图的邻接矩阵是用两个数组来表示图
一个一维数组vexs[MAXVER];用来存储顶点元素
一个二维数组arc[MAXVER][MAXVER];用来存储图的边或者弧度以及证明其存在
无向图的的二维数组 主对角元素不存在 二维数组呈现对称分布
因为边是双向的。
有向图的二维数组 主对角元素也是不存在 不呈现对称分布
arc[i][j]=w i=j时 arc为0 存在边是为w 边不存在时定义为无穷∞ 意味大于所有权值的值 也就是一个极限值
图的定义
#include<iostream>
#include <iomanip>
using namespace std;
typedef char vertextype;//顶点类型
typedef int edgetype;//边缘权值
typedef int Status;
#define MAXVER 25//最大顶点数
#define INF 65535//代表无穷
#define NULL 0
//定义一个图结构
typedef struct Graph
{
vertextype vexs[MAXVER];//保存顶点元素
edgetype arc[MAXVER][MAXVER];//保存边界的权值
int numver, numedg;//顶点数目 边界数目
}MGhaph;
//输入图 其实就是给顶点表和边输入数据的过程
图的构造
Status CreatGhaph(MGhaph &G)
{
int i, j, k, w;
cout << "Please enter the number of verticesof the graph ： "<< endl;
cin >> G.numver;
cout << "Please enter the number of edges the graph ： " << endl;
cin >> G.numedg;
for (i = 0; i < G.numver; i++){
cout <<"Please enter the NO."<<i+1<<"%d name of vex : " << endl;
cin >> G.vexs[i];
}
cout << "Diagonal infinity ..."<< endl;
for (i = 0; i < G.numver; i++)
for (j = 0; j < G.numver; j++)
{
G.arc[i][j] = INF;//简单图 不循环
//cout << G.arc[i][j] << endl;//不理解为啥是1
}
cout << "...Diagonal infinity" << endl;
for (int k = 0; k < G.numedg; k++){
//因为具体哪条边存在不一定 所以选择性输入边
cout << "Enter the subscripts and weights from vertex vi to vertex vj : " << endl;
cin >> i>>j>>w;
/*cout << "Please enter the subscript j of the edge : " << endl;
cin >> j;
cout << "Please enter the weight from vertex "<<i<<" to vertex "<<j<<" : " << endl;
cin >> w;*/
G.arc[i][j] = w;
G.arc[j][i] = G.arc[i][j];//无向图 边的信息 是对称的 //有向图的话 无需设置
}
return 0;
}
有向图相较于无向图 它的每一个权值都要分别定义
输出图
Status DispGraph(MGhaph &G)
{
int i, j, k, w;
//输出顶点元素
for (i = 0; i < G.numver; i++){
cout << i + 1 << " : " << G.vexs[i] << endl;
}
//输出边界权值
for (i = 0; i < G.numver; i++){
for (j = 0; j < G.numver; j++){
if (G.arc[i][j] == INF){
cout.flags(ios::left);//设置对齐方式
cout << setw(6) << "∞";
}
else{
cout.flags(ios::left);
cout << setw(6) << G.arc[i][j];
}
}cout << endl;
}
return 0;
}
代码实现
所有部分
#include<iostream>
#include <iomanip>
using namespace std;
typedef char vertextype;//顶点类型
typedef int edgetype;//边缘权值
typedef int Status;
#define MAXVER 25//最大顶点数
#define INF 65535//代表无穷
#define NULL 0
//定义一个图结构
typedef struct Graph
{
vertextype vexs[MAXVER];//保存顶点元素
edgetype arc[MAXVER][MAXVER];//保存边界的权值
int numver, numedg;//顶点数目 边界数目
}MGhaph;
//输入图 其实就是给顶点表和边输入数据的过程
//例子 无向图的构造
Status CreatGhaph(MGhaph &G)
{
int i, j, k, w;
cout << "Please enter the number of verticesof the graph ： "<< endl;
cin >> G.numver;
cout << "Please enter the number of edges the graph ： " << endl;
cin >> G.numedg;
for (i = 0; i < G.numver; i++){
cout <<"Please enter the NO."<<i+1<<"%d name of vex : " << endl;
cin >> G.vexs[i];
}
cout << "Diagonal infinity ..."<< endl;
for (i = 0; i < G.numver; i++)
for (j = 0; j < G.numver; j++)
{
G.arc[i][j] = INF;//简单图 不循环
//cout << G.arc[i][j] << endl;//不理解为啥是1
}
cout << "...Diagonal infinity" << endl;
for (int k = 0; k < G.numedg; k++){
//因为具体哪条边存在不一定 所以选择性输入边
cout << "Enter the subscripts and weights from vertex vi to vertex vj : " << endl;
cin >> i>>j>>w;
/*cout << "Please enter the subscript j of the edge : " << endl;
cin >> j;
cout << "Please enter the weight from vertex "<<i<<" to vertex "<<j<<" : " << endl;
cin >> w;*/
G.arc[i][j] = w;
G.arc[j][i] = G.arc[i][j];//无向图 边的信息 是对称的 //有向图的话 无需设置
}
return 0;
}
//输出图
Status DispGraph(MGhaph &G)
{
int i, j, k, w;
//输出顶点元素
for (i = 0; i < G.numver; i++){
cout << i + 1 << " : " << G.vexs[i] << endl;
}
//输出边界权值
for (i = 0; i < G.numver; i++){
for (j = 0; j < G.numver; j++){
if (G.arc[i][j] == INF){
cout.flags(ios::left);
cout << setw(6) << "∞";
}
else{
cout.flags(ios::left);
cout << setw(6) << G.arc[i][j];
}
}cout << endl;
}
return 0;
}
//若图存在顶点u 返回图的顶点u的位置
Status LocateVex(MGhaph &G)
{
int i, j;
vertextype vex;
cout << "Please enter a vertex"<< endl;
cin >> vex;
for (i = 0; i < G.numver; i++)
{
if (G.vexs[i] == vex)
{
j = i;
}
else
{
continue;
}
}
return j;
}
//将图的顶点替换 略
//销毁图
Status DelGraph(MGhaph &G)
{
for (int i = 0; i < G.numver; i++)
{
free((void *)G.vexs[i]);
}
free(G.arc);
for (int i = 0; i < G.numver; i++)
for (int j = 0; j < G.numver; j++)
{
free((void *)G.arc[i][j]);
}
free(G.arc);
return 0;
}
//返回顶点V的邻接顶点 若没有则返回为空
Status FirstVex(MGhaph &G)
{
int i, j;
vertextype vex,fis;
cout << "Please enter a vertex" << endl;
cin >> vex;
for (i = 0; i < G.numver; i++){
if (G.vexs[i] == vex){
for (j = 0; j < G.numver; j++){
if (G.arc[i][j]!=INF){
//如果存在
cout << G.vexs[j] << endl;}
/*if (G.arc[j][i]!=INF){//有向图 加这一步
cout << G.vexs[j]<<endl;
}*/
}
}
}
return 0;
}
//新增顶点
Status ADDVex(MGhaph &G)
{
vertextype vex;
int k, w, edg_num, v;
if (G.numver >= MAXVER)
{
//静态的 一旦确定不能扩大
cout << "Graph memory is full and cannot be expanded ";
return NULL;
}
else
{
cout << "Please enter a new vertex :" << endl;
cin >> vex;
G.numver++;
G.vexs[G.numver - 1] = vex;
cout << "Please enter the number of new edges" << endl;//新增边的数目
cin >> edg_num;
G.numedg = G.numedg + edg_num;
for (int j = 0; j < G.numver; j++)
{
G.arc[j][G.numver-1]=G.arc[G.numver-1][j] = INF;//简单图 不循环
//cout << G.arc[i][j] << endl;
}
for (k = 0; k < edg_num; k++)
{
cout << "Enter the weights : " << endl;
cin >> w;
cout << "Enter the vertex of the edge" << endl;
cin >> v;
G.arc[v][G.numver - 1] = w;
G.arc[G.numver - 1][v] = G.arc[v][G.numver - 1];
}
}
return 0;
}
//删除相关顶点和弧 偷个懒
//增加弧
//删除弧
int main()
{
MGhaph G;
CreatGhaph(G);
DispGraph(G);
cout << LocateVex(G) << endl;
FirstVex(G);
ADDVex(G);
DispGraph(G);
DelGraph(G);
DispGraph(G);
return 0;
}
