邻接矩阵实现图的基本操作

/*
	Author:Albert Tesla Wizard
	Time:2020/10/26 20:22
*/
	#include<bits/stdc++.h>
#define OK 1
#define Infinity INT_MAX
#define Error -1
const int MAXSIZE=20;
using namespace std;
typedef enum{
    
    DG,UDG,DN,UDN}Graphtype;
typedef int TypeElement;
struct Graph
{
    
    
    int vertexnum;
    int arcnum;
    TypeElement arc[MAXSIZE][MAXSIZE];
    char vertex[MAXSIZE];
    Graphtype type;
};
//找到顶点v在图中的位置
int Locate(char v,Graph&G)
{
    
    
    for(int i=1;i<=G.vertexnum;i++)
    {
    
    
        if(v==G.vertex[i])return i;
    }
    return -1;
}
//创建图G
void create(Graph&G)
{
    
    
    cout<<"请输入图的类型:0.有向图 1.无向图 2.有向网 3.无向网"<<endl;
    int type,v1,v2;
    char c1,c2;
    cin>>type;
    if(type==DG)
    {
    
    
        G.type=DG;
    }
    else if(type==UDG)
    {
    
    
        G.type=UDG;
    }
    else if(type==DN)
    {
    
    
        G.type=DN;
    }
    else if(type==UDN)
    {
    
    
        G.type=UDN;
    }
    cout<<"请输入图的顶点数目:"<<endl;
    cin>>G.vertexnum;
    cout<<"请输入图的弧的数目:"<<endl;
    cin>>G.arcnum;
    cout<<"请输入各个顶点的值:"<<endl;
    for(int i=1;i<=G.vertexnum;i++)cin>>G.vertex[i];
    if(G.type==DG||G.type==UDG)
    {
    
    
        for(int i=1;i<=G.vertexnum;i++)
        for(int j=1;j<=G.vertexnum;j++)G.arc[i][j]=0;
    }
    else if(G.type==DN||G.type==UDN)
    {
    
    
        for(int i=1;i<=G.vertexnum;i++)
        for(int j=1;j<=G.vertexnum;j++)G.arc[i][j]=INT_MAX;
    }
    for(int i=1;i<=G.arcnum;i++)
    {
    
    
    cout<<"请输入各条弧的两个节点v1,v2:"<<endl;
    cin>>c1>>c2;
    v1=Locate(c1,G);
    v2=Locate(c2,G);
    if(G.type==DG)
    {
    
    
        G.arc[v1][v2]=1;
    }
    else if(G.type==UDG)
    {
    
    
        G.arc[v1][v2]=G.arc[v2][v1]=1;
    }
    else if(G.type==DN)
    {
    
    
        cout<<"请输入该边的权值:"<<endl;
        int weight;
        cin>>weight;
        G.arc[v1][v2]=weight;
    }
    else if(G.type==UDN)
    {
    
    
        cout<<"请输入该边的权值:"<<endl;
        int weight;
        cin>>weight;
        G.arc[v1][v2]=weight;
        G.arc[v2][v1]=G.arc[v1][v2];
    }
    }
}
void print(Graph&G)
{
    
    
    if(G.type==DG)cout<<"图的类型:有向图"<<endl;
    else if(G.type==UDG)cout<<"图的类型:无向图"<<endl;
    else if(G.type==DN)cout<<"图的类型:有向网"<<endl;
    else if(G.type==UDN)cout<<"图的类型:无向网"<<endl;
    cout<<"图的顶点数目:"<<G.vertexnum<<endl;
    cout<<"图的弧的数目:"<<G.arcnum<<endl;
    cout<<"图的顶点集合:";
    for(int i=1;i<=G.vertexnum;i++)cout<<G.vertex[i]<<" ";
    cout<<endl;
    cout<<"图的邻接矩阵:"<<endl;
    bool flag=true;
        for(int i=1;i<=G.vertexnum;i++)
    {
    
    
        for(int j=1;j<=G.vertexnum;j++)
        {
    
    
            if(flag){
    
    flag=false;cout<<G.arc[i][j];}
            else {
    
    cout<<setw(4)<<G.arc[i][j]<<" ";}
        }
        flag=true;
        cout<<endl;
    }
}
//根据顶点在图中的相对位置返回顶点的值
char GetVertex(int index,Graph&G)
{
    
    
    if(index<=G.vertexnum)return G.vertex[index];
}
//对顶点v重新赋值
int putVertex(char v,char v1,Graph&G)//v为图中原有的顶点值,v1为新的顶点值
{
    
    
        int k=Locate(v,G);
        if(k!=-1)
        {
    
    
            G.vertex[k]=v1;
        }
        return OK;
}
//找到顶点v的第一个邻接点
int firstadjacent(char v,Graph&G)
{
    
    
    if(G.type==DG||G.type==UDG)
    {
    
    
        int k=Locate(v,G);
            for(int j=1;j<=G.vertexnum;j++)
                if(G.arc[k][j]!=0)return j;

    }
    else if(G.type==DN||G.type==UDN)
    {
    
    
        int k=Locate(v,G);
            for(int j=1;j<=G.vertexnum;j++)
                if(G.arc[k][j]!=Infinity)return j;
    }
    return -1;
}
//w是v的邻接顶点,找到v相对于w的下一个邻接顶点
int nextadjacent(char v,char w,Graph&G)
{
    
    
   int k1=Locate(v,G);
   int k2=Locate(w,G);
   if(G.type==DG||G.type==UDG)
   {
    
    
   for(int j=k2+1;j<=G.vertexnum;j++)
   {
    
    
       if(G.arc[k1][j]!=0)return j;
   }
   }
   else if(G.type==DN||G.type==UDN)
   {
    
    
       for(int j=k2+1;j<=G.vertexnum;j++)
   {
    
    
       if(G.arc[k1][j]!=Infinity)return j;
   }
   }
   return -1;
}
//在图中插入一个新的顶点
int Insert(char v,Graph&G)
{
    
    
    G.vertex[G.vertexnum+1]=v;
    if(G.type==DG||G.type==UDG)
    {
    
    
        for(int i=1;i<=G.vertexnum+1;i++)
        {
    
    
            G.arc[i][G.vertexnum+1]=G.arc[G.vertexnum+1][i]=0;
        }
    }
    else if(G.type==DN||G.type==UDN)
    {
    
    
        for(int i=1;i<=G.vertexnum+1;i++)
        {
    
    
            G.arc[i][G.vertexnum+1]=G.arc[G.vertexnum+1][i]=Infinity;
        }
    }
    G.vertexnum+=1;
}
//在图中删除一个顶点及与它相关联的边
int Delete(char v,Graph&G)
{
    
    
    int k=Locate(v,G);
    if(k==-1)return Error;
    for(int i=1;i<=G.vertexnum-1;i++)G.vertex[i]=G.vertex[i+1];
    for(int i=1;i<=G.vertexnum;i++)
        for(int j=1;j<=G.vertexnum-1;j++)
        G.arc[i][j]=G.arc[i][j+1];
    for(int i=1;i<=G.vertexnum-1;i++)
        for(int j=1;j<=G.vertexnum;j++)
        G.arc[i][j]=G.arc[i+1][j];
    G.vertexnum--;
}
//在图中插入一条弧
int Insertarc(char v,char w,Graph&G)
{
    
    
    int k1=Locate(v,G);
    int k2=Locate(w,G);
    if(k1<0||k2<0)return Error;
    if(G.type==DG)
    {
    
    
        G.arc[k1][k2]=1;
    }
    else if(G.type==UDG)
    {
    
    
        G.arc[k1][k2]=G.arc[k2][k1]=1;
    }
    else if(G.type==DN)
    {
    
    
        int weight;
        cout<<"请输入该边的权值:"<<endl;
        cin>>weight;
        G.arc[k1][k2]=weight;
    }
    else if(G.type==UDN)
    {
    
    
        int weight;
        cout<<"请输入该边的权值:"<<endl;
        cin>>weight;
        G.arc[k1][k2]=G.arc[k2][k1]=weight;
    }
    G.arcnum++;
}
//在图中删除一条弧
int Deletearc(char v,char w,Graph&G)
{
    
    
    int k1=Locate(v,G);
    int k2=Locate(w,G);
    if(k1<0||k2<0)return Error;
    if(G.type==DG)
    {
    
    
        G.arc[k1][k2]=0;
    }
    else if(G.type==UDG)
    {
    
    
        G.arc[k1][k2]=G.arc[k2][k1]=0;
    }
    else if(G.type==DN)
    {
    
    
        G.arc[k1][k2]=Infinity;
    }
    else if(G.type==UDN)
    {
    
    
        G.arc[k1][k2]=G.arc[k2][k1]=Infinity;
    }
    G.arcnum--;
}
bool visited[MAXSIZE];
int DFS(int index,Graph&G)
{
    
    
    visited[index]=true;
    cout<<G.vertex[index]<<" ";
    char v=GetVertex(index,G);
    for(index=firstadjacent(v,G);index!=-1;index=nextadjacent(v,GetVertex(index,G),G))
    if(!visited[index])DFS(index,G);
    return OK;
}
int DFS1(int index,Graph&G)
{
    
    
    visited[index]=true;
    cout<<G.vertex[index]<<" ";
    for(int i=1;i<=index;i++)
    {
    
    
        if(G.arc[index][i]!=0&&!visited[i])DFS1(i,G);
    }
}
//深度优先遍历图中顶点
int DFStraverse(Graph&G)
{
    
    
    for(int i=1;i<=G.vertexnum;i++)visited[i]=false;
    for(int i=1;i<=G.vertexnum;i++)
        if(!visited[i])DFS1(i,G);
        cout<<endl;
    return OK;
}
//广度优先遍历图中顶点
int BFStraverse(Graph&G)
{
    
    
    char v;
   queue<char>Q;
   for(int i=1;i<=G.vertexnum;i++)visited[i]=false;
   for(int i=1;i<=G.vertexnum;i++)
     if(!visited[i])
     {
    
    
       visited[i]=true;
       cout<<G.vertex[i]<<" ";
       v=G.vertex[i];
       Q.push(v);
       while(!Q.empty())
       {
    
    
         v=Q.front();
         Q.pop();
         for(int index=firstadjacent(v,G);index!=-1;index=nextadjacent(v,GetVertex(index,G),G))
           if(!visited[index])
           {
    
    
             visited[index]=true;
             cout<<G.vertex[index]<<" ";
             Q.push(G.vertex[index]);
           }
       }
     }
   cout<<endl;
}
int main()
{
    
    
    Graph G;
    create(G);
    print(G);
    cout<<"深度遍历:"<<endl;
    DFStraverse(G);
    cout<<"广度遍历:"<<endl;
    BFStraverse(G);
    return 0;
}