实验四图的操作及应用讲解.docx

1、实验四图的操作及应用讲解实验四 图的操作及应用实验课程名： 数据结构与算法一、实验目的及要求1、理解图的基本概念及术语。2、掌握图的两种存储结构(邻接矩阵和邻接表)的表示方法。3、熟练掌握图的两种遍历(深度优先搜索遍历和广度优先搜索遍历)的算法思想、步骤，并能列出在两种存储结构上按上述两种遍历算法得到的序列。二、实验内容任务一：构造如图1所示的图的邻接矩阵存储结构和邻接表存储结构。图1解答：（1）源代码：#include#include #include #define INFINITY 1000 #define MAX_VERTEX_NUM 20 #define OK 1 #define S

2、TARTS * typedef enumDG,DN,UDG,UDN GraphKind; typedef int EType; typedef int InfoType; typedef int VertexType; typedef struct ArcCell /define structure MGraph EType adj; InfoType *info; ArcCell,AdjMatrixMAX_VERTEX_NUMMAX_VERTEX_NUM; typedef struct VertexType vexsMAX_VERTEX_NUM; AdjMatrix arcs; int ve

3、xnum,arcnum; GraphKind kind; MGraph; int CreatUDN(MGraph &G) /CreatUDN() sub-function int IncInfo,i,j,k,v1,v2,w; coutendlG.vexnum; /input the number of vex coutG.arcnum; /input the number of arc coutIncInfo; for(i=0;iG.vexnum;+i) for(j=0;jG.vexnum;+j) G.arcsij.adj=INFINITY; /initial G.arcsij.adj G.a

4、rcsij.info=NULL; /initial G.arcsij.info coutV2), For example: (V1=1,V2=3),(V1=2,V2=4).endl; for(k=0;kG.arcnum;+k) /input arc(v1,v2) coutendlPlease input the k+1th arcs v1 (0v1v1; /input v1 coutPlease input the k+1th arcs v2 (0v2v2; /input v2 coutPlease input the k+1w; /input weight i=v1; j=v2;while(

5、iG.vexnum|jG.vexnum) /if (v1,v2) illegal,again coutPlease input the k+1th arcs v1 (0v1v1; coutPlease input the k+1th arcs v2 (0v1v2; coutPlease input the k+1w; i=v1; j=v2; /while end i-; j-; G.arcsij.adj=G.arcsji.adj=w; /weight coutG.arcsi+1j+1.adj=G.arcsj+1i+1.adj=wendl; if(IncInfo) coutPlease inpu

6、t the k+1*G.arcsij.info; /for end return (OK); /CreatUDN() end void Gprintf(MGraph G) /打印邻接矩阵 cout邻接矩阵数组为：n; for(int i=0;iG.vexnum;i+) for(int k=0;kG.vexnum;k+) coutG.arcsik.adjt; coutendl; /*邻接表*/ typedef struct ArcNode /define structure ALGraph int adjvex; struct ArcNode *nextarc; InfoType *info;

7、ArcNode; typedef struct VNode VertexType data; ArcNode *firstarc; VNode,AdjListMAX_VERTEX_NUM; typedef struct AdjList vertices; int vexnum,arcnum; int kind; ALGraph; int CreateDG(ALGraph &G) /CreateDG() subfunction int IncInfo,i,j,k,v1,v2,w; coutendlG.vexnum; /input the number of vex coutG.arcnum; /

8、input the numbe of arc coutIncInfo; /if no information, input 0 for(i=0;iG.vexnum;+i) G.verticesi.data=i; /initial G.verticesi.data G.verticesi.firstarc=NULL; /initial G.verticesi.firstarc coutV2), For example: (V1=1,V2=3),(V1=2,V2=4).endl; for(k=0;kG.arcnum;+k) /input arc(v1,v2) coutendlPlease inpu

9、t the k+1th arcs v1 (0v1v1; coutPlease input the k+1th arcs v2 (0v2v2; i=v1; j=v2; while(iG.vexnum|jG.vexnum) /if (v1,v2) illegal coutendlPlease input the k+1th arcs v1 (0v1v1; coutPlease input the k+1th arcs v2 (0v2v2; i=v1; j=v2; /while end i-; j-; ArcNode *p; p=(ArcNode *)malloc(sizeof(ArcNode);

10、/allocate memory if(!p) coutadjvex=j; /assign p-adjvex p-nextarc=G.verticesi.firstarc; p-info=NULL; G.verticesi.firstarc=p; if(IncInfo) cout*(p-info); /input information /for end return (OK); /CreateDG() end int main() MGraph MG; ALGraph AG; int a=-1; while(a!=0) coutSTARTSSTARTSendl; cout(1)邻接矩阵(无向

11、网)t(2)邻接表(有向图)t(3)退出endl; couta; switch(a) case 1: CreatUDN(MG);Gprintf(MG);break; case 2: CreateDG(AG);break; case 3: a=0;break; default:cout选择错误nendl; return 0; （2）运行结果：（3）运行结果分析： 运用数组与链表的结合来实现任务二：用邻接表的存储结构创建一个如图2所示的图a，分别打印出这两个图的深度优先遍历和广度优先遍历的结点信息序列。解答：（1）源代码：#include#include#includeusing namespac

12、e std;#define ERROR 1#define MAX_VERTEX_NUM 100typedef struct ArcNode int adjvex; struct ArcNode *nextarc; string info;ArcNode;typedef struct VNode char date; ArcNode * firstarc;VNode,AdjListMAX_VERTEX_NUM;typedef struct AdjList vertices; int vexnum,arcnum; /当前图的vexnum顶点数和arcnum弧数 int kind;ALGraph;i

13、nt LocateVex(ALGraph &G,char &v1) int i; for(i=0;i=G.vexnum) return ERROR; else return 0;void CreateDG(ALGraph &G) ArcNode *p,*q; char v1,v2; char v; int i,j,k,n; cout请输入图的顶点数和弧数：G.vexnum; cinG.arcnum; cout请输入顶点：endl; for(i=0;iv; G.verticesi.date=v; G.verticesi.firstarc=NULL; cout请输入弧尾和弧头：; for(k=0;

14、kv1; cinv2; i=LocateVex(G,v1);j=LocateVex(G,v2); if(G.verticesi.firstarc=NULL) p=(ArcNode *)new ArcNode; G.verticesi.firstarc=p; q=G.verticesi.firstarc; else q=G.verticesi.firstarc; for(n=0;nnextarc) if(!q-nextarc) break; p=(ArcNode *)new ArcNode; q-nextarc=p; q=q-nextarc; q-adjvex=j; q-nextarc=NULL

15、; coutadjvex; if(visitedi=false) n=i; return n;int NextAdjVex(ALGraph &G,int v) int i; int n=-1; ArcNode *p; p=G.verticesv.firstarc; for(i=p-adjvex;iadjvex; if(visitedi=false) n=i; break; else p=p-nextarc; return n;void VisitFuc(ALGraph &G,int v) coutG.verticesv.date=0;w=NextAdjVex(G,v) if(!visitedw

16、) DFS(G,w);void DFSTraverse(ALGraph &G) int v; for(v=0;vG.vexnum;v+) visitedv=false; cout深度优先搜索：endl; for(v=0;vG.vexnum;v+) if(!visitedv) DFS(G,v); /-广度优先遍历-/void BFSTraverse(ALGraph &G) int v; int w; queue q; /STL队列 for(v=0;vG.vexnum;v+) visitedv=false;/ InitQueue(Q); cout广度优先搜索：; for(v=0;v=0;w=Nex

17、tAdjVex(G,v) if(!visitedw) visitedw=true; VisitFuc(G,w); q.push(w); /void menu() coutn; cout /-图的基本操作-/endl; cout * 1、图的构建 *endl; cout * 2、深度优先遍历 *endl; cout * 3、广度优先遍历 *endl; cout -endl; cout请输入数字进行选择：i; while(i4) switch(i) case 1:CreateDG(G);break; case 2:DFSTraverse(G);coutendl;break; case 3:BFSTraverse(G);couti; return 0;（2）运行结果：（3）运行结果分析：运用图的深度优先和广度优先算法搜索。3、实验小结通过本次实验我知道了图的基本概念及术语。了解了图的两种存储结构(邻接矩阵和邻接表)的表示方法。熟练掌握图的两种遍历(深度优先搜索遍历和广度优先搜索遍历)的算法思想、步骤，并能列出在两种存储结构上按上述两种遍历算法得到的序列。