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1、一、实验目得与要求（1)掌握图得相关概念，包括图,有向图,无向图，完全图，子图,连通图,度,入度，出度,简单回路与环等定义.（2）重点掌握图得各种存储结构，包括邻接矩阵与邻接表等。(3）重点掌握图得基本运算，包括创建图,输出图,深度优先遍历,广度优先遍历等.（4）掌握图得其她运算,包括最小生成树,最短路径，拓扑排序与关键路径等算法。(5)灵活运用图这种数据结构解决一些综合应用问题。二、实验内容与方法（1）实验内容:、编写一个程序alo8-1、cpp，实现不带权图与带权图得邻接矩阵与邻接表得相互转换算法、输出邻接矩阵与邻接表得算法，并在此基础上设计一个程序exp8、cp实现如下功能:建立如图1所
2、示得有向图G得邻接矩阵,并输出;由有向图得邻接矩阵产生邻接表,并输出;再由得邻接表产生对应得邻接矩阵,并输出。1569758453015243图12、编写一个程序lgo82、cpp，实现图得遍历运算,并在此基础上设计一个程序xp82、cpp完成如下功能：输出图1所示得有向图从顶点0开始得深度优先遍历序列（递归算法）；输出图所示得有向图G从顶点0开始得深度优先遍历序列（非递归算法);输出图1所示得有向图G从顶点0开始得广度优先遍历序列。、设计一个程序exp83、cpp,采用邻接表存储图，并输出图8、1(a）中从指定顶点1出发得所有深度优先遍历序列。(2)实验方法:1、综合运用课本所学得知识，用不
3、同得算法实现在不同得程序功能.2、结合指导老师得指导，解决程序中得问题，正确解决实际中存在得异常情况，逐步改善功能。3、根据实验内容，编译程序。三、实验环境：Winows7,VisulC+6、0三、实验过程描述文件raph、h中定义了图得邻接矩阵表示类型与邻接表表示类型,该头文件在以下三个实验中都会使用到。其代码如下：#ifndef GRAPH_H_INCLUDED#define GRAPH_H_INCLUDEDtypedef int InfoType;#define MAXV 100 /最大顶点个数#define INF 32767 /INF表示无限大/以下定义邻接矩阵类型typedef s
4、truct int no; InfoType info;VertexType;typedef struct int edgesMAXVMAXV; int n,e; VertexType vexsMAXV;MGraph;/以下定义邻接表类型typedef struct ANode int adjvex; struct ANode* nextarc; InfoType info;ArcNode;typedef int Vertex;typedef struct VNode Vertex data; ArcNode* firstarc;VNode;typedef VNode AdjListMAXV;
5、typedef struct AdjList adjlist; int n,e;ALGraph;#endif / GRAPH_H_INCLUDED VertexType vexsMAXV;MGraph;/以下定义邻接表类型typedef struct ANode int adjvex; struct ANode* nextarc; InfoType info;ArcNode;typedef int Vertex;typedef struct VNode Vertex data; ArcNode* firstarc;VNode;typedef VNode AdjListMAXV;typedef
6、struct AdjList adjlist; int n,e;ALGraph;#endif / GRAPH_H_INCLUDED实验源程序。一、输入如下所示程序;/文件名:exp8-1、cpp#include #include #include graph、hextern void MatToList1(MGraph, ALGraph* &);extern void ListToMat1(ALGraph*, MGraph&);extern void DispMat1(MGraph);extern void DispAdj1(ALGraph*);int main() int i,j; MGra
7、ph g,g1; ALGraph *G; int AMAXV6 = 0,5,INF,7,INF,INF,INF,0,4,INF,INF,INF, 8,INF,0,INF,INF,9,INF,INF,5,0,INF,6, INF,INF,INF,5,0,INF,3,INF,INF,INF,1,0; g、n = 6; g、e = 10; for(i=0; ig、n; i+) for(j=0; jg、n; j+) g、edgesij = Aij; printf(有向图G得邻接矩阵:n); DispMat1(g); G = (ALGraph*)malloc(sizeof(ALGraph); print
8、f(图G得邻接矩阵转换成邻接表:n); MatToList1(g,G); DispAdj1(G); printf(图G得邻接表转换成邻接矩阵:n); ListToMat1(G,g1); DispMat1(g1); return 0;/文件名:algo8-1、cpp#include #include #include graph、h/不带权图得算法void MatToList(MGraph g, ALGraph *&G) int i,j; ArcNode *p; G = (ALGraph*)malloc(sizeof(ALGraph); for(i=0; i=0; j-) if(g、edgesi
9、j!=0) p = (ArcNode*)malloc(sizeof(ArcNode); p-adjvex = j; p-nextarc = G-adjlisti、firstarc; G-adjlisti、firstarc = p; G-n = g、n; G-e = g、e;void ListToMat(ALGraph *G,MGraph &g) int i,j; ArcNode *p; for(i=0; in; i+) for(j=0; jn; j+) g、edgesij = 0; for(i=0; in; i+) p = G-adjlisti、firstarc; while(p!=NULL)
10、 g、edgesip-adjvex = 1; p = p-nextarc; g、n = G-n; g、e = G-e;void DispMat(MGraph g) int i,j; for(i=0; ig、n; i+) for(j=0; jg、n; j+) printf(%3d,g、edgesij); printf(n); void DispAdj(ALGraph *G) int i; ArcNode *p; for(i=0; in; i+) p = G-adjlisti、firstarc; printf(%3d:,i); while(p!=NULL) printf(%3d,p-adjvex)
11、; p = p-nextarc; printf(n); /带权图得算法void MatToList1(MGraph g, ALGraph *&G) int i,j; ArcNode *p; G = (ALGraph*)malloc(sizeof(ALGraph); for(i=0; iadjlisti、firstarc = NULL; for(i=0; i=0; j-) if(g、edgesij!=0 & g、edgesij!=INF) p = (ArcNode*)malloc(sizeof(ArcNode); p-adjvex = j; p-info = g、edgesij; p-nexta
12、rc = G-adjlisti、firstarc; G-adjlisti、firstarc = p; G-n = g、n; G-e = g、e;void ListToMat1(ALGraph *G, MGraph &g) int i,j; ArcNode *p; for(i=0; in; i+) for(j=0; jn; j+) if(i=j) g、edgesij = 0; else g、edgesij = INF; for(i=0; in; i+) p = G-adjlisti、firstarc; while(p!=NULL) g、edgesip-adjvex = p-info; p = p
13、-nextarc; g、n = G-n; g、e = G-e;void DispMat1(MGraph g) int i,j; for(i=0; ig、n; i+) for(j=0; jg、n; j+) if(g、edgesij = INF) printf(%3s,); else printf(%3d,g、edgesij); printf(n); void DispAdj1(ALGraph *G) int i; ArcNode *p; for(i=0; in; i+) p = G-adjlisti、firstarc; printf(%3d:,i); while(p!=NULL) printf(
14、%3d(%d),p-adjvex,p-info); p = p-nextarc; printf(n); void DispAdj1(ALGraph *G) int i; ArcNode *p; for(i=0; in; i+) p = G-adjlisti、firstarc; printf(%3d:,i); while(p!=NULL) printf(%3d(%d),p-adjvex,p-info); p = p-nextarc; printf(n); 二、编译并链接程序;三、运行程序，结果如下图: 实验源程序一、输入如下所示程序;/文件名:exp8-2、cpp#include #includ
15、e #include graph、hextern void MatToList1(MGraph, ALGraph *&);extern void DispAdj1(ALGraph *G);extern void DFS(ALGraph *G,int v);extern void DFS1(ALGraph *G,int v);extern void DFS2(ALGraph *G,int v);extern void BFS(ALGraph *G,int v);int main() int i,j; MGraph g; ALGraph *G; int AMAXV6 = 0,5,INF,7,INF
16、,INF,INF,0,4,INF,INF,INF, 8,INF,0,INF,INF,9,INF,INF,5,0,INF,6, INF,INF,INF,5,0,INF,3,INF,INF,INF,1,0; g、n = 6; g、e = 10; for(i=0; ig、n; i+) for(j=0; jg、n; j+) g、edgesij = Aij; G = (ALGraph*)malloc(sizeof(ALGraph); MatToList1(g,G); printf(图G得邻接表:n); DispAdj1(G); printf(从顶点0开始得DFS(递归算法):n); DFS(G,0);
17、printf(n); printf(从顶点0开始得DFS(非递归算法):n); DFS1(G,0); printf(n); printf(从顶点0开始得BFS:n); BFS(G,0);printf(n);returne 0;/文件名:algo8-2、cpp#include #include #include graph、hint visitedMAXV;void DFS(ALGraph *G,int v) /递归深度优先遍历 ArcNode *p; visitedv = 1; printf(%3d,v); p = G-adjlistv、firstarc; while(p!=NULL) if(
18、visitedp-adjvex=0) DFS(G,p-adjvex); p = p-nextarc; void DFS1(ALGraph *G,int v) /非递归深度优先遍历 ArcNode *p; ArcNode *StMAXV; int top = -1,w,i; for(i=0; in; i+) visitedi = 0; printf(%3d,v); visitedv = 1; top+; Sttop = G-adjlistv、firstarc; while(top-1) p = Sttop; top-; while(p!=NULL) w = p-adjvex; if(visite
19、dw=0) printf(%3d,w); visitedw = 1; top+; Sttop = G-adjlistw、firstarc; break; p = p-nextarc; printf(n);void BFS(ALGraph *G,int v) ArcNode *p; int queueMAXV,front = 0,rear = 0; int visitedMAXV; int w,i; for(i=0;in;i+) visitedi = 0; printf(%3d,v); visitedv = 1; rear = (rear+1) % MAXV; queuerear = v; wh
20、ile(front!=rear) front = (front+1)%MAXV; w = queuefront; p = G-adjlistw、firstarc; while(p!=NULL) if(visitedp-adjvex=0) printf(%3d,p-adjvex); visitedp-adjvex = 1; rear = (rear+1) % MAXV; queuerear = p-adjvex; p = p-nextarc; printf(n);void MatToList1(MGraph g, ALGraph *&G) int i,j; ArcNode *p; G = (AL
21、Graph*)malloc(sizeof(ALGraph); for(i=0; iadjlisti、firstarc = NULL; for(i=0; i=0; j-) if(g、edgesij!=0 & g、edgesij!=INF) p = (ArcNode*)malloc(sizeof(ArcNode); p-adjvex = j; p-info = g、edgesij; p-nextarc = G-adjlisti、firstarc; G-adjlisti、firstarc = p; G-n = g、n; G-e = g、e;void DispAdj1(ALGraph *G) int
22、i; ArcNode *p; for(i=0; in; i+) p = G-adjlisti、firstarc; printf(%3d:,i); while(p!=NULL) printf(%3d(%d),p-adjvex,p-info); p = p-nextarc; printf(n); top+; Sttop = G-adjlistw、firstarc; break; p = p-nextarc; printf(n);void BFS(ALGraph *G,int v) ArcNode *p; int queueMAXV,front = 0,rear = 0; int visitedMA
23、XV; int w,i; for(i=0;in;i+) visitedi = 0; printf(%3d,v); visitedv = 1; rear = (rear+1) % MAXV; queuerear = v; while(front!=rear) front = (front+1)%MAXV; w = queuefront; p = G-adjlistw、firstarc; while(p!=NULL) if(visitedp-adjvex=0) printf(%3d,p-adjvex); visitedp-adjvex = 1; rear = (rear+1) % MAXV; qu
24、euerear = p-adjvex; p = p-nextarc; printf(n);void MatToList1(MGraph g, ALGraph *&G) int i,j; ArcNode *p; G = (ALGraph*)malloc(sizeof(ALGraph); for(i=0; iadjlisti、firstarc = NULL; for(i=0; i=0; j-) if(g、edgesij!=0 & g、edgesij!=INF) p = (ArcNode*)malloc(sizeof(ArcNode); p-adjvex = j; p-info = g、edgesi
25、j; p-nextarc = G-adjlisti、firstarc; G-adjlisti、firstarc = p; G-n = g、n; G-e = g、e;void DispAdj1(ALGraph *G) int i; ArcNode *p; for(i=0; in; i+) p = G-adjlisti、firstarc; printf(%3d:,i); while(p!=NULL) printf(%3d(%d),p-adjvex,p-info); p = p-nextarc; printf(n); void MatToList1(MGraph g, ALGraph *&G) in
26、t i,j; ArcNode *p; G = (ALGraph*)malloc(sizeof(ALGraph); for(i=0; iadjlisti、firstarc = NULL; for(i=0; i=0; j-) if(g、edgesij!=0 & g、edgesij!=INF) p = (ArcNode*)malloc(sizeof(ArcNode); p-adjvex = j; p-info = g、edgesij; p-nextarc = G-adjlisti、firstarc; G-adjlisti、firstarc = p; G-n = g、n; G-e = g、e;void
27、 DispAdj1(ALGraph *G) int i; ArcNode *p; for(i=0; in; i+) p = G-adjlisti、firstarc; printf(%3d:,i); while(p!=NULL) printf(%3d(%d),p-adjvex,p-info); p = p-nextarc; printf(n); 二、对程序进行编译链接；三、运行该程序,结果如图实验源程序。一、输入如下所示程序;#include #include #include graph、hextern void MatToList(MGraph,ALGraph *&);extern void
28、 DispAdj(ALGraph *);int visitedMAXV;void DFSALL(ALGraph *G,int v,int path,int d) ArcNode *p; visitedv = 1; pathd = v; d+; if(d=G-n) for(int k=0;kadjlistv、firstarc; while(p!=NULL) if(visitedp-adjvex=0) DFSALL(G,p-adjvex,path,d); p = p-nextarc; visitedv = 0;int main() int pathMAXV,i,j,v=1; MGraph g; A
29、LGraph *G; g、n = 5; g、e = 8; int AMAXVMAXV = 0,1,0,1,1,1,0,1,1,0,0,1,0,1,1, 1,1,1,0,1,1,0,1,1,0; for(i=0;ig、n;i+) for(j=0;jg、n;j+) g、edgesij = Aij; MatToList(g,G); for (i=0;ig、n;i+) visitedi = 0; printf(图G得邻接表: n); DispAdj(G); printf(从顶点%d出发得所有深度优先序列:n,v); DFSALL(G,v,path,0); printf(n); return 0;voi
30、d MatToList(MGraph g, ALGraph *&G) int i,j; ArcNode *p; G = (ALGraph*)malloc(sizeof(ALGraph); for(i=0; iadjlisti、firstarc = NULL; for(i=0; i=0; j-) if(g、edgesij!=0) p = (ArcNode*)malloc(sizeof(ArcNode); p-adjvex = j; p-nextarc = G-adjlisti、firstarc; G-adjlisti、firstarc = p; G-n = g、n; G-e = g、e;void DispAdj(ALGraph *G) int i; ArcNode *p; for(i=0; in; i+) p = G-adjlisti、firstarc; printf(%3d:,i); while(p!=NULL) printf(%3d,p-adjvex); p = p-nextarc; printf(n); if(visitedp-adjvex=0) DFSALL(G,p-adjvex,path,d); p = p-nextarc; visi