数据结构14：图的遍历

图G是由顶点集V和边集E组成，记为G=(V,E)，其中V(G)表示图G中顶点的有限非空集；E(G)表示图G中顶点之间的关系，也就是边的集合。

//定义图
typedef struct Graph
{
	int** connections;
	int numNodes;
 } *GraphPtr;
 
//初始化图
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(sizeof(int*) * paraSize);
		for(j = 0;j < paraSize;j++)
		{
			resultPtr->connections[i][j] = paraData[i][j];
		}
	}
	return resultPtr;
}

建立一个数组用来记录结点是否被访问，是则标记为1。

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

深度优先遍历类似于二叉树的先序遍历。

//深度优先
void depthFirstTransverse(GraphPtr paraGraphPtr, int paraNode)
{
	int i;
	visitedPtr[paraNode] = 1;
	printf("%d ",paraNode);
	for(i = 0; i < paraGraphPtr->numNodes;i ++)
	{
		if(!visitedPtr[i])
		{
			if(paraGraphPtr->connections[paraNode][i])
			{
				depthFirstTransverse(paraGraphPtr,i);
			}
		}
	}
 } 

广度优先遍历类似于二叉树的层序遍历，运用队列实现。

//广度优先
void widthFirstTransverse(GraphPtr paraGraphPtr, int paraStart)
{
	int i,j,tempNode;
	i = 0;
	QueuePtr tempQueuePtr = initQueue();
	printf("%d ",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("%d ",j);
			visitedPtr[j] = 1;
			enqueue(tempQueuePtr,j);
		}
	}
 } 

#include 
#include 
#include  
#define QUEUE_SIZE 10

int* visitedPtr;

//图结点，队列 
typedef struct GraphNodeQueue
{
	int* nodes;
	int front;
	int rear; 
} GraphNodeQueue, *QueuePtr;

//初始化 
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("Error, trying to enqueue %d. queue full.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("队空,不能出队.rn");
		return -1;
	}
	paraQueuePtr->front = (paraQueuePtr->front + 1) % QUEUE_SIZE;
	
	return paraQueuePtr->nodes[paraQueuePtr->front];
}

//定义图
typedef struct Graph
{
	int** connections;
	int numNodes;
 } *GraphPtr;
 
//初始化图
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(sizeof(int*) * paraSize);
		for(j = 0;j < paraSize;j++)
		{
			resultPtr->connections[i][j] = paraData[i][j];
		}
	}
	return resultPtr;
}


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

//深度优先
void depthFirstTransverse(GraphPtr paraGraphPtr, int paraNode)
{
	int i;
	visitedPtr[paraNode] = 1;
	printf("%d ",paraNode);
	for(i = 0; i < paraGraphPtr->numNodes;i ++)
	{
		if(!visitedPtr[i])
		{
			if(paraGraphPtr->connections[paraNode][i])
			{
				depthFirstTransverse(paraGraphPtr,i);
			}
		}
	}
 } 

//广度优先
void widthFirstTransverse(GraphPtr paraGraphPtr, int paraStart)
{
	int i,j,tempNode;
	i = 0;
	QueuePtr tempQueuePtr = initQueue();
	printf("%d ",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("%d ",j);
			visitedPtr[j] = 1;
			enqueue(tempQueuePtr,j);
		}
	}
 } 

//测试
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}};
		printf("图的数组形式:n");
	for(i = 0;i < 5;i ++)
	{
		for(j = 0;j < 5;j ++)
		{
			printf("%d ",myGraph[i][j]);
		}
		printf("n");
	}
	int** tempPtr;
	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];
		}
	}
	GraphPtr tempGraphPtr = initGraph(5, tempPtr);
	printf("结点数 = %d rn", tempGraphPtr -> numNodes);

	printf("深度优先:rn");
	initTransverse(tempGraphPtr);
	depthFirstTransverse(tempGraphPtr, 4);

	printf("n广度优先:rn");
	initTransverse(tempGraphPtr);
	widthFirstTransverse(tempGraphPtr, 4);
}

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

图的矩阵形式:
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
结点数 = 5
深度优先遍历:
4 1 0 3 2
广度优先遍历:
4 1 2 0 3