数据结构-邻接表及广度优先遍历

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前言

我们发现，当图中的边数相对于顶点较少时，邻接矩阵是对存储空间的极大浪费。我们可以考虑对边或弧使用链式存储的方式来避免空间浪费的问题。回忆树结构的孩子表示法，将结点存入数组，并对结点的孩子进行链式存储，不管有多少孩子，也不会存在空间浪费问题。

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一、邻接表结构

1、 图中顶点用一个一维数组存储，当然也可以用单链表来存储，不过用数组可以较容易的读取顶点信息，更加方便。另外，对于顶点数组中，每个数据元素还需要存储指向第一个邻接点的指针，以便于查找该顶点的边信息。

2、 图中每个顶点vi的所有邻接点构成一个线性表，由于邻接点的个数不定，所以用单链表存储，无向图称为顶点vi的边表，有向图则称为以vi为弧尾的出边表。
无向图的邻接表：

有向图的邻接表：

有向图的逆邻接表：

带权值的网图得邻接表：

二、完整代码

#include 
#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.\r\n", paraNode);
		return;
	}
	paraQueuePtr->nodes[paraQueuePtr->rear] = paraNode;
	paraQueuePtr->rear = (paraQueuePtr->rear + 1) % QUEUE_SIZE;
}

int dequeue(QueuePtr paraQueuePtr)
{
	if (isQueueEmpty(paraQueuePtr)) 
	{
		printf("Error, empty queue\r\n");
		return NULL;
	}

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

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



typedef struct AdjacencyNode 
{
	int column;
	struct 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");

	AdjacentNodePtr p;
	int 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);
	int tempNode,j;
	while (!isQueueEmpty(tempQueuePtr)) 
	{

		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);
		}
	}
	printf("\r\n");
}

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 ++) 
		{
			
			tempPtr[i][j] = myGraph[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;
}