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图的基本操作的实现

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图的三种表示方法

图的数组表示法

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#include<iostream>
#include <stdio.h>
#include <stdlib.h>
using namespace std;
#define MAX_NUM 20
#define INFINITY INT_MAX
typedef int VRType;
typedef char VertexType;
typedef enum{DG , DN , UDG , UDN} GraphKind;  //{有向图，有向网，无向图，无向网}

typedef struct ArcCell{
    VRType adj; // 无权图是0和1, 有权图是权值
    //InfoType *info;
}ArcCell , AdjMatrix[MAX_NUM][MAX_NUM];

typedef struct {
    VertexType vexs[MAX_NUM];   //顶点名称
    AdjMatrix arcs;             //邻接矩阵
    int vexnum , arcnum;        //顶点数 和 弧数
    //GraphKind kind;             //图的类型
}MGraph;

// 返回顶点在图中的位置 int
int LocateVex(MGraph G , VertexType v){
    for(int i = 0 ; i<G.vexnum ; ++i){
        if(G.vexs[i] == v){
            return i;
        }
    }
}

// 无向网  
void CreateUDN(MGraph &G){
    //scanf(&G.kind);
    cout<<"构造无向网："<<endl;
    cout<<"输入图的顶点数和边数："<<endl;
    cin>>G.vexnum>>G.arcnum;
    cout<<"输入顶点名称："<<endl;
    for(int i = 0 ; i<G.vexnum ; ++i){
        cin>>G.vexs[i];
    }
    for(int i = 0 ; i<G.vexnum ; ++i){
        for(int j = 0 ; j<G.vexnum ; ++j){
            G.arcs[i][j].adj = INFINITY;
        }
    }
    cout<<"输入顶点及其权值："<<endl;
    for(int k = 0 ; k<G.arcnum ; ++k){
        VertexType v1 , v2;
        int w;
        cin>>v1>>v2>>w;
        int i = LocateVex(G , v1);
        int j = LocateVex(G , v2);
        G.arcs[i][j].adj = w;
        G.arcs[j][i].adj = G.arcs[i][j].adj;
    }
}

// 有向网 (其实就是无向图去掉了最后一个语句)
void CreateDN(MGraph &G){
    cout<<"构造有向网："<<endl;
    cout<<"输入图的顶点数和边数："<<endl;
    cin>>G.vexnum>>G.arcnum;
    cout<<"输入顶点名称："<<endl;
    for(int i = 0 ; i<G.vexnum ; ++i){
        cin>>G.vexs[i];
    }
    for(int i = 0 ; i<G.vexnum ; ++i){
        for(int j = 0 ; j<G.vexnum ; ++j){
            G.arcs[i][j].adj = INFINITY;
        }
    }
    cout<<"输入顶点及其权值："<<endl;
    for(int k = 0 ; k<G.arcnum ; ++k){
        VertexType v1 , v2;
        int w;
        cin>>v1>>v2>>w;
        int i = LocateVex(G , v1);
        int j = LocateVex(G , v2);
        G.arcs[i][j].adj = w;
        //G.arcs[j][i].adj = G.arcs[i][j].adj;
    }
}

// 图的打印
void print(MGraph G){
    for(int i = 0 ; i<G.vexnum ; ++i){
        for(int j = 0 ; j<G.vexnum ; ++j){
            if(G.arcs[i][j].adj != INFINITY){
                cout<<'('<<G.vexs[i]<<','<<G.vexs[j]<<')'<<' ';
            }
        }
        cout<<endl;
    }
    cout<<endl;
    for(int i = 0 ; i<G.vexnum ; ++i){
        for(int j = 0 ; j<G.vexnum ; ++j){
            if(G.arcs[i][j].adj == INFINITY){
                cout<<0<<' ';
            }
            else cout<<G.arcs[i][j].adj<<' ';
        }
        cout<<endl;
    }
}

void InsertVex(MGraph &G , VertexType v){
    G.vexnum++;
    G.vexs[G.vexnum - 1] = v;
    for(int i = 0 ; i<G.vexnum ; ++i){
        G.arcs[i][G.vexnum - 1].adj = INFINITY;
    }
    for(int j = 0 ; j<G.vexnum ; ++j){
        G.arcs[G.vexnum - 1][j].adj = INFINITY;
    }
}

void InsertArc(MGraph &G , VertexType v , VertexType w){
    int i = LocateVex(G , v);
    int j = LocateVex(G , w);
    if(i == -1){
        G.vexnum++;
        G.vexs[G.vexnum - 1] = v;
        for(int i = 0 ; i<G.vexnum ; ++i){
            G.arcs[i][G.vexnum - 1].adj = INFINITY;
        }
        for(int j = 0 ; j<G.vexnum ; ++j){
            G.arcs[G.vexnum - 1][j].adj = INFINITY;
        }
        i = G.vexnum - 1;
    }
    if(j == -1){
        G.vexnum++;
        G.vexs[G.vexnum - 1] = w;
        for(int i = 0 ; i<G.vexnum ; ++i){
            G.arcs[i][G.vexnum - 1].adj = INFINITY;
        }
        for(int j = 0 ; j<G.vexnum ; ++j){
            G.arcs[G.vexnum - 1][j].adj = INFINITY;
        }
        j = G.vexnum - 1;
    }
    G.arcs[i][j].adj = 1;
    G.arcs[j][i].adj = 1;
    G.arcnum++;
}


bool DeleteVex(MGraph &G , VertexType v){
    int l = LocateVex(G , v);
    cout<<l<<endl;
    if(l == -1){
        cout<<"No such point!"<<endl;
        return false;
    }
    for(int i = 0 ; i<G.vexnum ; ++i){
        if(G.arcs[i][l].adj != INFINITY){
            G.arcs[i][l].adj = INFINITY;
            G.arcnum--;
        }
    }
    for(int j = 0 ; j<G.vexnum ; ++j){
        if(G.arcs[l][j].adj != INFINITY){
            G.arcnum--;
            G.arcs[l][j].adj = INFINITY;
        }
    }
    for(int i = l+1 ; i<G.vexnum ; ++i){
        for(int j = 0 ; j<G.vexnum ; ++j){
            G.arcs[i-1][j].adj = G.arcs[i][j].adj;
        }
    }
    for(int j = l+1 ; j<G.vexnum ; ++j){
        for(int i = 0 ; i<G.vexnum - 1 ; ++i){
            G.arcs[i][j-1].adj = G.arcs[i][j].adj;
        }
    }
    for(int i = l+1 ; i<G.vexnum ; ++i){
        G.vexs[i-1] = G.vexs[i];
    }
    G.vexnum--;

    return true;
}

bool DeleteArc(MGraph &G , VertexType v , VertexType w){
    int i = LocateVex(G , v);
    int j = LocateVex(G , w);
    G.arcnum--;
    G.arcs[i][j].adj = INFINITY;
    G.arcs[j][i].adj = INFINITY;
}


int main()
{
    MGraph G;
    CreateDN(G);
    print(G);
}

图的邻接表表示法

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#include<iostream>
#include <stdio.h>
#include <stdlib.h>
using namespace std;
#define MAX_NUM 20
#define INFINITY INT_MAX
typedef char VertexType;

//表结点
typedef struct ArcNode {
    int adjvex;             //表示头结点的邻接点的序号
    ArcNode *nextarc;       //指向表示头结点的下一个邻接点
    int weight;             //无权图是0,1 有权图是权值
    //InfoType *info;
}ArcNode;

//头结点
typedef struct VNode {
    VertexType data;        //表示头结点的data
    ArcNode *firstarc;      //指向头结点的第一个邻接点

}VNode , AdjList[MAX_NUM];

typedef struct{
    AdjList vertices;       //表结点的数组
    int vexnum , arcnum;    //顶点数和边数

}ALGraph;

int LocateVex(ALGraph *G , VertexType v){
    for(int i = 0 ; i<G->vexnum ; ++i){
        if(G->vertices[i].data == v){
            return i;
        }
    }
}

void Create(ALGraph *G){
    cout<<"输入图的顶点数和边数："<<endl;
    cin>>G->vexnum>>G->arcnum;
    cout<<"输入顶点信息："<<endl;
    for(int i = 0 ; i<G->vexnum ; ++i){
        cin>>G->vertices[i].data;
        G->vertices[i].firstarc = NULL;
    }
    cout<<"输入(v1,v2,w)："<<endl;
    for(int k = 0 ; k<G->arcnum ; ++k){
        VertexType v1 , v2;
        int w;
        cin>>v1>>v2>>w;
        int i = LocateVex(G , v1);
        int j = LocateVex(G , v2);
        ArcNode *p = (ArcNode *)malloc(sizeof(ArcNode));
        p->adjvex = j;
        p->nextarc = G->vertices[i].firstarc;
        G->vertices[i].firstarc = p;
        p->weight = w;


        //下面代码无向图有，有向图无
        p = (ArcNode *)malloc(sizeof(ArcNode));
        p->adjvex = i;
        p->nextarc = G->vertices[j].firstarc;
        G->vertices[j].firstarc = p;
        p->weight = w;
    }

    //打印图
    for(int i = 0 ; i<G->vexnum ; ++i){
        ArcNode *p = G->vertices[i].firstarc;
        while(p){
            cout<<'('<<G->vertices[i].data<<','<<G->vertices[p->adjvex].data<<','<<p->weight<<')'<<' ';
            p = p->nextarc;
        }
        cout<<endl;
    }
}

int main()
{
    ALGraph G;
    Create(&G);
}

图的十字链表表示法

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#include<iostream>
#include <stdio.h>
#include <stdlib.h>
using namespace std;
#define MAX_NUM 20
#define INFINITY INT_MAX
typedef char VertexType;

//表结点
typedef struct ArcBox{
    int tailvex , headvex;      //表示弧尾 和 弧头 的下标位置
    ArcBox *hlink , *tlink;     //hlink 指向头结点入度相同的表结点(即弧头相同),
                                //tlink指向弧尾相同的表结点
    //InfoType *info;
}ArcBox;

typedef struct VexNode{
    VertexType data;            //头结点的数据信息
    ArcBox *fristin , *fristout;// fristin 指向头结点的第一个入度的表结点，
                                // fristout指向头结点的第一个出度的表结点
}VexNode;

typedef struct {
    VexNode xlist[MAX_NUM];
    int vexnum , arcnum;        //顶点数和边数
}OLGraph;


int LocateVex(OLGraph G , VertexType v){
    for(int i = 0 ; i<G.vexnum ; ++i){
        if(G.xlist[i].data == v){
            return i;
        }
    }
}

//构造有向图
void CreateDG(OLGraph &G){
    cout<<"输入图的顶点数和边数："<<endl;
    cin>>G.vexnum>>G.arcnum;
    cout<<"输入图的头结点的数据信息："<<endl;
    for(int i = 0 ; i<G.vexnum ; ++i){
        cin>>G.xlist[i].data;
        G.xlist[i].fristin = NULL;
        G.xlist[i].fristout = NULL;
    }
    cout<<"输入(v1,v2)："<<endl;
    for(int k = 0 ; k<G.arcnum ; ++k){
        VertexType v1 , v2;
        cin>>v1>>v2;
        int i = LocateVex(G , v1);
        int j = LocateVex(G , v2);
        ArcBox *p = (ArcBox *)malloc(sizeof(ArcBox));
        p->tailvex = i;
        p->headvex = j;
        p->hlink = G.xlist[j].fristin;
        p->tlink = G.xlist[i].fristout;
        G.xlist[j].fristin = G.xlist[i].fristout = p;
    }
    for(int i = 0 ; i<G.vexnum ; ++i){
        ArcBox *p =G.xlist[i].fristout;
        while(p){
            cout<<'('<<G.xlist[i].data<<"->"<<G.xlist[p->headvex].data<<')'<<' ';
            p = p->tlink;
        }
        cout<<endl;
    }
    cout<<"---------------------------------------------"<<endl;
    for(int i = 0 ; i<G.vexnum ; ++i){
        ArcBox *p = G.xlist[i].fristin;
        while(p){
            cout<<'('<<G.xlist[i].data<<"<-"<<G.xlist[p->tailvex].data<<')'<<' ';
            p = p->hlink;
        }
        cout<<endl;
    }
}

int main()
{
    OLGraph G;
    CreateDG(G);
}