数据结构-图

1、图的定义

图：是一种灵活的数据结构，一般作为一种模型用来定义对象之间的关系或者联系。对象由顶点表示，而对象之间的关系或关联则通过顶点之间的边来表示。

２、图的应用

图算法、统计网络跳数、拓扑排序、图着色、哈密顿圈问题、分团问题、可序列化冲突

３、图的代码实现

/*graph.h*/
#ifndef	GRAPH_H
#define GRAPH_H
#include <stdlib.h>
#include "list.h"
#include "set.h"

/*define a structure for adjacency lists*/
typedef struct AdjList_
{
	void *vertex;
	Set adjacent;
}AdjList;

/*define structure for graphs*/
typedef struct Graph_
{
	int		vcount;
	int		ecount;
	int		(*match)(const void *key1,const void *key2);
	void	(*destroy)(void *data);
	List	adjlists;
}Graph;

/*define colors for vertices in graphs*/
typedef	enum VertexColor_ {white,gray,black}  VertexColor;

/*public interface*/
void graph_init(Graph *graph,int (*match)(const void *key1,const void *key2),void (*destroy)(void *data));
void graph_destroy(Graph *graph);
int graph_ins_vertex(Graph *graph,const void *data);
int graph_ins_edge(Graph *graph,const void *data1,const void *data2);
int graph_rem_vertex(Graph *graph,void **data);
int graph_rem_edge(Graph *graph,void *data1,void **data2);
int graph_adjlist(const Graph *graph,const void *data,AdjList **adjlist);
int graph_is_adjacent(const Graph *graph,const void *data1,const void *data2);
#define	graph_adjlists(graph) ((graph)->dajlists)
#define	graph_vcount(graph) ((graph)->vcount)
#define	graph_ecount(graph) ((graph)->ecount)

#endif

/*graph.c*/
#include<stdlib.h>
#include<string.h>
#include"graph.h"
#include"list.h"
#include"set.h"

void graph_init(Graph *graph,int (*match)(const void *key1,const void *key2),void (*destroy)(void *data))
{
	/*initialize the graph*/
	graph->vcount=0;
	graph->ecount=0;
	graph->match=match;
	graph->destroy=destroy;

	/*initialize the list of adjacentcy-list structure*/
	list_init(&graph->adjlists,NULL);
	return ;
}

void graph_destroy(Graph *graph)
{
	AdjList	*adjlist;

	/*remove each adjacency-list structure and destroy its adjacency list*/
	while(list_size(&graph->adjlists)>0)
	{
		if(list_rem_next(&graph->adjlists,NULL,(void **)&adjlist)==0)
		{
			set_destroy(&adjlist->adjacent);
			if(graph->destroy!=NULL)
				graph->destroy(adjlist->vertex);
			free(adjlist);
		}
	}

	/*destroy the list of adjacency-list structures,which is now empty*/
	list_destroy(&graph->adjlists);

	/*clear the structure*/
	memset(graph,0,sizeof(Graph));
	return ;
}

int graph_ins_vertex(Graph *graph,const void *data)
{
	ListElmt *element;
	AdjList	 *adjlist;
	int retval;

	/*do not allow the insertion of duplicate vertices*/
	for(element=list_head(&graph->adjlists);element !=NULL;element=list_next(element))
	{
		if(graph->match(data,((AdjList *)list_data(element))->vertex))
			return 1;
	}

	/*insert the vertex*/
	if((adjlist=(AdjList *)malloc(sizeof(AdjList)))==NULL)
		return -1;
	adjlist->vertex=(void *)data;
	set_init(&adjlist->adjacent,graph->match,NULL);
	if((retval=list_ins_next(&graph->adjlists,list_tail(&graph->adjlists),adjlist))!=0)
	{
		return retval;
	}

	/*adjust the vertex count to account for the inserted vetex*/
	graph->vcount++;
	return 0;
}

int graph_ins_edge(Graph *graph,const void *data1,const void *data2)
{
	ListElmt *element;
	int retval;

	/*do not allow insertion of an edge without both its vertices in the graph*/
	for(element=list_head(&graph->adjlists);element !=NULL;element=list_next(element))
	{
		if(graph->match(data2,((AdjList *)list_data(element))->vertex))
			break;
	}
	if(element==NULL)
		return -1;
	for(element=list_head(&graph->adjlists);element !=NULL;element=list_next(element))
	{
		if(graph->match(data1,((AdjList *)list_data(element))->vertex))
			break;
	}
	if(element==NULL)
		return -1;

	/*insert the second vertex into the adjacency list of the first vertex*/
	if((retval=set_insert(&((AdjList *)list_data(element))->adjacent,data2))!=0)
	{
		return retval;
	}

	/*Adjust the edge count to account for the inserted edge*/
	graph->ecount++;
	return 0;
}

int graph_rem_vertex(Graph *graph,void **data)
{
	ListElmt *element,*temp,*prev;
	AdjList *adjlist;
	int found;

	/*traverse each adjacency list and the vertice it contains*/
	prev=NULL;
	found=0;
	for(element=list_head(&graph->adjlists);element !=NULL;element=list_next(element))
	{
		/*do not allow removal of the vertex if it is in an adjacency list*/
		if(set_is_member(&((AdjList *)list_data(element))->adjacent,*data))
			return -1;

		/*keep a pointer to the vertex to be removed*/
		if(graph->match(*data,((AdjList *)list_data(element))->vertex))
		{
			temp=element;
			found=1;
		}

		/*keep a pointer to the vertex before the vertex to be removed*/
		if(!found)
			prev=element;
	}

	/*return if the vertex was not found*/
	if(!found)
		return -1;

	/*do not allow removal of the tex if its adjacency list is not empty*/
	if(set_size(&((AdjList *)list_data(temp))->adjacent)>0)
		return -1;

	/*remove the vertex*/
	if(list_rem_next(&graph->adjlists,prev,(void **)&adjlist)!=0)
		return -1;

	/*free the storage allocated by the abstract datatype*/
	*data=adjlist->vertex;
	free(adjlist);

	/*adjust the vertex count to account for the removed vertex*/
	graph->vcount--;
	return 0;

}

int graph_rem_edge(Graph *graph,void *data1,void **data2)
{
	ListElmt *element;

	/*locate the adjacency list for the first vertex*/
	for(element=list_head(&graph->adjlists);element !=NULL;element=list_next(element))
	{
		if(graph->match(data1,((AdjList *)list_data(element))->vertex))
			break;
	}
	if(element==NULL)
		return -1;

	/*remove the second vertex from the adjacency list of the first vertex*/
	if(set_remove(&((AdjList *)list_data(element))->adjacent,data2)!=0)
		return -1;

	/*adjust the edge count to account for the removed edge*/
	graph->ecount--;
	return 0;
}

int graph_adjlist(const Graph *graph,const void *data,AdjList **adjlist)
{
	ListElmt *element,*prev;

	/*locate the adjacency list for the  vertex*/
	prev=NULL;
	for(element=list_head(&graph->adjlists);element !=NULL;element=list_next(element))
	{
		if(graph->match(data,((AdjList *)list_data(element))->vertex))
			break;
	}

	/*return if the vertex was not found*/
	if(element==NULL)
		return -1;

	/*pass back the adjacency list for the vertex*/
	*adjlist=list_data(element);
	return 0;
}

int graph_is_adjacent(const Graph *graph,const void *data1,const void *data2)
{
		ListElmt *element,*prev;

	/*locate the adjacency list for the first vertex*/
	prev=NULL;
	for(element=list_head(&graph->adjlists);element !=NULL;element=list_next(element))
	{
		if(graph->match(data1,((AdjList *)list_data(element))->vertex))
			break;
		prev=element;
	}

	/*return if the vertex was not found*/
	if(element==NULL)
		return 0;

	/*return whether the second vertex is in the adjacency list of the first*/
	return set_is_member(&((AdjList *)list_data(element))->adjacent,data2);
}

应用实例：

后续补上

数据结构-图