Depth-first traversal of graph DFS (adjacency matrix implementation) c language

The traversal of the graph refers to starting from a certain vertex in the graph and visiting each vertex in the graph according to a certain strategy. Each vertex can be visited only once.

Depth-first traversal is also called depth-first search.

Its traversal rules: first select an initial vertex, and then specify a direction, such as traversing to the right. So go straight to the right, mark the visited vertices, and after visiting along the right, backtrack to the previously visited vertices to find out if there are any vertices that have not been visited. When all vertices are visited, the traversal is completed.

DFS is a process of recursively visiting all vertices in a graph, similar to a preorder traversal of a tree.

When implementing with an adjacency matrix, pay attention to setting a boolean type of access flag array   visited

For a graph with m vertices and e edges, since the adjacency matrix is ​​a two-dimensional array, the time complexity is O(㎡)

The specific implementation code is as follows,

#include<stdio.h>
#include<stdlib.h>
//邻接矩阵结构
typedef char VertexType;
typedef int EdgeType;

#define MAX 10
#define INFINITY 65535
#define TRUE 1
#define FALSE 0
typedef int Boole;  //布尔类型 存储TRUE FALSE
Boole visited[MAX];    //访问标志数组 

typedef struct
{
	VertexType vexs[MAX];   //顶点表 
	EdgeType arc[MAX][MAX];   //邻接矩阵 可看作边表   
	int numVertexes,numEdges;
	int GraphType;  //图的类型  无向0,有向1	
}MGraph;

//构造图   有向图和无向图 
void create(MGraph *G)
{
	int i,j,k,w;
	printf("请输入顶点数和边数:\n");
	scanf("%d%d",&G->numVertexes,&G->numEdges);
	fflush(stdin);
	for(i=0;i<G->numVertexes;i++)     //建立顶点表
	{ 
		printf("\n第%d个顶点",i+1);
		scanf("%c",&G->vexs[i]);
		getchar();
	}
	
	for(i=0;i<G->numVertexes;i++)   //矩阵初始化 
		for(j=0;j<G->numVertexes;j++)
			G->arc[i][j]=INFINITY;
			
	for(k=0;k<G->numEdges;k++)
	{
		printf("输入边（Vi,Vj）的上下标i,j和权w(空格隔开)：");
		scanf("%d%d%d",&i,&j,&w);
		G->arc[i][j]=w;
		if(G->GraphType==0)      //此时为无向图   有向图与无向的区别就只是这一行代码的有无 
		G->arc[j][i]=G->arc[i][j];
	}			 
} 

void Output(MGraph *G)     //输出邻接矩阵 
{
	int i,j,count=0;
	for(i=0;i<G->numVertexes;i++)
		printf("\t%c",G->vexs[i]);
	printf("\n");
	for(i=0;i<G->numVertexes;i++)
	{
		printf("%4c",G->vexs[i]);
		for(j=0;j<G->numVertexes;j++)
		{	
			
				printf("\t%d",G->arc[i][j]);
				count++;
				if(count%G->numVertexes==0)
				printf("\n");	
		} 
    }	 
 } 




/*深度优先遍历*/



//深度优先递归算法
void DFS(MGraph G,int i)
{
	int j;
	visited[i]=TRUE;   //被访问的标记 
	printf("%c->",G.vexs[i]);
	for(j=0;j<G.numVertexes;j++)
	{
		if(G.arc[i][j]==1&&!visited[j])   //边(i,j)存在且j顶点未被访问，递归 
			DFS(G,j);
	} 
}

//深度优先遍历
void DFStraverse(MGraph G)
{
	
	int i;
	for(i=0;i<G.numVertexes;i++)
		visited[i]=FALSE;
	for(i=0;i<G.numVertexes;i++)
			if(!visited[i])
				DFS(G,i);		
				
} 


int main()
{
	MGraph G;
	int i,j;
	printf("输入生成图的类型(无向图0/有向图1)：");
	scanf("%d",&G.GraphType);
	create(&G);	
	printf("邻接矩阵数据如下：\n");
	Output(&G);
	printf("\n");
	DFStraverse(G);
	printf("\n图遍历完毕");
	return 0;	 
}