图的基本算法实现（邻接矩阵与邻接表两种方法）

本博客前面文章已对图有过简单的介绍，本文主要是重点介绍有关图的一些具体操作与应用

阅读本文前，可以先参考本博客 各种基本算法实现小结（四）—— 图及其遍历

一、无向图

1 无向图——邻接矩阵

测试环境：VS2008

#include "stdafx.h"
#include <stdlib.h>
#include <malloc.h>
#define MAX_VEX 20
#define INFINITY 65535
int *visited;
struct _node
{
	int vex_num;
	struct _node *next;
};
typedef struct _node node, *pnode;
struct _graph
{
	char *vexs;
	int arcs[MAX_VEX][MAX_VEX];
	int vexnum, arcnum;
};
typedef struct _graph graph, *pgraph;
int locate(graph g, char ch)
{
	int i;
	for(i=1; i<=g.vexnum; i++)
		if(g.vexs[i]==ch)
			return i;
	return -1;
}
graph create_graph()
{
	int i, j, w, p1, p2;
	char ch1, ch2;
	graph g;
	printf("Enter vexnum arcnum: ");
	scanf("%d %d", &g.vexnum, &g.arcnum);
	getchar();
	for(i=1; i<=g.vexnum; i++)
		for(j=1; j<g.vexnum; j++)
			g.arcs[i][j]=INFINITY;
	g.vexs=(char *)malloc(sizeof(char));
	printf("Enter %d vexnum.../n", g.vexnum);
	for(i=1; i<=g.vexnum; i++)
	{
		printf("vex %d: ", i);
		scanf("%c", &g.vexs[i]);
		getchar();
	}
	printf("Enter %d arcnum.../n", g.arcnum);
	for(i=1; i<=g.arcnum; i++)
	{
		printf("arc %d: ", i);
		scanf("%c %c %d", &ch1, &ch2, &w);
		getchar();
		p1=locate(g, ch1);
		p2=locate(g, ch2);
		g.arcs[p1][p2]=g.arcs[p2][p1]=w;
	}
	return g;
}
int firstvex_graph(graph g, int i)
{
	int k;
	if(i>=1 && i<=g.vexnum)
		for(k=1; k<=g.vexnum; k++)
			if(g.arcs[i][k]!=INFINITY)
				return k;
	return -1;
}
int nextvex_graph(graph g, int i, int j)
{
	int k;
	if(i>=1 && i<=g.vexnum && j>=1 && j<=g.vexnum)
		for(k=j+1; k<=g.vexnum; k++)
			if(g.arcs[i][k]!=INFINITY)
				return k;
	return -1;
}
void dfs(graph g, int i)
{
	int k, j;
	if(!visited[i])
	{
		visited[i]=1;
		printf("%3c", g.vexs[i]);
		for(j=firstvex_graph(g, i); j>=1; j=nextvex_graph(g, i, j))
			if(!visited[j])
				dfs(g, j);
	}
}
void dfs_graph(graph g)
{
	int i;
	visited=(int *)malloc((g.vexnum+1)*sizeof(int));
	for(i=1; i<=g.vexnum; i++)
		visited[i]=0;
	for(i=1; i<g.vexnum; i++)
		if(!visited[i])
			dfs(g, i);
}
int _tmain(int argc, _TCHAR* argv[])
{
	graph g;
	g=create_graph();
	printf("DFS: ");
	dfs_graph(g);
	printf("/n");
	return 0;
}

运行结果：

==========================================================

2 无向图—— 邻接表

测试环境：VS2008

#include "stdafx.h"
#include <stdlib.h>
#include <malloc.h>
#define MAX_VEX 20
int *visited;
typedef struct _ArcNode
{
	int ivex; /* next ivex */
	struct _ArcNode *nextarc; /* next node */
	int *info; /* arc weight */
};
typedef struct _ArcNode ArcNode, *pArcNode;
struct _VNode
{
	char adjvex; /* note vex */
	ArcNode *firstarc;
};
typedef struct _VNode VNode;
struct _ALGraph
{
	VNode AdjList[MAX_VEX];
	int vexnum, arcnum;
	int kink;
};
typedef struct _ALGraph ALGraph;
int locate(ALGraph g, char ch)
{
	int i;
	for(i=1; i<=g.vexnum; i++)
		if(g.AdjList[i].adjvex==ch)
			return i;
	return -1;
}
ALGraph create_graph()
{
	int i, j, w, p1, p2;
	char ch1, ch2;
	pArcNode pnode, pnode1, pnode2;
	ALGraph g;
	printf("Enter vexnum arcnum: ");
	scanf("%d %d", &g.vexnum, &g.arcnum);
	getchar();
	
	printf("Enter %d vexnum.../n", g.vexnum);
	for(i=1; i<=g.vexnum; i++)
	{
		printf("vex %d: ", i);
		scanf("%c", &g.AdjList[i].adjvex);
		getchar();
		g.AdjList[i].firstarc=NULL;
	}
	printf("Enter arc.../n");
	for(i=1; i<=g.arcnum; i++)
	{
		printf("arc %d: ", i);
		scanf("%c %c", &ch1, &ch2);
		getchar();
		p1=locate(g, ch1);
		p2=locate(g, ch2);
		pnode1=(pArcNode)malloc(sizeof(ArcNode));
		pnode2=(pArcNode)malloc(sizeof(ArcNode));
		pnode1->ivex=p2; /* next ivex */
		pnode1->nextarc=g.AdjList[p1].firstarc;
		g.AdjList[p1].firstarc=pnode1;
		pnode2->ivex=p1; /* next ivex */
		pnode2->nextarc=g.AdjList[p2].firstarc;
		g.AdjList[p2].firstarc=pnode2;
	}
	return g;
}
int firstvex_graph(ALGraph g, int i)
{
	int k;
	if(i>=1 && i<=g.vexnum)	
		if(g.AdjList[i].firstarc)
			return g.AdjList[i].firstarc->ivex;
	return -1;
}
int nextvex_graph(ALGraph g, int i, int k)
{
	pArcNode pnode;
	if(i>=1 && i<=g.vexnum && k>=1 && k<=g.vexnum)
	{
		pnode=g.AdjList[i].firstarc;
		while(pnode->nextarc)
		{
			k=pnode->nextarc->ivex;
			if(!visited[k])
				return k;
			else
				pnode=pnode->nextarc;
		}
	}
	return -1;
}
void dfs(ALGraph g, int i)
{
	int k;
	if(!visited[i])
	{
		visited[i]=1;
		printf("%c", g.AdjList[i].adjvex);
		for(k=firstvex_graph(g, i); k>=1; k=nextvex_graph(g, i, k))
			if(!visited[k])
				dfs(g, k);
	}
}
void dfs_graph(ALGraph g)
{
	int i;
	visited=(int *)malloc((g.vexnum+1)*sizeof(int));
	for(i=1; i<=g.vexnum; i++)
		visited[i]=0;
	for(i=1; i<=g.vexnum; i++)
		if(!visited[i])
			dfs(g, i);
}
int _tmain(int argc, _TCHAR* argv[])
{
	ALGraph g;
	g=create_graph();
	dfs_graph(g);
	printf("/n");
	return 0;
}

运行结果：

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