邻接表及广度优先遍历

写在前面——

本文主要是在记录进一步学习图结构的一些心得。

1.邻接表

邻接表是由每个顶点以及它的相邻顶点组成的。前一章我们知道了可以用邻接矩阵表示了图结构，但是它有一个致命的缺点，那就是矩阵中存在着大量的0，这在程序中会占据大量的内存。所以我们采用了邻接表的方法，从而很好的来解决邻接矩阵的缺陷。

2.代码实现

#include 
#include 
#define QUEUE_SIZE 10



int* visitedPtr;


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

void deepFirst(GraphPtr paraGraphPtr, int paraNode);

GraphPtr initGraph(int paraSize, int** paraData) {
	int i, j;
	GraphPtr resultPtr = (GraphPtr)malloc(sizeof(struct Graph));
	resultPtr -> numNodes = paraSize;
	resultPtr -> connections = (int**)malloc(paraSize * paraSize * sizeof(int));
	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){
	printf("front = %d, rear = %d.\r\n", paraQueuePtr->front, paraQueuePtr->rear);
	if ((paraQueuePtr->rear + 1) % QUEUE_SIZE == paraQueuePtr->front % QUEUE_SIZE) {
		printf("Error, trying to enqueue %d. queue full.\r\n", paraNode);
		return;
	}
	paraQueuePtr->nodes[paraQueuePtr->rear] = paraNode;
	paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
	printf("enqueue %d ends.\r\n", paraNode);
}

int dequeue(QueuePtr paraQueuePtr){
	if (isQueueEmpty(paraQueuePtr)) {
		printf("Error, empty queue\r\n");
		return NULL;
	}
	paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;

	printf("dequeue %d ends.\r\n", paraQueuePtr->nodes[paraQueuePtr->front]);
	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("This is the graph:\r\n");
	for (i = 0; i < tempNum; i ++) {
		p = paraPtr->headers[i].next;
		while (p != NULL) {
			printf("%d, ", p->column);
			p = p->next;
		}
		printf("\r\n");
	}
}


void widthFirstTranverse(AdjacencyListPtr paraListPtr, int paraStart){
	printf("width first \r\n");
	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("%d\t", paraStart);
	visitedPtr[paraStart] = 1;
	enqueue(tempQueuePtr, paraStart);
	printf("After enqueue\r\n");
	while (!isQueueEmpty(tempQueuePtr)) {
		printf("First while\r\n");
		tempNode = dequeue(tempQueuePtr);

		for (p = &(paraListPtr->headers[tempNode]); p != NULL; p = p->next) {
			j = p->column;
			if (visitedPtr[j]) 
				continue;
			printf("%d\t", j);
			visitedPtr[j] = 1;
			enqueue(tempQueuePtr, j);
		}
	}
}

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 data\r\n");
		
	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 ++) {
			printf("i = %d, j = %d, ", i, j);
			printf("%d\r\n", tempPtr[i][j]);
			tempPtr[i][j] = myGraph[i][j];
			printf("i = %d, j = %d, %d\r\n", i, j, tempPtr[i][j]);
		}
	}
 
	printf("Data ready\r\n");
	GraphPtr tempGraphPtr = initGraph(5, tempPtr);
	AdjacencyListPtr tempListPtr = graphToAdjacentList(tempGraphPtr);
	printAdjacentList(tempListPtr);
	widthFirstTranverse(tempListPtr, 4);
}

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

3.广度优先遍历

    本质上就是从第一个顶点开始，尝试访问尽可能靠近它的顶点，即先访问最靠近它的所有顶点，再访问第二靠近它的所有顶点，以此类推，直到访问完所有的顶点。

以下图为例

第一次先搜索离 顶点1 最近的两个顶点，即 顶点2 和 顶点7

然后再搜索离 顶点1 第二近的所有顶点，也就是离 顶点2 和 顶点7 最近的所有顶点

离顶点2 最近的顶点为 顶点3 和 顶点5 ，离 顶点7 最近的顶点为 顶点8 ，因此这几个点以此被遍历

再继续往下搜索离 顶点1 第三近的所有顶点，也就是离 顶点3 、顶点5 和 顶点8 最近的所有顶点

由图可知，离 顶点3 最近的顶点有 顶点6 ；离 顶点5 最近的顶点有 顶点4 ；离 顶点8 最近的顶点有 顶点9，因此它们也逐一被遍历

到此为止，整个图结构就已经被遍历完成了，这就是一个广度优先搜索完整的过程