有向图的十字链表存储形式

弧结点结构：

十字链表形态：

实现：

/***********************************************
有向图的存储形式——十字链表
by Rowandjj
2014/6/27
***********************************************/
#include<IOSTREAM>
using namespace std;

#define MAX_VERTEX_NUM 20//顶点最大长度
#define MAX_INFO 20//弧信息的最大长度

typedef struct _ARCBOX_//弧结点
{
    int tailvex,headvex;//该弧的尾和头顶点的位置
    struct _ARCBOX_ *hlink,*tlink;//分别为弧头同样和弧尾同样的弧的链域
    char *info;
}ArcBox;

typedef struct _VEXNODE_//顶点
{
    char data;//顶点名称
    ArcBox *firstin,*firstout;
}VexNode;

typedef struct _OLGRAPH_//图
{
    VexNode xlist[MAX_VERTEX_NUM];//表头向量(数组)
    int vexnum,arcnum;//顶点数目，弧数目
}OLGraph;

//------------------操作定义---------------------------------
int LocateVex(OLGraph G,char u);//返回顶点u在有向图G中的位置(序号),如不存在则返回-1
bool CreateDG(OLGraph* G);//採用十字链表存储表示,构造有向图G
void Display(OLGraph G);//输出有向图G
void DestroyGraph(OLGraph* G);//销毁有向图G
char GetVex(OLGraph G,int v);//返回v的值
bool PutVex(OLGraph* G,char v,char value);//对v赋新值value
int FirstAdjVex(OLGraph G,char v);//返回v的第一个邻接顶点的序号。若顶点在G中没有邻接顶点,则返回-1
int NextAdjVex(OLGraph G,char v,char w);//返回v的(相对于w的)下一个邻接顶点的序号,若w是v的最后一个邻接顶点,则返回-1   
void InsertVex(OLGraph* G,char v);//在有向图G中增添新顶点v(不增添与顶点相关的弧,留待InsertArc()去做)   
bool DeleteVex(OLGraph* G,char v);//删除G中顶点v及其相关的弧
bool InsertArc(OLGraph* G,char v,char w);//在G中增添弧<v,w>
bool DeleteArc(OLGraph* G,char v,char w);//在G中删除弧<v,w> 
   
void DFSTravel(OLGraph G,void (*Visit)(char));
void DFS(OLGraph G,int v);
void BFSTravel(OLGraph G,void (*Visit)(char));

void (*VisitFunc)(char);  //全局函数指针 
bool visited[MAX_VERTEX_NUM]; /* 訪问标志数组(全局量) */
//-----------------------------------------------------------
void Visit(char p)
{
    cout<<p<<" ";    
}

//辅助队列
typedef struct _QUEUENODE_
{
    int data;
    struct _QUEUENODE_ *next;
}QueueNode;
typedef struct _QUEUE_
{
    QueueNode *pHead;
    QueueNode *pTail;
    int size;
}Queue;
bool InitQueue(Queue *Q);
bool DestroyQueue(Queue *Q);
bool DeQueue(Queue *Q,int* e);
bool EnQueue(Queue *Q, int e);
bool QueueEmpty(Queue Q);
//-----------------------------------------------------------
bool InitQueue(Queue *Q)
{
    Q->pHead = Q->pTail = (QueueNode*)malloc(sizeof(QueueNode));
    if(!Q->pHead)
    {
        return false;
    }
    Q->pHead->next = NULL;
    Q->size = 0;
    return true;
}
bool EnQueue(Queue *Q, int e)
{
    QueueNode *newNode = (QueueNode *)malloc(sizeof(QueueNode));
    if(!newNode)
    {
        return false;
    }
    newNode->data = e;
    newNode->next = NULL;
    Q->pTail->next = newNode;
    Q->pTail = newNode;
    Q->size++;
    return true;
}
bool DeQueue(Queue *Q,int* e)
{
    QueueNode *pDel = Q->pHead->next;
    if(!pDel)
    {
        return false;
    }
    *e = pDel->data;
    if(Q->pTail == pDel)
    {
        Q->pTail = Q->pHead;
    }
    Q->pHead->next = pDel->next;
    free(pDel);
    Q->size--;

    return true;
}
bool QueueEmpty(Queue Q)
{
    return Q.size == 0;
}
bool DestroyQueue(Queue *Q)
{
    QueueNode *p,*q;
    p = Q->pHead->next;
    while(p)
    {
        q = p->next;
        free(p);
        p = q;
    }
    free(Q->pHead);
    Q->pHead = NULL;
    Q->size = 0;
    return true;
}
//-----------------------------------------------------------
int LocateVex(OLGraph G,char u)
{
    int i;
    for(i = 0; i < G.vexnum; i++)//用循环查找该结点
    {
        if(u == G.xlist[i].data)
        {
            return i;
        }
    }
    return -1;
}
bool CreateDG(OLGraph* G)
{
    int i,j,k;
    int IncInfo;//弧是否包括其它信息
    ArcBox *pArc;
    char v1,v2;//弧尾、弧头
    char str[MAX_INFO];//弧的相关信息
    cout<<"请输入有向图的顶点数,弧数,弧是否含其它信息(是:1，否:0):";
    cin>>G->vexnum;
    cin>>G->arcnum;
    cin>>IncInfo;

    cout<<"请依次输入顶点的值"<<endl;
    for(i = 0; i < G->vexnum; i++)
    {
        cin>>G->xlist[i].data;
        G->xlist[i].firstin = NULL;
        G->xlist[i].firstout = NULL;
    }
    cout<<"请输入每条弧弧尾和弧头的值"<<endl;

    for(k = 0; k < G->arcnum; k++)//输入各弧并构造十字链表
    {
        //注意：假设i------>j 则代表i为弧尾，或者起始点。j代表弧头，又叫终端点
        cin>>v1;//输入弧尾(起始点)
        cin>>v2;//输入弧头(终端点)
        pArc = (ArcBox *)malloc(sizeof(ArcBox));
        //得到弧尾和弧头的位置
        i = LocateVex(*G,v1);//弧尾的位置
        j = LocateVex(*G,v2);//弧头的位置
        
        if(i == -1 || j == -1)
        {
            return false;
        }
        pArc->tailvex = i;
        pArc->headvex = j;
        
        pArc->tlink = G->xlist[i].firstout;
        pArc->hlink = G->xlist[j].firstin;

        G->xlist[i].firstout = pArc;
        G->xlist[j].firstin = pArc;

        if(IncInfo)
        {
            cout<<"输入弧的相关信息:"<<endl;
            cin>>str;
            
            pArc->info = (char *)malloc(sizeof(char)*(strlen(str)+1));
            strcpy(pArc->info,str);
        }else
        {
            pArc->info = NULL;
        }
    }
    
    return true;
}
void Display(OLGraph G)
{
    int i;
    ArcBox *pArc;
    cout<<"顶点个数"<<G.vexnum<<",弧个数"<<G.arcnum<<endl;
    cout<<"顶点";
    for(i = 0; i < G.vexnum; i++)
    {
        cout<<G.xlist[i].data<<" ";
    }
    cout<<endl;
    for(i = 0; i < G.vexnum; i++)
    {
        cout<<"顶点:"<<G.xlist[i].data<<"入度:";//弧头同样
        pArc = G.xlist[i].firstin;
        while(pArc)
        {
            cout<<G.xlist[pArc->tailvex].data<<" ";
            pArc = pArc->hlink;
        }
        cout<<"出度:";
        pArc = G.xlist[i].firstout;
        while(pArc)
        {
            cout<<G.xlist[pArc->headvex].data<<" ";
            if(pArc->info)
            {
                cout<<pArc->info<<"  ";
            }
            pArc = pArc->tlink;
        }
        cout<<endl;
    }
}
void DestroyGraph(OLGraph* G)
{
    int i;
    ArcBox *pArc1,*pArc2;
    for(i = 0 ; i < G->vexnum; i++)
    {
        pArc1 = G->xlist[i].firstout;
        
        while(pArc1)
        {
            pArc2 = pArc1->tlink;
            if(pArc1->info)
            {
                free(pArc1->info);
            }
            free(pArc1);
            pArc1 = pArc2;
        }
    }
}
char GetVex(OLGraph G,int v)
{
    if(v < 0 || v >= G.vexnum)
    {
        exit(0);
    }
    return G.xlist[v].data;
}
bool PutVex(OLGraph* G,char v,char value)
{
    int i = LocateVex(*G,v);
    if(i < 0)
    {
        return false;
    }

    G->xlist[i].data = value;
    return true;
}
int FirstAdjVex(OLGraph G,char v)
{
    int i;
    i = LocateVex(G,v);
    ArcBox *p = G.xlist[i].firstout;
    if(p)
    {
        return p->headvex;
    }else
    {
        return -1;
    }
}
int NextAdjVex(OLGraph G,char v,char w)
{
    int i,j;
    ArcBox *pArc;
    i = LocateVex(G,v);
    j = LocateVex(G,w);
    pArc = G.xlist[i].firstout;
    while(pArc && pArc->headvex!=j)
    {
        pArc = pArc->tlink;
    }
    if(pArc)
    {
        pArc = pArc->tlink;
    }
    if(pArc)
    {
        return pArc->headvex;
    }else
    {
        return -1;
    }
}
void InsertVex(OLGraph* G,char v)
{
    G->xlist[G->vexnum].data = v;
    G->xlist[G->vexnum].firstin = G->xlist[G->vexnum].firstout = NULL;
    G->vexnum++;
}
bool DeleteVex(OLGraph* G,char v)
{
    int j,k;
    ArcBox *p,*q;

    k = LocateVex(*G,v);
    if(k < 0)
    {
        return false;
    }
    //1.删除v的出弧
        //1.1v的出弧也就是其它顶点的入弧，我们须要在其它弧的入弧链表中删除v的出弧
    for(j = 0; j < G->vexnum; j++)
    {
        if(j == k)
        {
            continue;
        }
        p = G->xlist[j].firstin;
        while(p)
        {
            if(k == p->tailvex && p == G->xlist[j].firstin)//假设待删结点为首结点
            {
                G->xlist[j].firstin = p->hlink;
                break;
            }else if(k != p->tailvex)//当前结点不是待删结点
            {
                q = p;
                p = p->hlink;
            }else//待删结点不是首节点
            {
                q->hlink = p->hlink;
                break;
            }
        }
    }
        //1.2删除v的出弧
    p = G->xlist[k].firstout;
    while(p)
    {
        q = p->tlink;
        if(p->info)
        {
            free(p->info);
        }
        free(p);
        G->arcnum--;
        p = q;
    }
    //2.删除顶点v的入弧
        //2.1顶点v的入弧也就是其它顶点的出弧。我们须要在其它弧的出弧链表中删除v的入弧
    for(j = 0; j < G->vexnum; j++)
    {
        if(j == k)
        {
            continue;
        }
        p = G->xlist[j].firstout;
        while(p)
        {
            if(k == p->headvex && p == G->xlist[j].firstout)
            {
                G->xlist[j].firstout = p->tlink;
                break;
            }else if(k != p->headvex)
            {
                q = p;
                p = p->tlink;
            }else
            {
                q->tlink = p->tlink;
                break;
            }
        }
    }
        //2.2删除顶点v的入弧
    p = G->xlist[k].firstin;
    while(p)
    {
        q = p->hlink;
        if(p->info)
        {
            free(p->info);
        }
        free(p);
        p = q;
        G->arcnum--;
    }
    //3.序号>k的顶点依次向前移
    for(j = k+1; j < G->vexnum; j++)
    {
        G->xlist[j-1] = G->xlist[j];
    }
    G->vexnum--;
    //4.结点序号>k的要减1
    for(j = 0; j < G->vexnum; j++)
    {
        p = G->xlist[j].firstout;
        while(p)
        {
            if(p->headvex > k)
            {
                p->headvex--;
            }
            if(p->tailvex > k)
            {
                p->tailvex--;
            }
            p = p->tlink;
        }    
    }
    return true;
}
bool InsertArc(OLGraph* G,char v,char w)
{
    int IncInfo;
    char str[MAX_INFO];
    int i,j;
    ArcBox *pArc;
    i = LocateVex(*G,v);//弧尾
    j = LocateVex(*G,w);//弧头
    if(i < 0 || j < 0)
    {
        return false;
    }
    pArc = (ArcBox *)malloc(sizeof(ArcBox));
    pArc->tailvex = i;
    pArc->headvex = j;
    pArc->tlink = G->xlist[i].firstout;
    pArc->hlink = G->xlist[j].firstin;
    G->xlist[i].firstout = pArc;
    G->xlist[j].firstin = pArc;
    
    G->arcnum++;
    cout<<"要插入的弧是否含有其它信息(是: 1,否: 0):";
    cin>>IncInfo;
    if(IncInfo)
    {
        cout<<"输入弧信息:";
        cin>>str;
        pArc->info = (char *)malloc(sizeof(char)*(strlen(str)+1));
        strcpy(pArc->info,str);
    }else
    {
        pArc->info = NULL;
    }
    
    return true;
}
bool DeleteArc(OLGraph* G,char v,char w)
{
    int i,j;
    ArcBox *p,*q;
    i = LocateVex(*G,v);
    j = LocateVex(*G,w);
    if(i < 0 || j < 0)
    {
        return false;
    }
    //先删除顶点v出弧
    p = G->xlist[i].firstout;
    if(p && p->headvex == j)//待删结点为首节点
    {
        G->xlist[i].firstout = p->tlink;
    }
    else
    {
        while(p && p->headvex != j)
        {
            q = p;
            p = p->tlink;
        }
        if(p)
        {
            q->tlink = p->tlink;
        }
    }
    //删除顶点w的入弧
    p = G->xlist[j].firstin;
    if(p && p->tailvex == i)
    {
        G->xlist[j].firstin = p->hlink;
    }else
    {
        while(p && p->tailvex != i)
        {
            q = p;
            p = p->hlink;
        }
        if(p)
        {
            q->hlink = p->hlink;
        }
    }
    if(p->info)
    {
        free(p->info);
    }
    G->arcnum--;
    return true;
}
void DFS(OLGraph G,int v)
{
    int i;
    char v1,w1;
    v1 = GetVex(G,v);
    visited[v] = true;
    VisitFunc(v1);
    for(i = FirstAdjVex(G,v1);i>=0;i = NextAdjVex(G,v1,w1 = GetVex(G,i)))
    {
        if(!visited[i])
        {
            DFS(G,i);
        }
    }
}
void DFSTravel(OLGraph G,void (*Visit)(char))
{
    int i;
    for(i = 0; i < G.vexnum; i++)
    {
        visited[i] = false;
    }
    VisitFunc = Visit;
    for(i = 0; i < G.vexnum; i++)
    {
        if(!visited[i])
        {
            DFS(G,i);
        }
    }
}
void BFSTravel(OLGraph G,void (*Visit)(char))
{
    int i,u,w;
    char u1,w1;
    Queue queue;
    InitQueue(&queue);
    for(i = 0; i < G.vexnum; i++)
    {
        visited[i] = false;
    }
    for(i = 0; i < G.vexnum; i++)
    {
        if(!visited[i])
        {
            visited[i] = true;
            Visit(G.xlist[i].data);
            EnQueue(&queue,i);
            while(!QueueEmpty(queue))
            {
                DeQueue(&queue,&u);
                u1 = GetVex(G,u);
                for(w = FirstAdjVex(G,u1);w>=0;w = NextAdjVex(G,u1,w1=GetVex(G,w)))
                {
                    if(!visited[w])
                    {
                        visited[w] = true;
                        Visit(G.xlist[w].data);
                        EnQueue(&queue,w);
                    }
                }
            }

        }
    }
}
int main()
{
    OLGraph graph;
    CreateDG(&graph);
    Display(graph);
    cout<<"广度优先"<<endl;
    BFSTravel(graph,Visit);
    cout<<"\n深度优先"<<endl;
    DFSTravel(graph,Visit);
    return 0;
}