二叉树的遍历及相关知识

• • 1. 递归遍历
  • • 1.1 前序遍历
    • 1.2 中序遍历
    • 1.3 后序遍历
  • 2. 迭代遍历
  • • 2.1 前序遍历
    • 2.2 后序遍历
    • 2.3 中序遍历
  • 3. 层序遍历
  • 4. 二叉树的种类

vector res;
vector PreTravelsal(vector res, TreeNode* root)
{
	res.clear();
	travelsal(root);
	return res;	
}
void travelsal(TreeNode* cur)
{
	if(cur == NULL) return;
	res.push_back(cur->val);
	travelsal(cur->left);
	travelsal(cur->right);
}

vector res;
vector PreTravelsal(vector res, TreeNode* root)
{
	res.clear();
	travelsal(root);
	return res;	
}
void travelsal(TreeNode* cur)
{
	if(cur == NULL) return;
	res.push_back(cur->val);
	//travelsal(cur->left);
	res.push_back(cur->val);
	travelsal(cur->right);
}

vector res;
vector PreTravelsal(vector res, TreeNode* root)
{
	res.clear();
	travelsal(root);
	return res;	
}
void travelsal(TreeNode* cur)
{
	if(cur == NULL) return;
	//res.push_back(cur->val);
	travelsal(cur->left);
	travelsal(cur->right);
	res.push_back(cur->val);
}

vector travelsal(TreeNode* root)
{
	vector res;
	stack st;
	if(root == NULL) return res;
	st.push(root);
	while(!st.empty())
	{
		TreeNode* cur = st.top();
		st.pop();
		res.push_back(cur->val);
		if(cur->right) st.push(cur->right);
		if(cur->left) st.push(cur->left);
	}
	return res;
}

vector travelsal(TreeNode* root)
{
	vector res;
	stack st;
	if(root == NULL) return res;
	st.push(root);
	while(!st.empty())
	{
		TreeNode* cur = st.top();
		st.pop();
		res.push_back(cur->val);
		if(cur->left) st.push(cur->left);
		if(cur->right) st.push(cur->right);
	}
	reverse(res.begin(), res.end());
	return res;
}

vector travelsal(TreeNode* root)
{
	vector res;
	stack st;
	TreeNode* cur = root;
	while(cur != NULL || !st.empty())
	{
		if(cur != NULL)
		{
			st.push(cur);
			cur = cur->left;
		}
		else
		{
			cur = st.top();
			st.pop();
			res.push_back(cur->val);
			cur = cur->right;
		}
	}
	return res;

vector travelsal(TreeNode* root)
{
	vector res;
	queue que;
	if(root == NULL) return res;
	que.push(root);
	while(!que.empty())
	{
		int n = que.size();
		for(int i = 0; i < n; i++)
		{
			TreeNode* cur = que.front();
			que.pop();
			res.push_back(cur->val);
			if(cur->left) que.push(cur->left);
			if(cur->right) que.push(cur->right);
		}
	}
	return res;
}

1. 完全二叉树：一根二叉树只有度为0的结点和度为2的结点，并且度为0的结点在同一层上，其深度为k，结点数为2^k-1；
2. 完全二叉树：在完全二叉树中，除了最底层节点可能没填满外，其余每层节点数都达到最大值，并且最下面一层的节点都集中在该层最左边的若干位置。若最底层为第 h 层，则该层包含 1~ 2^(h-1) 个节点。
   
3. 二叉搜索树：若它的左子树不空，则左子树上所有结点的值均小于它的根结点的值；若它的右子树不空，则右子树上所有结点的值均大于它的根结点的值；它的左、右子树也分别为二叉排序树。
   
   4.平衡二叉搜索树：又被称为AVL（Adelson-Velsky and Landis）树，且具有以下性质：它是一棵空树或它的左右两个子树的高度差的绝对值不超过1，并且左右两个子树都是一棵平衡二叉树。