看数据结构写代码（38） 图的邻接多重表表示法与实现

图的邻接多重表 是 无向图的 另一种表示法。其与 邻接表 的差别 仅仅 在于 ，邻接表 用 两个 顶点 来表示 一条边，而 邻接多重表 用一个 顶点来表示一条边。这样使得 邻接多重表 在 某些操作 要 来的 方便。例如 将 搜索过的边 做记号 或者 删除 一条边。

下面是邻接多重表的结构：

下面的 6条边 用 6个弧 节点表示，用12个指针指向，每个弧节点被 指向2次。这样使得我们 在 释放内存的时候 需要格外小心。

下面上代码：

源码工程文件网盘地址：点击打开链接

// AMLGraph.cpp : 定义控制台应用程序的入口点。
//无向图的邻接多重表

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

#define MAX_VEX_NUM 20
enum E_State
{
	E_State_Error = 0,
	E_State_Ok = 1,
};
enum E_VisitIf
{
	unvisited = 0,
	visited = 1,
};
struct ArcNode
{
	E_VisitIf mark;
	int iIndex,jIndex;//顶点i,j在图中的位置
	ArcNode * iNext;//与i顶点点相关的下一个弧
	ArcNode * jNext;//与j顶点点相关的下一个弧
};

struct VNode
{
	char vexName;
	ArcNode * head;//头指针
};

struct AMLGraph
{
	VNode adjMuList[MAX_VEX_NUM];//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->iIndex = pNode->jIndex = -1;
		pNode->iNext = pNode->jNext = NULL;
		pNode->mark = unvisited;
	}
	return pNode;
}

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

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

void createGrahp(AMLGraph * 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->adjMuList[i].vexName = name;
		g->adjMuList[i].head = 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->iNext = g->adjMuList[location1].head->iNext;
		g->adjMuList[location1].head->iNext = pNode;
		pNode->jNext = g->adjMuList[location2].head->iNext;
		g->adjMuList[location2].head->iNext = pNode;
    }
}

void destoryGraph(AMLGraph * g){
	for (int i = 0; i < g->vexNum; i++){
		ArcNode * next = g->adjMuList[i].head->iNext;
		while (next != NULL){
			ArcNode * freeNode = next;
			next = next->iIndex == i ? next->iNext : next->jNext;
			if (freeNode->iIndex == i){////只释放 iIndex 等于 i的节点,要不会多次释放
				free(freeNode);
			}
		}
		free(g->adjMuList[i].head);
		g->adjMuList[i].head = NULL;
		g->adjMuList[i].vexName = ' ';
		g->vexNum = g->arcNum = 0;
	}
}

//顶点vex1 和顶点vex2 是否相邻
bool graphIsAdj(AMLGraph g,char vex1,char vex2){
	int location = vexLocation(g,vex1);
	ArcNode * next = g.adjMuList[location].head->iNext;
	while (next != NULL){
		if (g.adjMuList[next->iIndex].vexName == vex2 || g.adjMuList[next->jIndex].vexName == vex2){
			return true;
		}
		next = next->iIndex == location ? next->iNext : next->jNext;
	}
	return false;
}

int graphDegree(AMLGraph g,char vex){
	int degree = 0;
	int location = vexLocation(g,vex);
	ArcNode * next = g.adjMuList[location].head->iNext;//计算所有出度
	while (next != NULL){
		degree++;
		next = next->iIndex == location ? next->iNext : next->jNext;
	}
	return degree;
}

char firstAdj(AMLGraph g,char vex){
	int location = vexLocation(g,vex);
	ArcNode * next = g.adjMuList[location].head->iNext;
	if (next != NULL)
	{
		int index = next->iIndex == location ? next->jIndex : next->iIndex;
		return g.adjMuList[index].vexName;
	}
	return ' ';
}

char nextAdj(AMLGraph g,char vex1,char vex2){
	int location = vexLocation(g,vex1);
	ArcNode * next = g.adjMuList[location].head->iNext;
	while (next != NULL){//查找到 vex2
		char iName = g.adjMuList[next->iIndex].vexName;
		char jName = g.adjMuList[next->jIndex].vexName;
		if (iName == vex2 || jName == vex2){
			next = next->iIndex == location ? next->iNext : next->jNext;
			break;
		}
	}
	if (next != NULL){
		int index = next->iIndex == location ? next->jIndex : next->iIndex;
		return g.adjMuList[index].vexName;
	}
	return ' ';
}
//插入边（弧）
void insertArc(AMLGraph * g,char vex1,char vex2){
	int location1 = vexLocation(*g,vex1);
	int location2 = vexLocation(*g,vex2);
	ArcNode * node = getArcNode(location1,location2);
	node->iNext = g->adjMuList[location1].head->iNext;
	g->adjMuList[location1].head->iNext = node;
	node->jNext = g->adjMuList[location2].head->iNext;
	g->adjMuList[location2].head->iNext = node;
	g->arcNum ++;
}
//删除边（弧）
void deleteArc(AMLGraph * g,char vex1,char vex2){
	g->arcNum--;
	int location1 = vexLocation(*g,vex1);
	int location2 = vexLocation(*g,vex2);
	ArcNode * next = g->adjMuList[location1].head->iNext;
	ArcNode * pre = g->adjMuList[location1].head;
	while (next != NULL){
		if (next->iIndex == location2){
			if (pre == g->adjMuList[location1].head || pre->iIndex == location1){//删除的是第一个节点.或者 前驱的index = location1
				pre->iNext = next->jNext;
			}
			else{
				pre->jNext = next->jNext;
			}
			break;
		}
		else if(next->jIndex == location2){
			if (pre == g->adjMuList[location1].head || pre->iIndex == location1){//删除的是第一个节点.或者 前驱的index = location1
				pre->iNext = next->iNext;
			}
			else{
				pre->jNext = next->iNext;
			}
			break;
		}
		pre = next;
		next = next->iIndex == location1 ? next->iNext : next->jNext;
	}
	next = g->adjMuList[location2].head->iNext;
	pre = g->adjMuList[location2].head;
	while (next != NULL){
		if (next->iIndex == location1){
			if (pre == g->adjMuList[location2].head || pre->iIndex == location2){//删除的是第一个节点.或者 前驱的index = location1
				pre->iNext = next->jNext;
			}
			else{
				pre->jNext = next->jNext;
			}
			free(next);
			break;
		}
		else if(next->jIndex == location1){
			if (pre == g->adjMuList[location2].head || pre->iIndex == location2){//删除的是第一个节点.或者 前驱的index = location1
				pre->iNext = next->iNext;
			}
			else{
				pre->jNext = next->iNext;
			}
			free(next);
			break;
		}
		pre = next;
		next = next->iIndex == location2 ? next->iNext : next->jNext;
	}
}
//插入顶点
void insertVex(AMLGraph * g, char vex){
	if (g->vexNum < MAX_VEX_NUM){
		g->adjMuList[g->vexNum].vexName = vex;
		g->adjMuList[g->vexNum].head = getHeadNode();
		g->vexNum++;
	}
}
//删除顶点
void deleteVex(AMLGraph * 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->adjMuList[i].head->iNext;
		while (next != NULL){
			if (next->iIndex == location || next->jIndex == location){
				ArcNode * delNode = next;
				next = next->iIndex == location ? next->iNext : next->jNext;
				char delData1 = g->adjMuList[delNode->iIndex].vexName;
				char delData2 = g->adjMuList[delNode->jIndex].vexName;
				deleteArc(g,delData1,delData2);
			}
			else{
				next = next->iIndex == location ? next->iNext : next->jNext;
			}
		}
	}
	//更改因删除顶点 而导致的元素位置变化..
	for (int i = 0; i < g->vexNum; i++){
		ArcNode * next = g->adjMuList[i].head->iNext;
		while (next != NULL){
			if (next->iIndex == i){
				if(next->iIndex > location){
				next->iIndex --;
				}
				if(next->jIndex > location){
					next->jIndex --;
				}
			}
			next = next->iIndex == location ? next->iNext : next->jNext;
		}
	}
	free(g->adjMuList[location].head);//释放头节点
	//vex下面的 顶点上移
	for (int i = location + 1; i < g->vexNum; i++){
		g->adjMuList[i-1] = g->adjMuList[i];
	}
	g->vexNum --;
}

void printGrahp(AMLGraph g){
	for (int i = 0; i < g.vexNum; i++){
		printf("%c的 邻接点有：",g.adjMuList[i].vexName);
		ArcNode * next = g.adjMuList[i].head->iNext;//删除所有弧尾
		while (next != NULL){
			int index = next->iIndex == i ? next->jIndex : next->iIndex;
			printf("%c",g.adjMuList[index].vexName);
			next = next->iIndex == i ? next->iNext : next->jNext;
		}
		printf("\n");
	}
}
//邻接多重表
int _tmain(int argc, _TCHAR* argv[])
{
	AMLGraph 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,'f');
	printf("插入f顶点之后图结构如下：\n");
	printGrahp(g);
	insertArc(&g,'e','f');
	printf("插入(e,f) 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,'c');
	printf("删除顶点c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：

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