邻接表的认知

邻接表，存储方法跟树的孩子链表示法相类似，是一种顺序分配和链式分配相结合的存储结构。如这个表头结点所对应的顶点存在相邻顶点，则把相邻顶点依次存放于表头结点所指向的单向链表中。

对于无向图来说，使用邻接表进行存储也会出现数据冗余，表头结点A所指链表中存在一个指向C的表结点的同时，表头结点C所指链表也会存在一个指向A的表结点。

图的邻接表存储方法跟树的孩子链表示法相类似，是一种顺序分配和链式分配相结合的存储结构。如这个表头结点所对应的顶点存在相邻顶点，则把相邻顶点依次存放于表头结点所指向的单向链表中。如词条概念图所示，表结点存放的是邻接顶点在数组中的索引。对于无向图来说，使用邻接表进行存储也会出现数据冗余，表头结点A所指链表中存在一个指向C的表结点的同时，表头结点C所指链表也会存在一个指向A的表结点。

#include 
#include 
#define QUEUE_SIZE 10

int* visitedPtr;

typedef struct Graph{
	int** connections;
	int numNodes;
} *GraphPtr;

GraphPtr initGraph(int paraSize, int** paraData) {
	int i, j;
	GraphPtr resultPtr = (GraphPtr)malloc(sizeof(struct Graph));
	resultPtr -> numNodes = paraSize;
	resultPtr -> connections = (int**)malloc(paraSize * sizeof(int*));
	for (i = 0; i < paraSize; i ++) {
		resultPtr -> connections[i] = (int*)malloc(paraSize * sizeof(int));
		for (j = 0; j < paraSize; j ++) {
			resultPtr -> connections[i][j] = paraData[i][j];
		}
	}	
	return resultPtr;
}

typedef struct GraphNodeQueue{
	int* nodes;
	int front;
	int rear;
}GraphNodeQueue, *QueuePtr;


QueuePtr initQueue(){
	QueuePtr resultQueuePtr = (QueuePtr)malloc(sizeof(struct GraphNodeQueue));
	resultQueuePtr->nodes = (int*)malloc(QUEUE_SIZE * sizeof(int));
	resultQueuePtr->front = 0;
	resultQueuePtr->rear = 1;
	return resultQueuePtr;
}

bool isQueueEmpty(QueuePtr paraQueuePtr){
	if ((paraQueuePtr->front + 1) % QUEUE_SIZE == paraQueuePtr->rear) {
		return true;
	}

	return false;
}


void enqueue(QueuePtr paraQueuePtr, int paraNode){
	if ((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE) {
		printf("Error, trying to enqueue %d. queue full.rn", paraNode);
		return;
	}
	paraQueuePtr->nodes[paraQueuePtr->rear] = paraNode;
	paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
}


int dequeue(QueuePtr paraQueuePtr){
	if (isQueueEmpty(paraQueuePtr)) {
		printf("Error, empty queuern");
		return NULL;
	}

	paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;

	return paraQueuePtr->nodes[paraQueuePtr->front];
}

typedef struct AdjacencyNode {
	int column;
	AdjacencyNode* next;
}AdjacencyNode, *AdjacentNodePtr;

typedef struct AdjacencyList {
	int numNodes;
	AdjacencyNode* headers;
}AdjacencyList, *AdjacencyListPtr;


AdjacencyListPtr graphToAdjacentList(GraphPtr paraPtr) {
	int i, j, tempNum;
	AdjacentNodePtr p, q;
	tempNum = paraPtr->numNodes;
	AdjacencyListPtr resultPtr = (AdjacencyListPtr)malloc(sizeof(struct AdjacencyList));
	resultPtr->numNodes = tempNum;
	resultPtr->headers = (AdjacencyNode*)malloc(tempNum * sizeof(struct AdjacencyNode));
	
	for (i = 0; i < tempNum; i ++) {
		p = &(resultPtr->headers[i]);
		p->column = -1;
		p->next = NULL;

		for (j = 0; j < tempNum; j ++) {
			if (paraPtr->connections[i][j] > 0) {
				q = (AdjacentNodePtr)malloc(sizeof(struct AdjacencyNode));
				q->column = j;
				q->next = NULL;

				p->next = q;
				p = q;
			}
		}
	}

	return resultPtr;
}

void printAdjacentList(AdjacencyListPtr paraPtr) {
	int i;
	AdjacentNodePtr p;
	int tempNum = paraPtr->numNodes;

	printf("这就是宁要的邻接表:rn");
	for (i = 0; i < tempNum; i ++) {
		p = paraPtr->headers[i].next;
		while (p != NULL) {
			printf("%d, ", p->column);
			p = p->next;
		}
		printf("rn");
	}
}

void widthFirstTranverse(AdjacencyListPtr paraListPtr, int paraStart){
	printf("width first rn");
	int i, j, tempNode;
	AdjacentNodePtr p;
	i = 0;

	visitedPtr = (int*) malloc(paraListPtr->numNodes * sizeof(int));
	
	for (i = 0; i < paraListPtr->numNodes; i ++) {
		visitedPtr[i] = 0;
	}

	QueuePtr tempQueuePtr = initQueue();
	printf("%dt", paraStart);
	visitedPtr[paraStart] = 1;
	enqueue(tempQueuePtr, paraStart);
	while (!isQueueEmpty(tempQueuePtr)) {
		tempNode = dequeue(tempQueuePtr);

		for (p = &(paraListPtr->headers[tempNode]); p != NULL; p = p->next) {
			j = p->column;
			if (visitedPtr[j]) //如果if通过，那么进行下一个循环嗷
				continue;

			printf("%dt", j);
			visitedPtr[j] = 1; //用过啦
			enqueue(tempQueuePtr, j); //进去啊
		}
	}
	printf("rn");
}

void testGraphTranverse() {
	int i, j;
	int myGraph[5][5] = { 
		{0, 1, 0, 1, 0},
		{1, 0, 1, 0, 1}, 
		{0, 1, 0, 1, 1}, 
		{1, 0, 1, 0, 0}, 
		{0, 1, 1, 0, 0}};
	int** tempPtr;
	printf("准备数据嗷 0就是没关系，1就是有关系rn");
		
	tempPtr = (int**)malloc(5 * sizeof(int*));
	for (i = 0; i < 5; i ++) {
		tempPtr[i] = (int*)malloc(5 * sizeof(int));
	}//Of for i
	 
	for (i = 0; i < 5; i ++) {
		for (j = 0; j < 5; j ++) {
			tempPtr[i][j] = myGraph[i][j];
			printf("i = %d, j = %d, %drn", i, j, tempPtr[i][j]);
		}
	}
 
	printf("数据在上嗷rn");
	
	GraphPtr tempGraphPtr = initGraph(5, tempPtr);
	AdjacencyListPtr tempListPtr = graphToAdjacentList(tempGraphPtr);

	printAdjacentList(tempListPtr);

	widthFirstTranverse(tempListPtr, 4);
}

int main(){
	testGraphTranverse();
	return 1;
}

运算结果：

准备数据嗷 0就是没关系，1就是有关系
i = 0, j = 0, 0
i = 0, j = 1, 1
i = 0, j = 2, 0
i = 0, j = 3, 1
i = 0, j = 4, 0
i = 1, j = 0, 1
i = 1, j = 1, 0
i = 1, j = 2, 1
i = 1, j = 3, 0
i = 1, j = 4, 1
i = 2, j = 0, 0
i = 2, j = 1, 1
i = 2, j = 2, 0
i = 2, j = 3, 1
i = 2, j = 4, 1
i = 3, j = 0, 1
i = 3, j = 1, 0
i = 3, j = 2, 1
i = 3, j = 3, 0
i = 3, j = 4, 0
i = 4, j = 0, 0
i = 4, j = 1, 1
i = 4, j = 2, 1
i = 4, j = 3, 0
i = 4, j = 4, 0
数据在上嗷
这就是宁要的邻接表:
1, 3,
0, 2, 4,
1, 3, 4,
0, 2,
1, 2,
width first
4       1       2       0       3

附加图片方便大家理解这个答案是什么意思：

 这题是个无向图欸，如果是有向图的话......

比如

 那答案就是

V0 : ->1->3

V1:  ->2->4

V2:  ->3->4

V3:

V4:

为什么不画图，因为太丑啦！

#include 
#include 
#include 
#include 
#include 
using namespace std;
typedef char VertexType[4];
typedef char InfoPtr;
typedef int VRType;
#define  MAXSIZE 100
typedef enum {DG,DN,UG,UN}GraphKind;
typedef struct ArcNode
{
	int adjvex;
	InfoPtr *info;
	struct ArcNode *nextarc;
 
}ArcNode;
typedef struct VNode 
{
	VertexType data;
	ArcNode *firstarc;
}VNode,AdjList[MAXSIZE];
typedef struct 
{
	AdjList vertex;
	int vexnum, arcnum;
	GraphKind kind;
 
}AdjGraph;
int LocateVertex(AdjGraph G, VertexType v);
void CreateGraph(AdjGraph *G);
void DisplayGraph(AdjGraph G);
void DestoryGraph(AdjGraph *G);
int LocateVertex(AdjGraph G, VertexType v)
{
	int i;
	for (i = 0; i < G.vexnum; ++i)
	{
		if (strcmp(G.vertex[i].data, v) == 0)
		{
			return i;
		}
 
	}
	return -1;
}
void CreateGraph(AdjGraph *G)
{
	int i, j, k;
	VertexType v1, v2;
	ArcNode *p;
	cout << "请输入图的顶点数和边数 ";
	cin >> (*G).vexnum >> (*G).arcnum;
	cout << "请输入" <vexnum<< "个顶点的值：" << endl;
	for (i = 0; i < G->vexnum;i++)
	{
		cin >> G->vertex[i].data;
		G->vertex[i].firstarc = NULL;
	}
	cout << "请输入弧尾  弧头" << endl;
	for (k = 0; k < G->arcnum;k++)
	{
		cin >> v1 >> v2;
		i = LocateVertex(*G, v1);
		j = LocateVertex(*G, v2);
		p = (ArcNode*)malloc(sizeof(ArcNode));
		p->adjvex = j;
		p->info = NULL;
		p->nextarc = G->vertex[i].firstarc;
		G->vertex[i].firstarc = p;
 
	}
	(*G).kind = DG;
}
 
void DestoryGraph(AdjGraph *G)
{
	int i;
	ArcNode *p, *q;
	for (i = 0; i < (*G).vexnum;i++)
	{
		p = G->vertex[i].firstarc;
		if (p!=NULL)
		{
			q = p->nextarc;
			free(p);
			p = q;
 
		}
	}
	(*G).vexnum = 0;
	(*G).arcnum = 0;
}
 
void DisplayGraph(AdjGraph G)
{
	int i;
	ArcNode *p;
	cout << G.vexnum << "个顶点：" << endl;
	for (i = 0; i < G.vexnum;i++)
	{
		cout << G.vertex[i].data << " ";
	}
	cout << endl << G.arcnum << "条边："<adjvex].data << " ";
			p = p->nextarc;
		}
		cout << endl;
	}
}
 
int main()
{
	AdjGraph G;
	cout << "采用邻接矩阵创建有向图G：" << endl;
	CreateGraph(&G);
	cout << "输入有向图G的邻接表：" << endl;
	DisplayGraph(G);
	DestoryGraph(&G);
	system("pause");
	
	return 0;
}

运算内容加结果：

采用邻接矩阵创建有向图G：
请输入图的顶点数和边数 6 9
请输入6个顶点的值：
a b c d e f
请输入弧尾  弧头
a b
a c
a f
f c
b c
c d
d a
e d
b f
输入有向图G的邻接表：
6个顶点：
a b c d e f
9条边：
a→f a→c a→b
b→f b→c
c→d
d→a
e→d
f→c
请按任意键继续. . .

结束.