第六章 6.6 图的应用

6.6.1最小生成树

6.6.2 最短路径

6.6.3  拓扑排序

#include<bits/stdc++.h>
#include<stack>
using namespace std;
#define MVNum 100
#define OK 1
#define ERROR 0
typedef int OtherInfo;
typedef int Status;

typedef int VerTexType;

typedef struct ArcNode{//边结点 
    int adjvex;//该边所指向的顶点的位置 
    struct ArcNode *nextarc;//指向下一条边的指针 
    OtherInfo info;//和边有关的信息 
}ArcNode;
typedef struct VNode{ 
    VerTexType data;//顶点信息
    ArcNode *firstarc;//指向第一条依附该顶点边的指针 
}VNode,Adjlist[MVNum];//Adjlist表示邻接表类型 

typedef struct{//邻接表 
    Adjlist vertices;
    int vexnum,arcnum;//图的当前顶点数和边数 
}ALGraph;

Status LocateVex(ALGraph G,char ch)
{
    int i;
    for(i = 0; i < G.vexnum ; i ++)
    {
        if(G.vertices[i].data == ch -'0')
            return i;
    }
}
Status CreatUDG(ALGraph &G)
{
    char v1,v2;
    int i,j,k;
    ArcNode *p1,*p2;
    cin>>G.arcnum>>G.vexnum ;//读入图的总边数和顶点数
     for(i = 0; i < G.vexnum ; i ++)
     {
         cin>>G.vertices[i].data ;
         G.vertices[i].firstarc = NULL;
     }
    for(k = 0; k < G.vexnum ; k ++)
    {
        cin>>v1>>v2;
        i = LocateVex(G,v1);
        j = LocateVex(G,v2);
        p1 = new ArcNode;
        p1->adjvex = j;
        p1->info = i;
        p1->nextarc = G.vertices[i].firstarc ;
        G.vertices[i].firstarc = p1;
        
        p2 = new ArcNode;
        p2->adjvex = i;
        p2->info = j;
        p2->nextarc = G.vertices[j].firstarc ;
        G.vertices[j].firstarc = p2;
    }
    return OK;
}

int FindInDegree(ALGraph G,int indegree[])
{
    for(int i = 0;i < G.vexnum ;i ++)
    {
        ArcNode *p1 = G.vertices[i].firstarc;
        while(p1->nextarc !=NULL)
        {
            indegree[p1->nextarc->adjvex]++;
            p1 = p1->nextarc ;
        }
    }
    return OK;
}
Status TopologicalSort(ALGraph G,int topo[])
{
    stack<int>S;
    int indegree[MVNum];
    int i,m,k;
    ArcNode *p;
    memset(indegree,0,sizeof(indegree));
    FindInDegree(G,indegree);//求出各顶点的入度存入数组indegree中
    for(i = 0; i < G.vexnum ; i ++)
    {
        if(!indegree[i])//入度为0者进栈 
            S.push(i);    
    }
    m = 0;
    while(!S.empty())
    {
        i = S.top();//将栈顶vi出栈 
        S.pop();
        topo[m++] = i;//对输出顶点计数 //将vi保存在拓扑排序数组topo中 
        p = G.vertices[i].firstarc ;//p指向vi的第一个邻接点 
        while(p != NULL)
        {
            k = p->adjvex ;//vk为vi的邻接点 
            -- indegree[k];//vi的每个邻接点的入度减1 
            if(indegree[k] == 0)//若入度减为0，则入度 
                S.push(k);
            p = p->nextarc ;//p指向顶点vi的下一个邻接点 
        }
    }
    if(m < G.vexnum )//该图有回路 
        return ERROR;
    return OK;
}
int main()
{
    ALGraph G; 
    int topo[MVNum];
    CreatUDG(G);
    TopologicalSort(G,topo);
    return 0;
}