實驗要求
- 實現圖的抽象數據類型
- 在鄰接矩陣結構上實現圖的建立運算
- 在鄰接表結構上實現圖的建立運算
- 實現網的遍歷運算（廣度優先）
- 實現最短路徑算法（floyd）
實驗代碼
- 實現圖的抽象數據類型
//鄰接矩陣結構
typedef struct ArcCell
{
EType adj;
InfoType info;
}ArcCell,AdjMatrix[MAX_VERTEX_NUM][MAX_VERTEX_NUM];
typedef struct
{
VertexType vexs[MAX_VERTEX_NUM];
AdjMatrix arcs;
int vexnum,arcnum;
GraphKind kind;
}MGraph;
//鄰接表結構
typedef struct ArcNode
{ int adjvex;
struct ArcNode *nextarc;
InfoType *info;
}ArcNode;
typedef struct VNode //define structure ALGraph
{ VertexType data;
ArcNode *firstarc;
}VNode,AdjList[MAX_VERTEX_NUM];
typedef struct
{ AdjList vertices;
int vexnum,arcnum;
int kind;
}ALGraph;
- 在鄰接矩陣結構上實現圖的建立運算
int CreatUDN(MGraph &G)
{
int i=0,j=0,k,vi,vj,w;
//-----Demo G.vexnum and G.arcnum------
G.vexnum=3;
G.arcnum=5;
//-----------------------------------------
printf("Please input the number of G.vexnum(eg,G.vexnum=3) : ");
scanf("%d",&G.vexnum);
printf("Please input the number of G.arcnum(eg,G.arcxnum=5) : ");
scanf("%d",&G.arcnum);
for(i=0;i<G.vexnum;++i)
for(j=0;j<G.vexnum;++j)
{
G.arcs[i][j].info=INFINITY;
if(i==j) G.arcs[i][j].info=0;
}//end of for(j=0;j<G.vexnum;++j)
cout<<"Please input arc(Vi-->Vj):"<<endl
<<"For example:"<<endl<<"=============="<<endl
<<"(Vi=1,Vj=2,Weight=4),(Vi=1,Vj=3,Weight=11),(Vi=2,Vj=1,Weight=6)"<<endl
<<"(Vi=2,Vj=3,Weight=2),(Vi=3,Vj=1,Weight=3)..."<<endl;
for(k=0;k<G.arcnum;++k)
{
cout<<endl<<"Please input the "<<k+1<<"the arc's vi (0<vi<"<<G.vexnum+1<<"): ";
cin>>vi;
cout<<"Please input the "<<k+1<<"the arc's vj (0<vj<"<<G.vexnum+1<<"): ";
cin>>vj;
cout<<"Please input the "<<k+1<<"the arc's weight (0<weight<"<<INFINITY<<"): ";
cin>>w;
i=vi;
j=vj;
while(i<1||i>G.vexnum||j<1||j>G.vexnum||w<0)
{
cout<<"Input ERROR!"<<endl
<<"Please input the "<<k+1<<"the arc's vi (0<vi<"<<G.vexnum+1<<"): ";
cin>>vi;
cout<<"Please input the "<<k+1<<"the arc's vj (0<vj<"<<G.vexnum+1<<"): ";
cin>>vj;
cout<<"Please input the "<<k+1<<"the arc's weight (0<weight<"<<INFINITY<<"): ";
cin>>w;
i=vi;
j=vj;
}//end of while
i--;
j--;
G.arcs[i][j].info=w;
}//end of for
return (OK);
}//end of CreateUDN() function
- 在鄰接表結構上實現圖的建立運算
int CreateDG(ALGraph &G) //CreateDG() sub-function
{
int IncInfo,i,j,k,v1,v2,w;
cout<<endl<<"請輸入圖的頂點個數(eg. G.vexnum=4)：";
cin>>G.vexnum;
cout<<"請輸入圖的弧的條數(eg. G.arcnum=4):";
cin>>G.arcnum;
cout<<"請輸入圖的弧上的信息(0 for none) :";
cin>>IncInfo;
for(i=0;i<G.vexnum;++i)//initial G.vertices
{G.vertices[i].data=i;
G.vertices[i].firstarc=NULL;}
cout<<"請輸入弧arc(v1->v2),fo example:(v1=1,v2=3),(v1=2,v2=4)...";
for(k=0;k<G.arcnum;++k) //input arc(v1,v2)
{
cout<<endl<<"請輸入第"<<k+1<<"條弧的起始頂點 v1(0<v1<G.vexnum):";
cin>>v1;
cout<<"請輸入第"<<k+1<<"條弧的終止頂點 v2(0<v2<G.vexnum):";
cin>>v2;
i=v1;
j=v2;
while(i<1||i>G.vexnum||j<1||j>G.vexnum)//if(v1,v2) illedal again
{
cout<<endl<<"請輸入第"<<k+1<<"條弧的起始頂點 v1(0<v1<G.vexnum):";
cin>>v1;
cout<<"請輸入第"<<k+1<<"條弧的終止頂點 v2(0<v2<G.vexnum):";
cin>>v2;
}//while end
i--;
j--;
ArcNode *p;
p=(ArcNode *)malloc(sizeof(ArcNode));//allocate memory
if(!p)
{cout<<"Overflow!"; return(0);}
p->adjvex=j; //assign p
p->nextarc=G.vertices[i].firstarc;
p->info=NULL;
G.vertices[i].firstarc=p;
if(IncInfo)
{cout<<"請輸入info:";
cin>>*(p->info);}
}//end of if
return (OK);
}//end of CreateDG()
- 實現網的遍歷運算（廣度優先）
void BFSTraverse(ALGraph G)//BFSTraverse() sub-function
{
int v,w,u;
int visited[MAX_VERTEX_NUM];
SqQueue Q;
for(v=0;v<G.vexnum;++v)
visited[v]=0;
InitQueue(Q);
for(v=0;v<G.vexnum;++v)
if(visited[v]==0)
{
visited[v]=1;
cout<<v+1<<"-->";
EnQueue(Q,v);
while(!QueueEmpty(Q))
{
DeQueue(Q,u);
for(w=G.vertices[u].data;
G.vertices[u].firstarc!=NULL;
w=G.vertices[u].firstarc->adjvex,
G.vertices[u].firstarc=G.vertices[u].firstarc->nextarc)//"右)"
if(visited[w]==0)
{
visited[w]=1;
cout<<w+1<<"-->";
EnQueue(Q,w);
}//if end
if(visited[w]==0)
{
visited[w]=1;
cout<<w+1<<"-->";
EnQueue(Q,w);
}//if end
}//while end
}//if end
}//BFSTraverse() end
- 實現最短路徑算法（floyd）
void ShortestPath_FLOYD(MGraph G,
PathMatrix Path[MAX_VERTEX_NUM][MAX_VERTEX_NUM][MAX_VERTEX_NUM],
DistancMatrix Dist[MAX_VERTEX_NUM][MAX_VERTEX_NUM])
{
int i,j,u,v,w;
for(v=0;v<G.vexnum;++v)
for(w=0;w<G.vexnum;++w)
{ Dist[v][w]=G.arcs[v][w].info;
for(u=0;u<G.vexnum;++u)
Path[v][w][u]=FALSE;
if(Dist[v][w]<INFINITY)
{ Path[v][w][v]=TRUE;
Path[v][w][w]=TRUE;
}//end of if
}//end of for
for(u=0;u<G.vexnum;++u)
for(v=0;v<G.vexnum;++v)
for(u=0;u<G.vexnum;++u)
if(Dist[v][u]+Dist[u][w]<Dist[v][w])
{ Dist[v][w]=Dist[v][u]+Dist[u][w];
for(i=0;i<G.vexnum;++i)
Path[v][w][i]=Path[v][u][i]||Path[u][w][i];
}//end of if
//------------print the last Dist[i][j]---------------
printf("Vertice");
for(i=0;i<G.vexnum;i++)
printf("%5d",i+1);
printf("\n");
for(i=0;i<G.vexnum;i++)
{
printf("%5d ",i+1);
for(j=0;j<G.vexnum;j++)
printf("%5d",Dist[i][j]);
printf("\n");
}//end of for
//---------------------------------------------------
}//shortestPath_FLOYD() end
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