BFS—— Breadth First Search 广度优先算法

Breadth First Search

              

        　BFS家伙还是很有用的，特地从wiki扒了一个动态的图，来帮助感性的理解这个动态搜索的过程。

对于如下一个无权值的有向图，在进行广度优先搜索呢？这里我们的代码实现是，以节点３为入口

对于BFS的理论基础介绍，个人觉得还是看《DSAA》比较好.这里不做介绍，注重分析该搜索算法的实现。

如果对于图这种数据结构不熟悉，这个BFS一般是搞不定的...

下面分别是无向图的邻接表实现和邻接矩阵实现

http://blog.csdn.net/cinmyheart/article/details/41381845

http://blog.csdn.net/cinmyheart/article/details/41370465

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

如果看过上面的图的实现，看下面的代码应该是非常“熟悉”的。很部分都是在上面的图基础上修改而来的。

首先我们，这里对图进行抽象，然后把关键的实现的API 放到头文件中。

/************************************************************
code file	: BFS.h
code writer	: EOF
code date	: 2014.11.22
e-mail		: [email protected]

code description:
	This file is a header file for out test program.
We are using digraph but not undirected graph in BFS.

************************************************************/

#ifndef _BFS_H_
#define _BFS_H_

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

	#define CONNECTED    1
	#define DISCONNECTED 0

	#define SUCCESS  0
	#define FAILED  -1

	#define QUEUE_SIZE 10
	#define ARRAY_SIZE 20

	#define EMPTY_QUEUE   -1
	#define UNEMPTY_QUEUE  0 

	/*
	**	We use these macro as index for struct table
	*/
	#define KNOW_OFFSET 0 //vertex that have been found
	#define DIST_OFFSET 1 //distance of vertex
	#define PATH_OFFSET 2 //parent vertex of current vertex
	
	#define FOUND	    1
	#define NOT_FOUND   0

	/*
	**	Liitle trick. I use minus one to 
	** represent positive infinite :)
	*/
	#define INFINITE   -1

	#define ENTRY_POINT 3

	struct node
	{
		struct node* previous;
		struct node* next;
		int data;
	};

	struct vertex
	{
		int value;
		struct vertex* next;
		struct vertex* end;
	};

	struct graph
	{
		int num_vertex;
		int num_edge;
		struct vertex adjacent[0];
	};

	struct table
	{
		int height;
		int width;
		int msg[0];//we store message of table in this array.
	};

	void unweighted_path(struct table* p_table,struct graph* p_graph);

	struct graph* init_graph(int vertex,int edge);
	void   release_graph(struct graph* p_graph);
	
	int add_edge(struct graph* p_graph,char from_v,char to_v);
	int print_graph(struct graph* p_graph);

	/*
	**	Creat and desctory a table which's size is row*col.
	*/
	struct table* init_table(int row,int col);
	void table_print(struct table* p_table);
	void release_table(struct table* p_table);

	/*
	**	I implement some API to use ADT-Queue
	*/
	int queue_destory(struct node* p_queue_tail);

	int queue_enter(struct node** pp_queue_header,
			struct node** pp_queue_tail,
			int number);

	int queue_init(struct node** pp_queue_header,
 		       struct node** pp_queue_tail);

	int queue_out(struct node** pp_queue_header,
		      struct node** pp_queue_tail);

	void queue_print(struct node* p_queue_tail);

#endif

add_edge.c

/************************************************************
code file	: add_edge.c
code writer	: EOF
code date	: 2014.11.22
e-mail		: [email protected]

code description:
	This function will help us to add a new connection
between different vertex which is in the graph.

*************************************************************/
#include "BFS.h"

int add_edge(struct graph* p_graph,char from_v,char to_v)
{
	if(!p_graph || from_v < 0 || to_v < 0)
	{
		return FAILED;
	}

	struct vertex* p_to_v    = (struct vertex*)malloc(sizeof(struct vertex));

	if(!p_to_v)
	{
		printf("malloc failed in function %s()\n",__FUNCTION__);

		return FAILED;		
	}

	if(!(p_graph->adjacent[from_v].end))
	{
		p_graph->adjacent[from_v].next  = p_to_v;
		p_graph->adjacent[from_v].end   = p_to_v;
		p_to_v->next  = NULL;
		p_to_v->value = to_v;
	}
	else
	{
		p_graph->adjacent[from_v].end->next = p_to_v;
		p_graph->adjacent[from_v].end       = p_to_v;//update the new end node.
		p_to_v->next  = NULL;
		p_to_v->value = to_v;
		
	}

	return SUCCESS;
}

init_graph.c

/************************************************************
code file	: init_graph.c
code writer	: EOF
code date	: 2014.11.22
e-mail		: [email protected]

code description:
	This function is used for initializing the graph
with inputed parameter @vertex and @edge.

************************************************************/
#include "BFS.h"

struct graph* init_graph(int num_vertex,int num_edge)
{

	if(num_vertex <= 0 || num_edge <= 0)
	{
		return NULL;
	}

	struct graph* p_graph = NULL;

        p_graph = (struct graph*)malloc(sizeof(struct graph) +\
		  num_vertex*sizeof(struct vertex));

	if(!p_graph)
	{
		printf("malloc failed in function %s()\n",__FUNCTION__);
		return NULL;
	}
	
	p_graph->num_vertex = num_vertex;
	p_graph->num_edge   = num_edge;

	int temp = 0;
	//initialize the adjacent relationship
	for(temp = 0;temp < num_vertex;temp++)
	{
		p_graph->adjacent[temp].value = temp;
		p_graph->adjacent[temp].next  = NULL;
		p_graph->adjacent[temp].end   = NULL;
	}
	
	return p_graph;
}

init_table.c

/************************************************************
code file	: init_table.c
code writer	: EOF
code date	: 2014.11.23
e-mail		: [email protected]

code description:
	
	This function will help us to create a table which's
size is @row multiply @col. And the size of each unit int
this table is sizeof(int).

************************************************************/

#include "BFS.h"

struct table* init_table(int row,int col)
{
	if(row <= 0 || col <= 0)
	{
		return NULL;
	}

	struct table* p_table = (struct table*)malloc(sizeof(struct table) + row*col*sizeof(int));

	if(!p_table)
	{
		return NULL;
	}
	
	p_table->height = row;
	p_table->width  = col;

	int num_row = row;
	int num_col = col;

	//We must initialize the table !
	for(row = 0;row < num_row;row++)
	{
		*((int*)(p_table->msg) + row*num_col + KNOW_OFFSET) = NOT_FOUND;
		if(row != ENTRY_POINT)
		{
			*((int*)(p_table->msg) + row*num_col + DIST_OFFSET) = INFINITE;
		}
		else
		{
			*((int*)(p_table->msg) + row*num_col + DIST_OFFSET) = 0;
		}
		*((int*)(p_table->msg) + row*num_col + PATH_OFFSET) = 0;
		
	}

	return p_table;
}

/************************************************************
code file	: print_graph.c
code writer	: EOF
code date	: 2014.11.22
e-mail		: [email protected]

code description:
	This function will print out the connection of graph
which @p_graph point to.

************************************************************/

#include "BFS.h"

int print_graph(struct graph* p_graph)
{
	if(!p_graph)
	{
		return FAILED;
	}

	int from_v = 0;
	int to_v = 0;

	int num_vertex = p_graph->num_vertex;

	struct vertex* p_vertex = NULL;

	for(from_v = 0;from_v < num_vertex;from_v++)
	{	
		p_vertex = &(p_graph->adjacent[from_v]);
		while(p_vertex)
		{
			printf("\t%d",p_vertex->value);
			p_vertex = p_vertex->next;
		}
		printf("\n");
	}

	return SUCCESS;
}

/******************************************************************
code writer : EOF
code   date : 2014.09.13
e-mail : [email protected]
Attention:
	Just a implementation of function queue_init. I would be
happy, if my code will help you to know what is queue.
we assuem that ...

Input data ---> tail | | |queue| | |  header ---> Output data
	
If something wrong with my code please touch me by e-mail.

*******************************************************************/
#include "BFS.h"

int queue_init(struct node** pp_queue_header,struct node** pp_queue_tail)
{
	(*pp_queue_header) = NULL;
	(*pp_queue_tail)   = NULL;

	return SUCCESS;	
}

/****************************************************************
code writer : EOF
code date: 2014.03.07
e-mail: [email protected]
code purpose:
		Just a implementation of function queue_enter. I would be
happy, if my code will help you to know what is queue.
****************************************************************/
#include "BFS.h"

int queue_enter(struct node** pp_queue_header ,
		struct node** pp_queue_tail,
		int number)
{
	struct node* p_new_node = NULL;
	struct node* p_temp_node = NULL;

	p_new_node = (struct node*)malloc(sizeof(struct node));
	if(p_new_node == NULL)
	{
		printf("malloc error!\nqueue enter failed\n");
		return FAILED;
	}

	if(!(*pp_queue_tail))	
	{
		*pp_queue_tail   = p_new_node;
		*pp_queue_header = p_new_node;

		p_new_node->data = number;
		//Before 2014.11.22, I forgot to add this line and this is a 
		//little bug, but now everything goes right after I adding this :)

		p_new_node->previous = NULL;
		p_new_node->next     = NULL;
	}
	else
	{
		
		p_temp_node = (*pp_queue_tail);
	
		p_new_node->data = number;

		p_new_node->next = p_temp_node;
		p_new_node->previous = NULL;

	
		p_temp_node->previous = p_new_node;
	
		(*pp_queue_tail) = p_new_node;

	}

	return SUCCESS;
}

/***********************************************************************
code writer : EOF
code date : 2014.09.13
e-mail: [email protected]
code purpose:
		Just a implementation of function queue_out. I would be
happy, if my code will help you to know what is queue.

If something wrong with my code, please touch me by e-mail.

************************************************************************/
#include "BFS.h"

int queue_out(struct node** pp_queue_header,struct node** pp_queue_tail)
{
	struct node* p_temp_node = NULL;
	int ret = 0;

	if( !(*pp_queue_header))
	{
		/*
		**	There is no way to check the return value.
		** when we use "queue_out()". So, you needn't to do
		** that.
		*/
		printf("ATTENTION! There is nothing in the queue.\n");
		return EMPTY_QUEUE;
	}

	p_temp_node = (*pp_queue_header);
	
	(*pp_queue_header) = (*pp_queue_header)->previous;

	if(*pp_queue_header)//If there are not only one element left in the queue
	{
		(*pp_queue_header)->next = NULL;
	}
	else
	{
		*pp_queue_tail   = NULL;
		*pp_queue_header = NULL;
	}
	
	ret = p_temp_node->data;
	free(p_temp_node);
	p_temp_node = NULL;

	return ret;
}

/******************************************************************************
code writer : EOF
code date : 2014.03.07
e-mail: [email protected]
code purpose:
		Just a implementation of function queue_print. I would be
happy, if my code will help you to know what is queue.

If something wrong with my code, please touch me by e-mail.

***********************************************************************************/

#include "BFS.h"
void queue_print(struct node* p_queue_tail)
{
	struct node* p_temp_node = NULL;
	
	p_temp_node = p_queue_tail;

	printf("queue data at this time:\n");

	while(p_temp_node != NULL)
	{
		printf("%d ",p_temp_node->data);
		p_temp_node = p_temp_node->next;
	}

	printf("\n");
}

/*********************************************************************
code writer : EOF
code date : 2014.03.07
e-mail: [email protected]
code purpose:
		Just a implementation of function queue_enter. I would be
happy, if my code will help you to know what is queue.
*******************************************************************/
#include "BFS.h"

int queue_destory(struct node* p_queue_tail)
{
	if(!p_queue_tail)
	{
		return SUCCESS;
	}
	struct node* p_temp_node = NULL;
	
	p_temp_node = p_queue_tail->next;
	while(p_temp_node != NULL)
	{
		p_queue_tail->next = p_temp_node->next;
		free(p_temp_node);
		p_temp_node = p_queue_tail->next;
	}	
	
	free(p_queue_tail);

	return SUCCESS;
}

/************************************************************
code file	: release_graph.c
code writer	: EOF
code date	: 2014.11.22
e-mail		: [email protected]

code description:
	It's easy and convenient for us to call this API once
and free all the graph.

*************************************************************/
#include "BFS.h"

void release_graph(struct graph* p_graph)
{
	if(!p_graph)
	{
		return ;
	}
	
	int temp = 0;
	int num_vertex = p_graph->num_vertex;
	struct vertex* p_temp = NULL;

	for(temp = 0;temp < num_vertex;temp++)
	{
		if(p_graph->adjacent[temp].next)
		{
			p_temp = (p_graph->adjacent[temp].next->next);
			while(p_temp)
			{
				free(p_graph->adjacent[temp].next);
				p_graph->adjacent[temp].next = p_temp;
				p_temp = p_temp->next;
			}
			free(p_graph->adjacent[temp].next);
		}
	}

	free(p_graph);
}

#include "BFS.h"


void release_table(struct table* p_table)
{
	if(!p_table)
	{
		return;
	}

	free(p_table);
}

#include "BFS.h"

void table_print(struct table* p_table)
{
	if(!p_table)
	{
		return;
	}

	int row_num = p_table->height;
	int col_num = p_table->width;

	int row = 0;

	int know = 0;
	int dist = 0;
	int path = 0;

	printf("\tknow\tdist\tpath\n");

	for(row = 0;row < row_num;row++)
	{
		know = p_table->msg[row*col_num + KNOW_OFFSET];

		switch(know)
		{
			case FOUND:
			{
				printf("\tFound");
				break;
			}
			
			case NOT_FOUND:
			{
				printf("\tNFond");
				break;
			}

			default:
				printf("error value of varible @know\n");
				return;
		}

		dist = p_table->msg[row*col_num + DIST_OFFSET];

		switch(dist)
		{
			case INFINITE:
			{
				printf("\tINF");
				break;
			}

			default:
				printf("\t%d",dist);
		}

		path = p_table->msg[row*col_num + PATH_OFFSET];
		
		switch(path)
		{
			case 0:
			{
				printf("\t0");
				break;
			}
	
			default:
				printf("\tv%d",path);
		}

		printf("\n");
	}

	printf("\n\n\n");
}

/************************************************************
code file	: unweighted_path.c
code writer	: EOF
code date	: 2014.11.23
e-mail		: [email protected]

code description:

	This function will do the work of searching.
This job is based on a ADT--Queue. You could read "BFS.h"
and find that decleration of these functions which is used
for Queue.

************************************************************/

#include "BFS.h"

void unweighted_path(struct table* p_table,struct graph* p_graph)
{
	if(!p_table || !p_graph)
	{
		return;
	}

	struct node* p_queue_tail;
	struct node* p_queue_header;
	
	queue_init(&p_queue_header,&p_queue_tail);	
	
	queue_enter(&p_queue_header,
		    &p_queue_tail,
		    p_graph->adjacent[ENTRY_POINT].value);

	int vertex_index = 0;
	struct vertex* p_vertex = NULL;

	while(!!p_queue_header)
	{
		
		vertex_index = queue_out(&p_queue_header,&p_queue_tail);
		printf("v%d dequeue\n",vertex_index);


		*((int*)(p_table->msg)\
		+ vertex_index*(p_table->width) + KNOW_OFFSET) = FOUND;

		p_vertex = (struct vertex*)p_graph->adjacent + vertex_index;
		p_vertex = p_vertex->next;
		for(;p_vertex;p_vertex = p_vertex->next)
		{
			if(*((int*)(p_table->msg) \
			+ (p_vertex->value)*(p_table->width)
			+ DIST_OFFSET ) == INFINITE)
			{

				*((int*)(p_table->msg) \
				+ (p_vertex->value)*(p_table->width)
				+ DIST_OFFSET ) = \
				*((int*)(p_table->msg)\
				+ (vertex_index)*(p_table->width)\
				+ DIST_OFFSET) + 1;
				
				*((int*)(p_table->msg) \
				+ (p_vertex->value)*(p_table->width)
				+ PATH_OFFSET ) = vertex_index;

				queue_enter(&p_queue_header,
					    &p_queue_tail,
					    p_vertex->value);
			}
		}

		table_print(p_table);
	}

	queue_destory(p_queue_tail);
}

测试主程序：

/****************************************************************
code file	: test_graph.c
code writer	: EOF
code date	: 2014.11.22
e-mail		: [email protected]

code description:
	
	This test program is used for testing BFS.

*****************************************************************/
#include "BFS.h"

int main()
{
	struct graph* p_graph = NULL;

	FILE* fp = fopen("./text.txt","r+");

	if(!fp)
	{
		printf("fopen() failed!\n");
		return 0;
	}

	int ret    = 0;
	int vertex = 0;
	int edge   = 0;

	int from_v = 0;
	int to_v   = 0;

	fscanf(fp,"%d",&vertex);
	fscanf(fp,"%d",&edge);

	p_graph = init_graph(vertex,edge);

	int temp = 0;
	for(temp;temp < edge;temp++)
	{
		/*
		**	I think it's necessary to check the returned value
		** of scanf() family.
		*/
		ret = fscanf(fp,"%d %d",&from_v,&to_v);
		if(ret != 2)
		{
			break;
		}

		add_edge(p_graph,from_v,to_v);
	}

		
	struct table* p_table =  init_table(vertex,3);

	unweighted_path(p_table,p_graph);

	print_graph(p_graph);
	release_table(p_table);
	release_graph(p_graph);
	fclose(fp);
	return 0;
}

测试用文本文件text.txt:

测试结果：

图的邻接关系表示及实际图对照

由出队的顺序，各个元素出对后的table的情况

最后，所有的节点都会被检索到(０节点不考虑，这里我们初始数据中没有０节点，这是哑节点～)

我们可以知道，Found 0 0 的是入口节点，即节点３，而Found 1 v3，表示距离初始节点有１个edge距离，而该节点的上一个节点为v3, 同样的，Found 3 v4　表示，距离初始节点有３个edge距离，而该节点的上一个节点为v4.