邻接矩阵无向图 有无环 C实现 (dfs)

核心思想:

       根据图与树的关系 到 图与连通分量关系 知 

           无环时候： 顶点数 -边数  =  树个数 （连通分量数）

           有环时候：顶点数-边数 < 树个数（连通分量数）   

         连通分量数可以在dfs中求得    

void dfs_trvsal(Graph g){int i;for (i = 0; i < g.vex_num; i++) {visited[i] = FALSE;}link_component = 0;for (i = 0; i < g.vex_num; i++) {if (!visited[i]) {link_component++;  //图连通的话 该for循环只进行一次 就可以遍历整个图了 连通分量也就是1dfs(g, i);}}}

完整代码实现:

#include<stdio.h>#include<stdlib.h>#include<ctype.h>#define MAXVEX 100#define INFINITY 65535#define TRUE 1#define FALSE 0#define Bool int Bool visited[MAXVEX];int link_component; //连通分量的数量 typedef int EdgeType;typedef char VertexType;typedef struct Graph {VertexType vex[MAXVEX];EdgeType edge[MAXVEX][MAXVEX];int vex_num, edge_num;}Graph;void init_graph(Graph *g){int i, j;for (i = 0; i < g->vex_num; i++) {for (j = 0; j < g->vex_num; j++) {if (i == j) {g->edge[i][j] = 0;}elseg->edge[i][j] = INFINITY;}}}char read_char(){char ch;do {ch = getchar();} while (!isalpha(ch));return ch;}int get_pos(Graph g, char ch){int i;for (i = 0; i < g.vex_num; i++) {if (g.vex[i] == ch)return i;}return -1;}void create_graph(Graph *g){int i, w, k;//printf("请输入顶点数与边数:\n");scanf("%d%d", &g->vex_num, &g->edge_num);init_graph(g);// 初始化//printf("请输入顶点信息:\n");for (i = 0; i < g->vex_num; i++) {g->vex[i] = read_char();}//printf("请输入边的信息:\n");char c1, c2;int p1, p2;for (k = 0; k < g->edge_num; k++) {c1 = read_char();c2 = read_char();scanf("%d", &w);p1 = get_pos(*g, c1);p2 = get_pos(*g, c2);g->edge[p1][p2] = w;g->edge[p2][p1] = g->edge[p1][p2];}}void print_graph(Graph g){int i, j;for (i = 0; i < g.vex_num; i++) {for (j = 0; j < g.vex_num; j++) {if (g.edge[i][j] == INFINITY)printf("%5c", '*');else {printf("%5d", g.edge[i][j]);}}printf("\n");}}void dfs(Graph g, int i){int j;visited[i] = TRUE;printf("%c ", g.vex[i]);for (j = 0; j < g.vex_num; j++) {if (!visited[j] && g.edge[i][j] != INFINITY && i != j) {dfs(g, j);visited[j] = TRUE;}}}void dfs_trvsal(Graph g){int i;for (i = 0; i < g.vex_num; i++) {visited[i] = FALSE;}link_component = 0;for (i = 0; i < g.vex_num; i++) {if (!visited[i]) {link_component++;dfs(g, i);}}}int main(){int i;Graph g;create_graph(&g);//print_graph(g);dfs_trvsal(g);printf("\n");if ((link_component + g.edge_num) > g.vex_num) { // 核心printf("有环.");}else {printf("无环.\n");}if (link_component == 1) {printf("图连通.");}else {printf("图不连通.");}getchar();getchar();return 0;}