二叉树的实现

BTree *Create_BTree()//创建一个二叉树
{
	BTree *btree = (BTree*)malloc(sizeof(BTree)/sizeof(char));
	if (btree == NULL)
		return NULL;
	
	btree->count = 0;
	btree->root  = NULL;
	
	
	return btree;
}


int Btree_Insert(BTree *tree, BTreeData data, int pos, int count, int flag)//增加孩子
{
	if (tree == NULL || (flag != BLEFT && flag != BRIGHT))
		return FALSE;
	
	BTreeNode *node = (BTreeNode*)malloc(sizeof(BTreeNode)/sizeof(char));//创建一个节点
	if (node == NULL)
		return FALSE;
	
	node->data = data;
	node->lchild = NULL;
	node->rchild = NULL;
	
	
	
	BTreeNode *parent = NULL;
	BTreeNode *current = tree->root; 
	int way;   // 保存当前走的位置
	while (count > 0 && current != NULL)
	{
		way = pos & 1;    // 取出当前走的方向
		pos = pos >> 1;   // 移去走过的路线
		
		parent = current;
		
		if (way == BLEFT)   
			current = current->lchild;
		else
			current = current->rchild;
		
		count--;
	}
	
	
	if (flag == BLEFT)
		node->lchild = current;
	else
		node->rchild = current;
	
	
	if (parent != NULL)
	{
		if (way == BLEFT)
			parent->lchild = node;
		else
			parent->rchild = node;
	}
	else
	{
		tree->root = node;  // 替换根节点
	}

	
	tree->count ++;
	
	return TRUE;
}

void r_display(BTreeNode* node, Print_BTree pfunc,int gap)//打印孩子
{
	int i;
	if (node == NULL)
	{
		for (i = 0; i < gap; i++)
		{
			printf ("-");
		}
		printf ("\n");
		return;
	}
	
	for (i = 0; i < gap; i++)
	{
		printf ("-");
	}
	
	// 打印结点
 printf ("%c\n", node->data);
	
	if (node->lchild != NULL || node->rchild != NULL)
	{
		
		r_display (node->lchild, pfunc, gap+4);// 打印左孩子
		r_display (node->rchild, pfunc, gap+4);// 打印右孩子

	}
}

void Display (BTree* tree, Print_BTree pfunc)//打印树
{
	if (tree == NULL)
		return;
	
	r_display(tree->root, pfunc, 0);
}

void r_delete (BTree *tree, BTreeNode* node)//删除孩子
{
	if (node == NULL || tree == NULL)
		return ;
	
	
	r_delete (tree, node->lchild);// 先删除左孩子
	r_delete (tree, node->rchild);// 删除右孩子

	
	free (node);
	
	tree->count --;
}

int Delete (BTree *tree, int pos, int count)//删除
{
	if (tree == NULL)
		return FALSE;
	
	BTreeNode* parent  = NULL;
	BTreeNode* current = tree->root;
	int way;
	while (count > 0 && current != NULL)
	{
		way = pos & 1;
		pos = pos >> 1;
		
		parent = current;
		
		if (way == BLEFT)
			current = current->lchild;
		else
			current = current->rchild;
		
		count --;
	}
	
	if (parent != NULL)
	{
		if (way == BLEFT)
			parent->lchild = NULL;
		else
			parent->rchild = NULL;
	}
	else
	{
		tree->root = NULL;
	}
	r_delete (tree, current);
	
	return TRUE;
}

int r_height (BTreeNode *node)//得到孩子高
{
	if (node == NULL)
		return 0;
	
	int lh = r_height (node->lchild);
	int rh = r_height (node->rchild);
	
	return (lh > rh ? lh+1 : rh+1);
}

int BTree_Height (BTree *tree)//得到树高
{
	if (tree == NULL)
		return FALSE;
	
	int ret = r_height(tree->root);
	
	return ret;
}

int r_degree (BTreeNode * node)//得到度
{
	if (node == NULL)
		return 0;
	
	int degree = 0;
	if (node->lchild != NULL)
		degree++;
	if (node->rchild != NULL)
		degree++;
	
	if (degree == 1)
	{
		int ld = r_degree (node->lchild);
		if (ld == 2)
			return 2;
		
		int rd = r_degree (node->rchild);
		if (rd == 2)
			return 2;
	}

	return degree;
}

int BTree_Degree (BTree *tree)//度
{
	if (tree == NULL)
		return FALSE;
	
	int ret = r_degree(tree->root);
	
	return ret;
}

int BTree_Clear (BTree *tree)//清空树
{
	if (tree == NULL)
		return FALSE;
	
	Delete (tree, 0, 0); 
	
	tree->root = NULL;
	
	return TRUE;
}

int BTree_Destroy (BTree **tree)//销毁树
{
	if (tree == NULL)
		return FALSE;
	
	BTree_Clear(*tree);
	
	free (*tree);
	*tree = NULL;
	return TRUE;
}


void pre_order (BTreeNode *node)//前序遍历
{
	if (node == NULL)
		return;
	
	printf ("%4c", node->data);
	pre_order (node->lchild);
	pre_order (node->rchild);
}

void mid_order (BTreeNode *node)//中序遍历
{
	if (node == NULL)
		return;
	
	mid_order (node->lchild);
	printf ("%4c", node->data);
	mid_order (node->rchild);
}


void last_order (BTreeNode *node)//后序遍历
{
	if (node == NULL)
		return;
	
	last_order (node->lchild);	
	last_order (node->rchild);
	printf ("%4c", node->data);
}

在计算机科学中，二叉树是每个节点最多有两个子树的树结构。通常子树被称作“左子树”（left subtree）和“右子树”（right subtree）。二叉树常被用于实现二叉查找树和二叉堆。

二叉树的每个结点至多只有二棵子树(不存在度大于2的结点)，二叉树的子树有左右之分，次序不能颠倒。二叉树的第i层至多有2^{i-1}个结点；深度为k的二叉树至多有2^k-1个结点；对任何一棵二叉树T，如果其终端结点数为n_0，度为2的结点数为n_2，则n_0=n_2+1。

一棵深度为k，且有2^k-1个节点称之为满二叉树；深度为k，有n个节点的二叉树，当且仅当其每一个节点都与深度为k的满二叉树中，序号为1至n的节点对应时，称之为完全二叉树。

1、先序遍历：先序遍历是先输出根节点，再输出左子树，最后输出右子树。先序遍历结果就是：ABCDEF

2、中序遍历：中序遍历是先输出左子树，再输出根节点，最后输出右子树。中序遍历结果就是：CBDAEF

3、后序遍历：后序遍历是先输出左子树，再输出右子树，最后输出根节点。后序遍历结果就是：CDBFEA