++)visited[i] =0;for(i=0; i<n; i++)if(visited[i] ==0)dfs(i,visited,adj,adjc, n);}Status JudgeNodei_jgraph(int x,int y,int visited[],int adj[][max],char adjc[],int n) {int i,j;visited[x]=1;//printf("%c结点被访问\n",adjc[x]);for(i=0;i<n;i++)if(adj[x][i] ==1 && visited[i] ==0)JudgeNodei_jgraph(i,y,visited,adj,adjc,n);if(visited[y] == 0)return ORROR;elsereturn OK;Status AccountConnectComponent_Undigraph(int visited[],int adjj[][max],char adjc[],int n) {int i,j=0;for(i=0; i<n; i++){//printf("i=%d",i);if(visited[i] ==0){j++;dfs(i,visited,adjj,adjc,n);//printf("j=%d\n",j);}}return j;}Status AccountConnectComponent_Undigraph_1(int adjj[][max],char adjc[],int n){int node;int visited[max];int i;for(i=0; i<n; i++)visited[i] =0;node = AccountConnectComponent_Undigraph(visited,adjj,adjc,n);printf("\n该图的联通分量为%d",node);return OK;}Status find_char_num(char adjc[],char a){int i;for(i=0;i<max;i++)if(a == adjc[i])return i;}Status JudgeNodei_jgraph_1(int adjj[][max],char adjc[],int n){char a,b;int x,y;int visited[max];int i;for(i=0; i<n; i++)visited[i] =0;printf("\n请输入你要判断的两个结点,用空格隔开");scanf("%c %c",&a,&b);x = find_char_num(adjc,a);y = find_char_num(adjc,b);if(JudgeNodei_jgraph(x,y,visited,adjj,adjc,n))printf("两点联通");elseprintf("两点不联通");return OK;}char adjc[10] = {'a','b','c','d','e','f','g','h','k','?'};int adjj[10][10] ={{0,0,1,1,1, 1,0,0,0,0}, // a{0,0,0,0,0, 0,1,0,0,0}, // b{1,0,0,0,0, 0,0,1,0,0}, // c{1,0,0,0,0, 0,0,1,0,0}, // d{1,0,0,0,0, 0,0,1,0,0}, // e{1,0,0,0,0, 0,0,1,0,0}, // f{0,1,0,0,0, 0,0,0,0,0}, // g{0,0,1,1,0, 1,0,0,1,0}, // h{0,0,0,0,1, 1,0,1,0,0}, // k{0,0,0,0,0, 0,0,0,0,0} // ?};Status menu_select(){int sn;for(;;){printf("\n请输入您要进行的功能选项");scanf("%d",&sn);getchar();if(sn<1||sn>4)printf("\n\t输入错误，请重新输入\n");elsebreak;}return sn;}void main(){int adj[max][max],n;n = 9;printf("1.现有图并判断现有图的联通分量;\n2.判断现有图中两个点是否联通;\n3.建立一个新图，遍历并打印;\n4.结束;\n");while(1){switch(menu_select()){case 1:AccountConnectComponent_Undigraph_1(adjj,adjc,n);printf("\n");break;case 2:JudgeNodei_jgraph_1(adjj,adjc,n);getchar;printf("\n");break;case 3:buildadjm_1(adj,adjc,n);getchar;printf("\n");break;case 4:printf("\nend\n");return;}}}//————————*********用邻接表实现#include<stdio.h>#include<malloc.h>#include<stdlib.h>#define MAX_VERTEX_NUM 20#define OK 1#define ERROR 0typedef int Status;typedef int VRType;typedef int InfoType;typedef char VertexType;/*------------------------图的邻接表存储表示-----------------*/typedef struct ArcNode //每个结点由三个域构成{int adjvex; //adjvex邻接点域该弧所指向的顶点的位置struct ArcNode *nextarc; //nextarc链域指向下一条弧的指针InfoType *info; //info数据域该孤相关信息的指针}ArcNode;typedef struct VNode //每个链表上附一个表头结点存储顶点名以及有关信息域{int mark; //标记该图是否被访问过VertexType data; //数据域顶点信息ArcNode *firstarc; //链域指向第一条依附该顶点的弧的指针}VNode,AdjList[MAX_VERTEX_NUM];typedef struct{AdjList vertices;int vexnum,arcnum; //图的当前顶点数int kind; //图的种类标志}ALGraph;///元素在图中的位置int LocateNode__ALGraph(ALGraph g,VertexType v){for(int i=0;i<g.vexnum;i++){if(g.vertices[i].data == v)return i;}return -1;}//当前有向图中是否存在边<i,j>Status Exist_Graph(ALGraph G,int i,int j){ArcNode *s;//printf("i=%d j=%d\n",i,j);s=G.vertices[i].firstarc;while(s && s->adjvex!=j)s=s->nextarc;if(s)return OK;elsereturn ERROR;}//图是否存在Status ExistG(ALGraph g){if(g.vexnum < 0){printf("图不存在,请先创建图\n");return 0;}return OK;}//创建一个图Status Create_ADG(ALGraph &g){int i,j,k,l;ArcNode *p;VertexType v1,v2;char c;printf("请输入有向图的顶点数:");scanf("%d",&g.vexnum);//printf("%d",g.vexnum);while(g.vexnum>MAX_VERTEX_NUM){printf("\n请输入有向图的顶点数：");scanf("%d",&g.vexnum);}i=g.vexnum*(g.vexnum-1);printf("请输入有向图的边数:");scanf("%d",&g.arcnum);while(g.arcnum > i){printf("\n请输入有向图的边数：");scanf("%d",&g.arcnum);}printf("请依次输入有向图的各个顶点(用回车分隔):");for(i=0;i<g.vexnum;i++) //输入顶点信息{//printf("&&&&&%d",g.vexnum);//printf("i=%d",i);scanf("%c",&c); scanf("%c",&c); ////什么情况为什么写两个才能通过——————原因：回车也是一个字符，所以出错l=LocateNode__ALGraph (g,c);if(l>=0){printf("输入的顶点重复，请重新输入\n");i--;continue;}g.vertices[i].data=c;g.vertices[i].firstarc=NULL;}for(k=0;k<g.arcnum;k++) //输入边的信息{printf("\n请输入第%d条弧的起点与终点(用逗号分隔)：",k+1);scanf("%c,%c",&v1,&v2);i=LocateNode__ALGraph(g,v1);j=LocateNode__ALGraph (g,v2);if( i<0 || j<0 || i==j || Exist_Graph(g,i,j) ){k--;continue;}p=(ArcNode*)malloc(sizeof(ArcNode)); //建立结点if(!p)return ERROR;p->adjvex=j;p->nextarc=g.vertices[i].firstarc; //顶点i的链表g.vertices[i].firstarc=p; //添加到最左边}printf("有向图的邻接表创建成功\n");return OK;}/*------------------------------输出图的信息-------------------*/void Print_Gra(ALGraph G){ArcNode *p;int i;printf("图中有%d个顶点，%d条弧：\n",G.vexnum,G.arcnum);for(i=0;i<G.vexnum;i++){p=G.vertices[i].firstarc;printf("%c\t",G.vertices[i].data);while(p){printf("<%c,%c>",G.vertices[i].data,G.vertices[p->adjvex].data);p=p->nextarc;}printf("\n");}}/*----------------------------判断联通分量————————*/Status Dfs(ALGraph G,int visited[],int i) //深度遍历{int j;visited[i] = 1;printf("%c结点被访问\n",G.vertices[i].data);for(j=0;j<G.vexnum;j++)if( (Exist_Graph(G, i, j) ==1 || Exist_Graph(G,j,i)) && visited[j] == 0) Dfs(G,visited,j);return 0;}Status AccountConnectComponent(ALGraph G){int i,j=0;int visited[MAX_VERTEX_NUM-1];for(i=0; i<G.vexnum; i++)visited[i] =0;for(i=0; i<G.vexnum; i++){//printf("i=%d",i);if(visited[i] ==0){j++;Dfs(G,visited,i);//("+++++++j=%d\n",j);}}printf("该图联通分量的个数为%d",j);return OK;}Status JudgeNodei_jgraph_1( ALGraph G,int i,int j,int visited[],int &ok) {int k,m;for(k=0;k<G.vexnum;k++){if((Exist_Graph(G,i,k) || Exist_Graph(G,k,i)) && i != k){//printf("%d被访问",i);visited[i]=1;if(visited[k] == 0 && k != j)JudgeNodei_jgraph_1(G,k,j,visited,ok);}if(Exist_Graph(G,k,j))ok=1;if(Exist_Graph(G,i,j))ok=1;}return OK;}Status find_Node_num(char a,ALGraph G){int i;for(i=0;1<G.vexnum;i++)if(G.vertices[i].data == a)return i;}Status JudgeNodei_jgraph (ALGraph G){int i,j;char a,b;int visited[MAX_VERTEX_NUM-1],ok=0;for(i=0; i<G.vexnum; i++)visited[i] =0;printf("\n请输入你要判断的两个结点，用，隔开：");scanf("%c,%c",&a,&b);i = find_Node_num(a,G)+1;j = find_Node_num(b,G)+1;//printf("i=%d,j=%d",i,j);JudgeNodei_jgraph_1(G,i,j,visited,ok);if(ok==0)printf("两个结点联通");elseprintf("两个结点不联通");return OK;}Status menu_select(){int sn;for(;;){printf("\n请输入您要进行的功能选项");scanf("%d",&sn);getchar();if(sn<1||sn>5)printf("\n\t输入错误，请重新输入\n");elsebreak;}return sn;}void main(){ALGraph g;printf("1.创建一个图;\n2.打印您创建的图;\n3.计算图的联通分量;\n4.判断两点是否联通;\n5.结束;\n");while(1){switch(menu_select()){case 1:printf("1*");Create_ADG(g);printf("\n");break;case 2:printf("2*");Print_Gra(g);printf("\n");break;case 3:printf("3*");AccountConnectComponent(g);getchar();printf("\n");break;case 4:printf("4*");JudgeNodei_jgraph (g);printf("\n");break;case 5:printf("\n5* end\n");return;}}}（2）运行结果邻接矩阵：邻接表：四、实验感想1、无向图和联通图在实际储存中是一样的2、图的两种存储方式中邻接矩阵和邻接表，邻接表不如邻接矩阵方便。