数据结构与算法学习：12.图的遍历以及邻接表

• 图
• • 图的定义
  • 图的遍历
  • • 队列的定义（多个索引）
    • 判断队列是否为空
    • 入队
    • 出队
    • 图的结构
    • 深度优先遍历
    • 广度优先遍历
    • 完整代码以及运行结果
• 邻接表以及广度优先遍历
• • 定义
  • 代码
  • • 图的初始化
    • 队列的初始化
    • 判断队列是否为空
    • 入队
    • 出队
    • 邻接表的定义
    • 邻接表的创建
    • 打印邻接表
    • 广度优先遍历
    • 完整代码以及运行结果

图是由顶点的有穷非空集合和顶点之间边的集合组成， 通常表示为: G（V，E）， 其中，G表示一个图，V是图G中顶点的集合，E是图G中边的集合。

注意:线性表可以是空表，树可以是空树，但图不可以是空图。就是说，图中不能一个顶点也没有，图的顶点集V一定非空，但边集E可以为空，此时图中只有顶点而没有边。

// 队列的定义 
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;
}

// 判断队列是否为空 
bool isQueueEmpty(QueuePtr paraQueuePtr){
	if ((paraQueuePtr->front + 1) % QUEUE_SIZE == paraQueuePtr->rear) {
		return true;
	}
	return false;
}

// 入队 
void enqueue(QueuePtr paraQueuePtr, int paraNode){
	if ((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE) {
		printf("错误，元素%d无法入队. 队列已经满了.rn", paraNode);
		return;
	}
	paraQueuePtr->nodes[paraQueuePtr->rear] = paraNode;
	paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
}

// 出队 
int dequeue(QueuePtr paraQueuePtr){
	if (isQueueEmpty(paraQueuePtr)) {
		printf("错误，队列为空rn");
		return NULL;
	}
	paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;

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

// 图的结构 
typedef struct Graph{
	int** connections;
	int numNodes;
} *GraphPtr;

void depthFirstTranverse(GraphPtr paraGraphPtr, int paraNode) {
	int i;
	
	visitedPtr[paraNode] = 1;
	printf("%dt", paraNode);
	
	for (i = 0; i < paraGraphPtr -> numNodes; i ++) {
		if (!visitedPtr[i]){ 
			if (paraGraphPtr -> connections[paraNode][i]) {
				depthFirstTranverse(paraGraphPtr, i);
			}
		}
	}
}

// 广度优先遍历 
void widthFirstTranverse(GraphPtr paraGraphPtr, int paraStart){
	int i, j, tempNode;
	i = 0;
	QueuePtr tempQueuePtr = initQueue();
	printf("%dt", paraStart);
	visitedPtr[paraStart] = 1;
	enqueue(tempQueuePtr, paraStart);
	while (!isQueueEmpty(tempQueuePtr)) {
		tempNode = dequeue(tempQueuePtr);
		visitedPtr[tempNode] = 1;
		
		i ++;

		for (j = 0; j < paraGraphPtr->numNodes; j ++) {
			if (visitedPtr[j]) 
				continue;

			if (paraGraphPtr->connections[tempNode][j] == 0)
				continue;
			
			printf("%dt", j);
			visitedPtr[j] = 1;
			enqueue(tempQueuePtr, j);
		}
	}
}

#include 
#include 

#define QUEUE_SIZE 10

int* visitedPtr;

// 队列的定义 
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;
}

// 判断队列是否为空 
bool isQueueEmpty(QueuePtr paraQueuePtr){
	if ((paraQueuePtr->front + 1) % QUEUE_SIZE == paraQueuePtr->rear) {
		return true;
	}
	return false;
}

// 入队 
void enqueue(QueuePtr paraQueuePtr, int paraNode){
	if ((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE) {
		printf("错误，元素%d无法入队. 队列已经满了.rn", paraNode);
		return;
	}
	paraQueuePtr->nodes[paraQueuePtr->rear] = paraNode;
	paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
}

// 出队 
int dequeue(QueuePtr paraQueuePtr){
	if (isQueueEmpty(paraQueuePtr)) {
		printf("错误，队列为空rn");
		return NULL;
	}
	paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;

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

// 图的结构 
typedef struct Graph{
	int** connections;
	int numNodes;
} *GraphPtr;


GraphPtr initGraph(int paraSize, int** paraData) {
	int i, j;
	GraphPtr resultPtr = (GraphPtr)malloc(sizeof(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;
}


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

void depthFirstTranverse(GraphPtr paraGraphPtr, int paraNode) {
	int i;
	
	visitedPtr[paraNode] = 1;
	printf("%dt", paraNode);
	
	for (i = 0; i < paraGraphPtr -> numNodes; i ++) {
		if (!visitedPtr[i]){ 
			if (paraGraphPtr -> connections[paraNode][i]) {
				depthFirstTranverse(paraGraphPtr, i);
			}
		}
	}
}

// 广度优先遍历 
void widthFirstTranverse(GraphPtr paraGraphPtr, int paraStart){
	int i, j, tempNode;
	i = 0;
	QueuePtr tempQueuePtr = initQueue();
	printf("%dt", paraStart);
	visitedPtr[paraStart] = 1;
	enqueue(tempQueuePtr, paraStart);
	while (!isQueueEmpty(tempQueuePtr)) {
		tempNode = dequeue(tempQueuePtr);
		visitedPtr[tempNode] = 1;
		
		i ++;

		for (j = 0; j < paraGraphPtr->numNodes; j ++) {
			if (visitedPtr[j]) 
				continue;

			if (paraGraphPtr->connections[tempNode][j] == 0)
				continue;
			
			printf("%dt", j);
			visitedPtr[j] = 1;
			enqueue(tempQueuePtr, j);
		}
	}
}
// 测试函数 
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("Preparing datarn");
		
	tempPtr = (int**)malloc(5 * sizeof(int*));
	for (i = 0; i < 5; i ++) {
		tempPtr[i] = (int*)malloc(5 * sizeof(int));
	}
	 
	for (i = 0; i < 5; i ++) {
		for (j = 0; j < 5; j ++) {
			tempPtr[i][j] = myGraph[i][j];
		}
	}
 
	printf("Data readyrn");
	
	GraphPtr tempGraphPtr = initGraph(5, tempPtr);
	printf("num nodes = %d rn", tempGraphPtr -> numNodes);
	printf("Graph initializedrn");

	printf("Depth first visit:rn");
	initTranverse(tempGraphPtr);
	depthFirstTranverse(tempGraphPtr, 4);

	printf("rnWidth first visit:rn");
	initTranverse(tempGraphPtr);
	widthFirstTranverse(tempGraphPtr, 4);
}

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

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。

// 图的初始化 
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;
}

// 队列的初始化 
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;
}

// 判断队列是否为空 
bool isQueueEmpty(QueuePtr paraQueuePtr){
	if ((paraQueuePtr->front + 1) % QUEUE_SIZE == paraQueuePtr->rear) {
		return true;
	}
	return false;
}

// 入队 
void enqueue(QueuePtr paraQueuePtr, int paraNode){
	if ((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE) {
		printf("错误，元素%d无法入队. 队列已经满了.rn", paraNode);
		return;
	}
	paraQueuePtr->nodes[paraQueuePtr->rear] = paraNode;
	paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
}

// 出队 
int dequeue(QueuePtr paraQueuePtr){
	if (isQueueEmpty(paraQueuePtr)) {
		printf("错误，队列为空rn");
		return NULL;
	}

	paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;
	return paraQueuePtr->nodes[paraQueuePtr->front];
}

// 邻接表的定义 
typedef struct AdjacencyNode {
	int column;
	AdjacencyNode* next;
}AdjacencyNode, *AdjacentNodePtr;

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

// 邻接表的创建 
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;
}

// 打印邻接表 
void printAdjacentList(AdjacencyListPtr paraPtr) {
	int i;
	AdjacentNodePtr p;
	int tempNum = paraPtr->numNodes;

	printf("This is the graph:rn");
	for (i = 0; i < tempNum; i ++) {
		p = paraPtr->headers[i].next;
		while (p != NULL) {
			printf("%d, ", p->column);
			p = p->next;
		}
		printf("rn");
	}
}

// 广度优先遍历 
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]) 
				continue;
			printf("%dt", j);
			visitedPtr[j] = 1;
			enqueue(tempQueuePtr, j);
		}
	}
	printf("rn");
}

#include 
#include 
#define QUEUE_SIZE 10

int* visitedPtr;
// 图的初始化 
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;
}

// 队列的初始化 
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;
}

// 判断队列是否为空 
bool isQueueEmpty(QueuePtr paraQueuePtr){
	if ((paraQueuePtr->front + 1) % QUEUE_SIZE == paraQueuePtr->rear) {
		return true;
	}
	return false;
}
// 入队 
void enqueue(QueuePtr paraQueuePtr, int paraNode){
	if ((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE) {
		printf("错误，元素%d无法入队. 队列已经满了.rn", paraNode);
		return;
	}
	paraQueuePtr->nodes[paraQueuePtr->rear] = paraNode;
	paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
}

// 出队 
int dequeue(QueuePtr paraQueuePtr){
	if (isQueueEmpty(paraQueuePtr)) {
		printf("错误，队列为空rn");
		return NULL;
	}

	paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;
	return paraQueuePtr->nodes[paraQueuePtr->front];
}

// 邻接表的定义 
typedef struct AdjacencyNode {
	int column;
	AdjacencyNode* next;
}AdjacencyNode, *AdjacentNodePtr;

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

// 邻接表的创建 
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;
}

// 打印邻接表 
void printAdjacentList(AdjacencyListPtr paraPtr) {
	int i;
	AdjacentNodePtr p;
	int tempNum = paraPtr->numNodes;

	printf("This is the graph:rn");
	for (i = 0; i < tempNum; i ++) {
		p = paraPtr->headers[i].next;
		while (p != NULL) {
			printf("%d, ", p->column);
			p = p->next;
		}
		printf("rn");
	}
}

// 广度优先遍历 
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]) 
				continue;
			printf("%dt", j);
			visitedPtr[j] = 1;
			enqueue(tempQueuePtr, j);
		}
	}
	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("Preparing datarn");
		
	tempPtr = (int**)malloc(5 * sizeof(int*));
	for (i = 0; i < 5; i ++) {
		tempPtr[i] = (int*)malloc(5 * sizeof(int));
	}
	 
	for (i = 0; i < 5; i ++) {
		for (j = 0; j < 5; j ++) {
			tempPtr[i][j] = myGraph[i][j];
		}
	}
	printf("Data readyrn");	
	GraphPtr tempGraphPtr = initGraph(5, tempPtr);
	AdjacencyListPtr tempListPtr = graphToAdjacentList(tempGraphPtr);

	printAdjacentList(tempListPtr);

	widthFirstTranverse(tempListPtr, 4);
}

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