看数据结构写代码（37） 图的十字链表的表示与实现

图的邻接表在 查找 有向图的 出度 很 方便，但是 在 查找 入度 时，需要遍历整个图。如果想要 方便的 查找 入度，需要 建立 逆邻接表。十字链表 正好 就是 邻接表 和 逆邻接表的集合。具体结构图如下：

感觉 十字链表 在 查找 入度时 方便 一些，其他 跟 邻接表没什么区别。

源代码 网盘地址：点击打开链接

代码如下：

// CrossLinkGraph.cpp : 定义控制台应用程序的入口点。
//有向图的十字链表表示法

#include "stdafx.h"
#include <cstdlib>

#define MAX_VEX_NUM 20
enum E_State
{
	E_State_Error = 0,
	E_State_Ok = 1,
};

struct ArcNode//弧节点
{
	int tailIndex;//弧尾位置
	int headIndex;//弧头位置
	ArcNode * tailNext;//下一个弧尾相同的弧
	ArcNode * headNext;//下一个弧头相同的弧
};

typedef struct VNode
{
	char vexName;//顶点名称
	ArcNode * firstIn;
	ArcNode * firstOut;
}GraphList[MAX_VEX_NUM];//

struct Graph
{
	GraphList list;//顶点数组.
	int vexNum,arcNum;
};
//获取弧 的 头节点
ArcNode * getHeadNode(){
	ArcNode * pNode = (ArcNode *)malloc(sizeof(ArcNode));
	if (pNode){
		pNode->headIndex = pNode->tailIndex = -1;
		pNode->headNext = pNode->tailNext = NULL;
	}
	return pNode;
}

ArcNode * getArcNode(int tailIndex,int headIndex){
	ArcNode * pNode = getHeadNode();
	if (pNode){
		pNode->headIndex = headIndex;
		pNode->tailIndex = tailIndex;
	}
	return pNode;
}

int vexLocation(Graph g,char vex){
	for (int i = 0; i < g.vexNum; i++){
		if (g.list[i].vexName == vex){
			return i;
		}
	}
	return -1;
}

void createGrahp(Graph * g){
	printf("输入图的顶点数 和 边（弧）数\n");
	scanf("%d%d%*c",&g->vexNum,&g->arcNum);
    //构造顶点集
    printf("请输入顶点集\n");
    for (int i = 0; i < g->vexNum; i++){
        char name;
		scanf("%c",&name);
		g->list[i].vexName = name;
		g->list[i].firstIn = g->list[i].firstOut = getHeadNode();//建立 头节点，并让头指针指向头节点
    }
    //构造顶点关系
    fflush(stdin);
    printf("请输入顶点的关系\n");
    for (int i = 0; i < g->arcNum; i++){
        char vex1,vex2;
		scanf("%c%c%*c",&vex1,&vex2);
		int location1 = vexLocation(*g,vex1);
		int location2 = vexLocation(*g,vex2);
		ArcNode * pNode = getArcNode(location1,location2);
		pNode->tailNext = g->list[location1].firstOut->tailNext;
		g->list[location1].firstOut->tailNext = pNode;
		pNode->headNext = g->list[location2].firstIn->headNext;
		g->list[location2].firstIn->headNext = pNode;
    }
}

//只要删除所有顶点的弧尾（或者弧头）节点即可，
//同时删除弧头弧尾 ，内存错误
void destoryGraph(Graph * g){
	for (int i = 0; i < g->vexNum; i++){
		ArcNode * next = g->list[i].firstOut;//删除所有弧尾
		while (next != NULL){
			ArcNode * freeNode = next;
			next = next->tailNext;
			free(freeNode);
		}
		g->list[i].firstIn = g->list[i].firstOut = NULL;
		g->list[i].vexName = ' ';
		g->vexNum = g->arcNum = 0;
	}
}

//顶点vex1 和顶点vex2 是否相邻
bool graphIsAdj(Graph g,char vex1,char vex2){
	int location = vexLocation(g,vex1);
	ArcNode * next = g.list[location].firstOut->tailNext;
	while (next != NULL){
		if (g.list[next->headIndex].vexName == vex2){
			return true;
		}
		next = next->tailNext;
	}
	return false;
}

int graphDegree(Graph g,char vex){
	int degree = 0;
	int locaiton = vexLocation(g,vex);
	ArcNode * next = g.list[locaiton].firstOut->tailNext;//计算所有出度
	while (next != NULL){
		degree++;
		next = next->tailNext;
	}
	next = g.list[locaiton].firstIn->headNext;//计算所有入度
	while (next != NULL){
		degree++;
		next = next->headNext;
	}
	return degree;
}

char firstAdj(Graph g,char vex){
	int location = vexLocation(g,vex);
	ArcNode * next = g.list[location].firstOut->tailNext;
	if (next != NULL)
	{
		return g.list[next->headIndex].vexName;
	}
	return ' ';
}

char nextAdj(Graph g,char vex1,char vex2){
	int location = vexLocation(g,vex1);
	ArcNode * next = g.list[location].firstOut->tailNext;
	while (next != NULL){//查找到 vex2
		if (g.list[next->headIndex].vexName == vex2){
			break;
		}
		next = next->tailNext;
	}
	if (next != NULL){
		ArcNode * nextNode = next->tailNext;
		if (nextNode != NULL){
			return g.list[nextNode->headIndex].vexName;
		}
	}
	return ' ';
}
//插入边（弧）
void insertArc(Graph * g,char vex1,char vex2){
	int location1 = vexLocation(*g,vex1);
	int location2 = vexLocation(*g,vex2);
	ArcNode * node = getArcNode(location1,location2);
	node->tailNext = g->list[location1].firstOut->tailNext;
	g->list[location1].firstOut->tailNext = node;
	node->headNext = g->list[location2].firstIn->headNext;
	g->list[location2].firstIn->headNext = node;
	g->arcNum ++;
}
//删除边（弧）
void deleteArc(Graph * g,char vex1,char vex2){
	g->arcNum--;
	int location1 = vexLocation(*g,vex1);
	int location2 = vexLocation(*g,vex2);
	ArcNode * next = g->list[location1].firstOut->tailNext;
	ArcNode * pre = g->list[location1].firstOut;
	while (next != NULL){//在更改 尾部相同的 链表时，不能删除 弧
		if (next->headIndex == location2){
			pre->tailNext = next->tailNext;
			//free(next);
			break;
		}
		pre = next;
		next = next->tailNext;
	}
	next = g->list[location2].firstIn->headNext;
	pre = g->list[location2].firstIn;
	//在更改弧头相同的链表时，释放空间.
	while (next != NULL){
		if (next->tailIndex == location1){
			pre->headNext = next->headNext;
			free(next);
			break;
		}
		pre = next;
		next = next->headNext;
	}
}
//插入顶点
void insertVex(Graph * g, char vex){
	if (g->vexNum < MAX_VEX_NUM){
		g->list[g->vexNum].vexName = vex;
		g->list[g->vexNum].firstIn = g->list[g->vexNum].firstOut = getHeadNode();
		g->vexNum++;
	}
}
//删除顶点
void deleteVex(Graph * g,char vex){
	int location = vexLocation(*g,vex);
	//删除顶点 同样需要 遍历整个 图 查找 与 vex 相关的弧节点
	for (int i = 0; i < g->vexNum; i++){
		ArcNode * next = g->list[i].firstOut->tailNext;
		while (next != NULL){
			if (next->headIndex == location || next->tailIndex == location){
				ArcNode * delNode = next;
				next = next->tailNext;
				char delData1 = g->list[delNode->tailIndex].vexName;
				char delData2 = g->list[delNode->headIndex].vexName;
				deleteArc(g,delData1,delData2);
			}
			else{
				next = next->tailNext;
			}
		}
	}
	for (int i = 0; i < g->vexNum; i++){
		ArcNode * next = g->list[i].firstOut->tailNext;
		while (next != NULL){
			if(next->headIndex > location){
				next->headIndex --;
			}
			if(next->tailIndex > location){
				next->tailIndex --;
			}
			next = next->tailNext;
		}
	}
	free(g->list[location].firstIn);//释放头节点
	//vex下面的 顶点上移
	for (int i = location + 1; i < g->vexNum; i++){
		g->list[i-1] = g->list[i];
	}
	g->vexNum --;
}

void printGrahp(Graph g){
	for (int i = 0; i < g.vexNum; i++){
		printf("以%c为弧尾的 顶点有：",g.list[i].vexName);
		ArcNode * next = g.list[i].firstOut->tailNext;//删除所有弧尾
		while (next != NULL){
			printf("%c",g.list[next->headIndex].vexName);
			next = next->tailNext;
		}
		printf("\n以%c为弧头的 顶点有：",g.list[i].vexName);
		next = g.list[i].firstIn->headNext;//删除所有弧尾
		while (next != NULL){
			printf("%c",g.list[next->tailIndex].vexName);
			next = next->headNext;
		}
		printf("\n");
	}
}

int _tmain(int argc, _TCHAR* argv[])
{
	Graph g;
	createGrahp(&g);
	printGrahp(g);
	printf("图的顶点数：%d,边（弧）树为：%d\n",g.vexNum,g.arcNum);
	char * isAdj = graphIsAdj(g,'b','d')? "相邻" : "不相邻";
	int degree = graphDegree(g,'d');
	char first = firstAdj(g,'c');
	char next = nextAdj(g,'d','c');
	printf("c的第一个邻接点是%c,d的c邻接点的下一个邻接点是：%c\n",first,next);
	printf("b 和 d %s,d的度为：%d\n",isAdj,degree);
	insertVex(&g,'e');
	printf("插入e顶点之后图结构如下：\n");
	printGrahp(g);
	insertArc(&g,'a','e');
	printf("插入(a,e) 之后图结构如下：\n");
	printGrahp(g);
	deleteArc(&g,'d','c');
	printf("删除(d,c)之后图结构如下：\n");
	printGrahp(g);
	deleteVex(&g,'a');
	printf("删除顶点a之后图结构如下：\n");
	printGrahp(g);
	printf("图的顶点数：%d,边（弧）数为：%d\n",g.vexNum,g.arcNum);
	destoryGraph(&g);
	return 0;
}

运行截图：