Implementation of Depth Traversal of Undirected Graph Represented by Adjacency Matrix
C language
Realization of Undirected Graph Represented by Adjacency Matrix
1. Define the adjacency matrix structure
#define VerType int //定义顶点信息的类型
#define MVNum 10 //定义数组的最大长度
typedef int ArcType; //假设边的权值类型为整型
//定义邻接矩阵结构
typedef struct{
//定义顶点表
VerType vexs[MVNum];
//定义邻接矩阵的边关系
ArcType arcs[MVNum][MVNum];
//定义顶点、弧/边的数量
int vexnum,arcnum;
}AMGraph;
2. Functions to create an adjacency matrix
Creating Undirected Networks with Adjacency Matrix Notation, Algorithm Ideas
- Enter the total number of vertices and total number of edges
- The information of the input points in turn is stored in the vertex table
*Initialize the adjacency matrix, so that each weight is initialized to 0- Construct an adjacency matrix
The space complexity of the adjacency matrix is O(n^2)
//创建邻接矩阵
void CreateUND(AMGraph *G){
//输入顶点数和边数
printf("please input the vexnum and arcnum:\n");
scanf("%d %d",&(G->vexnum),&(G->arcnum));
//初始化顶点表
printf("please input the info of vexs matrix:\n");
for (int i = 0; i < G->vexnum; i++)
{
scanf("%d",&(G->vexs[i]));
}
//初始化邻接矩阵
for (int i = 0; i < G->vexnum; i++)
{
for (int j = 0; j < G->vexnum; j++)
{
G->arcs[i][j]= 0;//边的权值均为0
}
}
//根据边/弧赋值矩阵
for (int k = 0; k < G->arcnum; k++)
{
// 一条边所依附的两个点
//输入点和权值
VerType v1,v2;
int w;
printf("please input the value of point v1 and point v2 and w:\n");
scanf("%d %d %d",&v1,&v2,&w);
//找寻这两个点的下标
int i = LocateG(*G,v1);
int j = LocateG(*G,v2);
if ((i!=-1) && (j!=-1))
{
G->arcs[i][j] = w;
G->arcs[j][i] = w;
}
}
}
//定位元素下标位置的函数
int LocateG(AMGraph p,VerType v){
for (int i = 0; i < p.vexnum; i++)
{
if(p.vexs[i]==v) return i;
}
return -1;
}
3. Depth traversal
method
- After visiting a certain starting point v of the graph, starting from v, visit any critical vertex w1 of it;
- Starting from w1, visit the vertex w2 that is adjacent to w1 but has not been visited yet;
- Then proceed from w2 to conduct a similar visit;
- This continues until all adjacent points have been visited.
- Then, take a step back, go back to the vertex that was just visited before and start again, and perform a visit similar to the above;
- If not, take another step back and search. Repeat the above process until all vertices in the connected graph have been visited
void DFS(AMGraph G,int v,int visited[]){
//访问第v+1个顶点，1<= v+1 <=vexnum
visited[v] = 1;
printf("%d\t",G.vexs[v]);//输出访问顶点的值
//依次检查邻接矩阵v所在的行
for (int w = 0; w < G.vexnum; w++)
{
if ((G.arcs[v][w]!=0) && (visited[w]==0))
{
DFS(G,w,visited);
}
}
}
4. Run the test
int main(){
AMGraph G;
AMGraph *p = &G;
//创建邻接矩阵
CreateUND(p);
//输出邻接矩阵
printf("\t");
for (int i = 0; i < G.vexnum; i++) printf("%d\t",i+1);
printf("\n");
for (int i = 0; i < G.vexnum; i++)
{
printf("%d\t",i+1);
for (int j = 0; j <G.vexnum; j++)
{
printf("%d\t",G.arcs[i][j]);
}
printf("\n");
}
//深度优先遍历图
//声明并初始化数组visited
int visited[G.vexnum];
for (int i = 0; i < G.vexnum; i++)
{
visited[i] = 0;
}
//输入起始点在顶点表中的下标0<=k<vexnum
printf("please input the index of initial point:\n");
int k;
scanf("%d",&k);
DFS(G,k,visited);
return 0;
}
The graph to be established is shown in the figure.
The input and output results of the operation are as follows:
