图的储存结构之邻接矩阵

邻接矩阵是表示图中相邻顶点之间关系的矩阵。

说白了就是我们有一个图，我们利用矩阵来表示这个图顶点之间的关系。

图的特性：

1.有向与无向：有向就是顶点从一个顶点指向另外一个顶点。下面两个图分别就是有向与无向

2.有权或者无权：就是顶点之间边的权值。下面两个图就是有权与无权。（边上带权的图为带权图，也称网）

把上面的两个图分别用矩阵表示：

第一个为无权无向图。0表示顶点间并未相互连接，1表示两顶点有连接。在无向无权矩阵图中，该表关于角对角线对称。

#include<iostream>using namespace std;typedef char node_type;const int MAX_NUM = 100;typedef struct Graph {node_type vetex[MAX_NUM];//节点信息int arcs[MAX_NUM][MAX_NUM];//矩阵，用于储存权值，如果为有向的话类型应为floatint vetexs, brim;//节点数，边数};void g_create(Graph &graph) {int i, j, k;cout << "请输入节点数与边数（空格隔开）：";cin >> graph.vetexs >> graph.brim;cout << "创建节点，一次输入一个字符，回车结束：" << endl;for (i = 0; i < graph.vetexs; cin >> graph.vetex[i++]);for (i = 0; i < graph.vetexs; ++i)for (j = 0; j < graph.vetexs; ++j)graph.arcs[i][j] = 0;    //初始化矩阵cout << "请输入边(vi,vj)的下边i,j（空格隔开）:" << endl;for (k = 0; k < graph.brim; ++k) {cin >> i >> j;graph.arcs[i][j] = 1;graph.arcs[j][i] = graph.arcs[i][j];//无向图直接倒置就行}}void main() {Graph graph;g_create(graph);cout << "输出图的矩阵图：" << endl;for(int i=0;i<graph.vetexs;++i)for (int j = 0; j < graph.vetexs; ++j) {cout << graph.arcs[i][j] << " ";if (j == graph.vetexs - 1)cout << endl;}cout << "输出图的边：" << endl;for (int i = 0; i < graph.vetexs; ++i)//输出节点的边，因为无向图的矩阵关于对角线对称，只需遍历一半的数组for (int j = 0; j < i; ++j)if (graph.arcs[i][j] == 1)cout << graph.vetex[i] << "-" << graph.vetex[j] << endl;system("pause");}

运行结果

第二个为有权有向图。0表示顶点不能指向自身，∞表示顶点间不存在连接

#include<iostream>using namespace std;typedef int node_type;const int MAX_NUM = 100;const int Infinity = 65535;typedef struct Graph {node_type vetex[MAX_NUM];//节点信息float arcs[MAX_NUM][MAX_NUM];//矩阵，用于储存权值，如果为有向的话类型应为floatint vetexs, brim;//节点数，边数};void g_create(Graph &graph) {int i, j, k;float w;cout << "请输入节点数与边数（空格隔开）：";cin >> graph.vetexs >> graph.brim;cout << "创建节点，一次输入一个字符，回车结束：" << endl;for (i = 0; i < graph.vetexs; cin >> graph.vetex[i++]);for (i = 0; i < graph.vetexs; ++i)for (j = 0; j < graph.vetexs; ++j) {    //初始化if (i == j)graph.arcs[i][j] = 0;elsegraph.arcs[i][j] = Infinity;}cout << "请输入边(vi,vj)的下边i,j（空格隔开）以及权值:" << endl;for (k = 0; k < graph.brim; ++k) {cin >> i >> j >> w;graph.arcs[i][j] = w;}}void main() {Graph graph;g_create(graph);cout << "输出图的矩阵图：" << endl;for(int i=0;i<graph.vetexs;++i)for (int j = 0; j < graph.vetexs; ++j) {float tmp = graph.arcs[i][j];if (tmp == Infinity)cout << "∞" << " ";elsecout << tmp << " ";if (j == graph.vetexs - 1)cout << endl;}cout << "输出图的边：" << endl;for (int i = 0; i < graph.vetexs; ++i)for (int j = 0; j < graph.vetexs; ++j)if (graph.arcs[i][j] != 0 && graph.arcs[i][j] != Infinity)cout << graph.vetex[i] << "->" << graph.vetex[j] <<":" << graph.arcs[i][j] << endl;system("pause");}

运行结果