二叉树的基本操作

 

#include "queue.h" 

BTNode* BuyBTNode(BTDataType x)
{
	BTNode* root = (BTNode*)malloc(sizeof(BTNode));
	root->_data = x;
	root->_left = NULL;
	root->_right = NULL;
	return root;
}
// 创建二叉树 
BTNode* CreateBTree(BTDataType* a, size_t* pIndex, BTDataType invalid)
{
	BTNode* root = NULL;
	while (a[*pIndex] != invalid)//invalid是'#'
	{
		root = BuyBTNode(a[*pIndex]);
		(*pIndex)++;
			root->_left = CreateBTree(a, pIndex, invalid);
		(*pIndex)++;
			root->_right = CreateBTree(a, pIndex, invalid);
	}
	return root;
}

void BTreePrevOrder(BTNode* root)
{
	if (root == NULL)
		return; 
	printf("%d ", root->_data);
	BTreePrevOrder(root->_left);
	BTreePrevOrder(root->_right);
}
void BTreeInOrder(BTNode* root)
{
	if (root == NULL)
		return;
	BTreeInOrder(root->_left);
	printf("%d ", root->_data);
	BTreeInOrder(root->_right);
}
void BTreePostOrder(BTNode* root)
{
	if (root == NULL)
		return;
	BTreePostOrder(root->_left);
	BTreePostOrder(root->_right);
	printf("%d ", root->_data);
}

//结点大小
size_t BTreeSize(BTNode* root)
{
	if (root == NULL)
		return 0;
	return BTreeSize(root->_left) + BTreeSize(root->_right) + 1;
}

//叶子数(叶子指一个结点既无左结点也无右结点)
size_t BTreeLeafSize(BTNode* root)
{
	if (root == NULL)
		return 0;
	if (root->_left == NULL&&root->_right == NULL)
		return 1;
	return BTreeLeafSize(root->_left) + BTreeLeafSize(root->_right);
}

//第k层结点数
size_t BTreeKLevelSize(BTNode* root, size_t k)
{	
	if (root == NULL)
		return 0;
	//已经分置到第k层
	if (k == 1)
	{
		return 1;
	}
	return BTreeKLevelSize(root->_left, k - 1) + BTreeKLevelSize(root->_right,k-1);
}

//最大深度
size_t BTreeDepth(BTNode* root)
{
	size_t LeftDepth;
	size_t RightDepth;
	if (root == NULL)
		return 0;
	LeftDepth = BTreeDepth(root->_left);
	RightDepth = BTreeDepth(root->_right);
	if (LeftDepth > RightDepth)
		return LeftDepth+1;
	else
		return RightDepth+1;	
}

BTNode* BTreeFind(BTNode* root, BTDataType x)
{
	BTNode* Left;
	BTNode* Right;
	if (root == NULL)
		return NULL;
	//本节点找到了
	if (root->_data == x)
		return root;
	//接收左节点的查找结果
	Left = BTreeFind(root->_left, x);
	if (Left != NULL)
		return Left;
	//接收右节点的查找结果
	Right = BTreeFind(root->_right, x);
	if (Right != NULL)
		return Left;
	//子节点和父结点都没有返回空
	return NULL;
}

//利用队列先进后出的性质来层序遍历二叉树
//层序遍历
void BTreeLevelOrder(BTNode* root)
{
	Queue queue;
	BTNode*  front;
	//先初始化
	QueueInit(&queue);
	QueuePush(&queue,root);
	while (QueueSize(&queue) > 0)
	{
		front = QueueFront(&queue);
		printf("%d ", front->_data);
		if (front->_left != NULL)
		{
			QueuePush(&queue, front->_left);
		}
		if (front->_right != NULL)
		{
			QueuePush(&queue, front->_right);
		}
		QueuePop(&queue);
	}
}

// 判断完全二叉树 
//类比层序遍历的方法 
//如果同一层从左边开始查找，遇到了为空的点，那么此点后面如果全部为空说明该为完全二叉树，反之不是
int IsCompleteBTree(BTNode* root)
{
	int flag = 0;
	Queue queue;
	BTNode*  front;
	//先初始化
	QueueInit(&queue);
	QueuePush(&queue, root);
	while (QueueSize(&queue) > 0)
	{
		front = QueueFront(&queue);
		if (front->_left != NULL)
		{
			QueuePush(&queue, front->_left);
		}
		else // 在前面遇到空就停下来
		{
			flag=1;
		}
		if (front->_right != NULL)
		{
			QueuePush(&queue, front->_right);
		}
		else//在前面遇到空就停下来
		{
			flag=1;
		}
		QueuePop(&queue);
		if (flag == 1)
		{
			break;
		}
	}
	QueuePop(&queue);
	//停下来后判断同一层
	while (QueueSize(&queue) > 0)
	{
		front = QueueFront(&queue);
		if (front->_left != NULL)
			return 0;
		if (front->_left != NULL)
			return 0;
		QueuePop(&queue);
	}
	return 1;
}