数据结构实战

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本文作者:李德强
          第五节 深度优先搜索
 
 

        图的顶点访问可以使用深度优先和广度优先两种搜索方法。深度优先即先访问一个顶点,接着访问这个顶点所能连通的其它顶点,而在多个连通的顶点中优先访问它们的连通节点。例如下图:

        这个无向连通图如果从节点0开始,使用深度优先搜索结果为:

0 -> 1 -> 3 -> 4 -> 7 -> 2 -> 5 -> 8 -> 11 -> 6 -> 9 -> 10 -> 12

        深度优先的实现算法如下:

//深度优先搜索
bool graph_depth_first_search(s_graph *graph)
{
	if (graph == null)
	{
		return false;
	}

	//设置顶点已访问标志
	bool visited[graph->size];
	for (int i = 0; i < graph->size; i++)
	{
		visited[i] = false;
	}

	//访问所有的顶点
	for (int i = 0; i < graph->size; i++)
	{
		//深度优先访问顶点
		graph_dfs(graph, i, visited);
	}

	return true;
}

//深度优先访问顶点递归算法
void graph_dfs(s_graph *graph, int v_ind, bool *visited)
{
	//如果此顶点已被访问,则直接返回
	if (visited[v_ind])
	{
		return;
	}

	//设置此顶点为已访问
	visited[v_ind] = true;

	//调用访问回调函数访问此节点
	graph->visit_vertex(graph->vertex[v_ind]);

	//取得下一条边
	s_arccell *ac = graph->vertex[v_ind].arccel_first;
	//循环所有关联i的边
	while (ac != null)
	{
		//深度优先访问
		graph_dfs(graph, ac->i_index, visited);

		//如果还有下一条j相关的边
		s_arccell *ac_p = graph->vertex[ac->j_index].arccel_first;
		while (ac_p != null)
		{
			//深度优先访问
			graph_dfs(graph, ac_p->j_index, visited);
			ac_p = ac_p->next_j;
		}

		//下一条i边
		ac = ac->next_i;
	}
}

        main函数中构建图的顶点和边:

#include <stdio.h>
#include <stdlib.h>
#include "graph.h"

void visit_int(int *i)
{
	if (i != null)
	{
		printf("%d ", *i);
	}
}

int main(int argc, char **args)
{
	//邻接表
	s_graph graph;
	graph_init(&graph, 13, &visit_int, &visit_int);

	//顶点数据项
	int *t0 = (int *) malloc(sizeof(int));
	int *t1 = (int *) malloc(sizeof(int));
	int *t2 = (int *) malloc(sizeof(int));
	int *t3 = (int *) malloc(sizeof(int));
	int *t4 = (int *) malloc(sizeof(int));
	int *t5 = (int *) malloc(sizeof(int));
	int *t6 = (int *) malloc(sizeof(int));
	int *t7 = (int *) malloc(sizeof(int));
	int *t8 = (int *) malloc(sizeof(int));
	int *t9 = (int *) malloc(sizeof(int));
	int *t10 = (int *) malloc(sizeof(int));
	int *t11 = (int *) malloc(sizeof(int));
	int *t12 = (int *) malloc(sizeof(int));
	//顶点数据
	*t0 = 0;
	*t1 = 1;
	*t2 = 2;
	*t3 = 3;
	*t4 = 4;
	*t5 = 5;
	*t6 = 6;
	*t7 = 7;
	*t8 = 8;
	*t9 = 9;
	*t10 = 10;
	*t11 = 11;
	*t12 = 12;

	//设置顶点数据
	graph_set_vertex(&graph, 0, t0);
	graph_set_vertex(&graph, 1, t1);
	graph_set_vertex(&graph, 2, t2);
	graph_set_vertex(&graph, 3, t3);
	graph_set_vertex(&graph, 4, t4);
	graph_set_vertex(&graph, 5, t5);
	graph_set_vertex(&graph, 6, t6);
	graph_set_vertex(&graph, 7, t7);
	graph_set_vertex(&graph, 8, t8);
	graph_set_vertex(&graph, 9, t9);
	graph_set_vertex(&graph, 10, t10);
	graph_set_vertex(&graph, 11, t11);
	graph_set_vertex(&graph, 12, t12);

	//插入边数据
	graph_insert_arccell(&graph, 0, 1, 0, null);
	graph_insert_arccell(&graph, 0, 2, 0, null);
	graph_insert_arccell(&graph, 1, 3, 0, null);
	graph_insert_arccell(&graph, 1, 4, 0, null);
	graph_insert_arccell(&graph, 2, 5, 0, null);
	graph_insert_arccell(&graph, 2, 6, 0, null);
	graph_insert_arccell(&graph, 3, 4, 0, null);
	graph_insert_arccell(&graph, 3, 7, 0, null);
	graph_insert_arccell(&graph, 5, 8, 0, null);
	graph_insert_arccell(&graph, 6, 9, 0, null);
	graph_insert_arccell(&graph, 6, 10, 0, null);
	graph_insert_arccell(&graph, 8, 11, 0, null);
	graph_insert_arccell(&graph, 10, 11, 0, null);
	graph_insert_arccell(&graph, 10, 12, 0, null);

	//显示顶点和边的关系
	graph_visit(&graph);

	//深度优先遍历图
	graph_depth_first_search(&graph);

	//销毁邻接表
	graph_destroy(&graph);

	return 0;
}

        运行结果:

0 1 3 4 7 2 5 8 11 6 9 10 12 

        本例代码:

code path   chapter.06/e.g.6.5/

https       https://github.com/magicworldos/datastructure.git
git         git@github.com:magicworldos/datastructure.git
subverion   https://github.com/magicworldos/datastructure

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