图论（三）--深度优先搜索（DFS）

基于算法导论图算法-深度优先搜索

• 题目描述
• 问题分析
• 源代码
• 结果截图

题目描述

深度优先搜索（用递归和栈分别实现）：对图进行遍历，得到连通分支数，并求出每个顶点的发现时间和完成时间

问题分析

与广搜相同，每个顶点白色->灰色->黑色

伪代码

递归实现（栈实现伪代码未提供，可参见源代码）

源代码

void DFS(Graph G);//dfs图void DFS_VISIT(Graph G, Vertex u);//从某个结点dfs递归实现void DFS_visit_stack(Graph G, Vertex v);//深搜用栈实现void print_path(Graph G, Vertex v);//打印一个点的深搜路径，沿着pred向上找void print_path_everyPoint(Graph G);//打印每个顶点的深搜路径

图的顶点数据结构有所变化（添加发现时间和完成时间）

struct VertexRecord {    Vertex pred;//先驱结点    int in_degree;//入度     int out_degree;//出度     int color;//顶点状态    int dist;//距离源点的距离    int discover_time;//深搜发现时间    int finish_time;//深搜时的结束时间    List  adjto;//指向第一个邻接结点的指针};

#include<stack>void print_path(Graph G, Vertex v) {//打印一个点的深搜路径，沿着pred向上找    if (G->vertices[v].pred != -1) {        print_path(G, G->vertices[v].pred);    }    printf(" %d", v);}void print_path_everyPoint(Graph G) {//打印每个顶点的深搜路径    for (int i = 0; i < G->vexnum; i++) {        printf("顶点%d的深搜路径为：",i);         print_path(G, i);        printf("\n");    }}void print_time_dfs(Graph G) {//打印每个顶点的发现时间和结束时间     for (int i = 0; i < G->vexnum; i++) {        printf("顶点%d发现时间:%d,结束时间为：%d", i, G->vertices[i].discover_time, G->vertices[i].finish_time);        printf("\n");    }}int Time;//int count_finishTime_descreasing = VertexNum;void DFS_VISIT(Graph G, Vertex u) {//递归实现深搜    Time = Time + 1;    G->vertices[u].discover_time = Time;    //if (G->vertices[u].pred == -1) G->vertices[u].dist = 0;    //else G->vertices[u].dist = G->vertices[G->vertices[u].pred].dist + 1;//权为1计算，此处为距离的计算    G->vertices[u].color = 1;//gray    PtrToNode ptr = G->vertices[u].adjto;    while (ptr != NULL) {        Vertex v = ptr->adjvex;        if (G->vertices[v].color == 0) {            G->vertices[v].pred = u;            DFS_VISIT(G, v);        }        ptr = ptr->next;    }    G->vertices[u].color = 2;//black    Time = Time + 1;    G->vertices[u].finish_time = Time;}void DFS_visit_stack(Graph G, Vertex v) {//深搜用栈实现    PtrToNode ptr;    stack<int> S;    S.push(v);    //G->vertices[v].dist = 0;    G->vertices[v].color = 1;//灰色    G->vertices[v].discover_time = ++Time;    printf("\n%d", v);    while (!S.empty()) {        Vertex u = S.top();        ptr = G->vertices[u].adjto;        while (ptr != NULL) {            if (G->vertices[ptr->adjvex].color == 0) {                S.push(ptr->adjvex);                //G->vertices[ptr->adjvex].dist = G->vertices[u].dist + 1;//权为1计算，此处为距离的计算                G->vertices[ptr->adjvex].color = 1;//灰色                Time++;                G->vertices[ptr->adjvex].discover_time = Time;                G->vertices[ptr->adjvex].pred = u;                printf(" %d", ptr->adjvex);                break;            }            ptr = ptr->next;        }        if (S.top() == u) {            G->vertices[u].color = 2;//黑色            Time++;            G->vertices[u].finish_time = Time;            //finishTime_descreasing[--count_finishTime_descreasing] = u;            S.pop();        }    }    printf("\n");}void DFS(Graph G) {    int count = 0;    for (int i = 0; i < G->vexnum; i++) {        G->vertices[i].color = 0;//白色        G->vertices[i].pred = -1;    }    Time = 0;    for (int i = 0; i < G->vexnum; i++) {        if (G->vertices[i].color == 0) {            //DFS_VISIT(G, i);            DFS_visit_stack(G, i);            count++;        }    }    printf("共有%d个连通分量\n", count);    print_path_everyPoint(G);//打印每个顶点的深搜路径     print_time_dfs(G);//打印每个顶点距离0的距离 }int main() {    //有向图的随机生成（20个顶点，100左右的边，可以进行修改）    //CreateRandomDirectGraph();    //Graph G = CreateDirectGraph();    //无向边的随机生成（20个顶点，50左右的边）    CreateRandomUndirectGraph();    Graph G = CreateUndirectGraph();    printf("打印图结构：\n");     print_graph(G);//打印图    //printf("\n打印各顶点入度和出度：\n");    //print_VertexDegree(G);//打印顶点度数    //printf("\n打印每条边的权值：\n");    //print_EdgeWeight(G);//打印边权    //printf("\n下面是bfs:\n");    //BFS(G, 0);    printf("\n下面是dfs:");    DFS(G);    return 0;   } 

结果截图