二叉树的遍历（递归，迭代，Morris遍历）

二叉树的三种遍历方法：

先序，中序，后序，这三种遍历方式每一个都可以用递归，迭代，Morris三种形式实现，其中Morris效率最高，空间复杂度为O(1)。

主要参考博客：

二叉树的遍历(递归，迭代，Morris遍历）

Morris Traversal方法遍历二叉树（非递归，不用栈，O(1)空间）

#include <iostream>
#include <vector>
#include <stack>
using namespace std;

struct TreeNode{
	int val;
	TreeNode* left;
	TreeNode* right;
	TreeNode(int _val) :val(_val){
		left = NULL; right = NULL;
	}

};

TreeNode* BuildTree()
{
	TreeNode* root = new TreeNode(6);

	int array[] = { 2, 7, 1, 4, 9, 3, 5, 8 };
	vector<TreeNode*>  list;
	//cout << sizeof(array) / sizeof(array[0]) << endl;
	for (size_t i = 0; i <sizeof(array)/sizeof(array[0]); i++)
	{
		TreeNode* t = new TreeNode(array[i]);
		list.push_back(t);
	}
	root->left = list[0];
	root->right = list[1];
	list[0]->left = list[2];
	list[0]->right = list[3];
	list[1]->right = list[4];
	list[3]->left = list[5];
	list[3]->right = list[6];
	list[4]->left = list[7];

	return root;
}

void preorderRecursive(TreeNode* t)
{
	if (t == NULL)
		return;
	cout << t->val << " ";
	preorderRecursive(t->left);
	preorderRecursive(t->right);

}

void preorderIterative(TreeNode* root)
{
	if (root == NULL)
		return;
	stack<TreeNode*> stk;
	TreeNode* cur = root;
	while (cur || !stk.empty())
	{
		while (cur)
		{
			cout << cur->val << " ";
			stk.push(cur);
			cur = cur->left;
		}
		if (!stk.empty())
		{
			cur = stk.top();
			stk.pop();
			cur = cur->right;
		}
	}

}

void preorderMorris(TreeNode* root)
{
	if (root == NULL)
		return;
	TreeNode* cur = root;
	TreeNode* pre = NULL;//前驱节点
	while (cur)
	{
		if (cur->left == NULL){
			cout << cur->val << " ";
			cur = cur->right;
		}
		else{
			pre = cur->left;
			while (pre->right != NULL &&  pre->right != cur)
				pre = pre->right;
			if (pre->right == NULL){
				cout << cur->val << " ";
				pre->right = cur;
				cur = cur->left;
			}
			else{
				pre->right = NULL;
				cur = cur->right;
			}
		}
	}
}

void inorderRecursive(TreeNode* root)
{
	if (root == NULL)
		return;
	inorderRecursive(root->left);
	cout << root->val << " ";
	inorderRecursive(root->right);
}

void inorderIterative(TreeNode* root)
{
	stack<TreeNode* > stk;
	TreeNode* cur = root;
	while (cur || !stk.empty())
	{
		while (cur){
			stk.push(cur);
			cur = cur->left;
		}
		if (!stk.empty()){

			cur = stk.top();
			cout << cur->val << " ";
			stk.pop();
			cur = cur->right;
		}

	}
}

void inorderMorris(TreeNode* root)
{
	TreeNode* cur = root;
	TreeNode* pre = NULL;  //前驱节点
	while (cur)
	{
		if (cur->left == NULL){
			cout << cur->val << " ";
			cur = cur->right;
		}
		else{
			pre = cur->left;
			while (pre->right != NULL && pre->right != cur)
				pre = pre->right;
			if (pre->right == NULL){
				pre -> right = cur;
				cur = cur->left;
			}
			else{
				cout << cur->val << " ";
				pre->right = NULL;
				cur = cur->right;
			}
		}
	}
}

void postorderRecursive(TreeNode* root)
{
	if (root == NULL)
		return;
	postorderRecursive(root->left);
	postorderRecursive(root->right);
	cout << root->val << " ";

}

void postorderIterative(TreeNode* root)
{
	stack<TreeNode*> stk;
	TreeNode* cur = root;
	TreeNode* pre = NULL;
	while (cur || !stk.empty()){
		while (cur){
			stk.push(cur);
			cur = cur->left;
		}
		if (!stk.empty()){
			cur = stk.top();
			if (cur->right != NULL && cur->right != pre){
				cur = cur->right;
			}
			else{
				cout << cur->val<<" ";
				pre = cur;
				stk.pop();
				cur = NULL;
			}
		}
	}
}

void reverse(TreeNode *begin, TreeNode *end) {
	if (begin == end)
		return;
	TreeNode *pre = begin;
	TreeNode *cur = begin->right;
	TreeNode *next;
	while (pre != end) {
		TreeNode* temp = cur->right;
		cur->right = pre;
		pre = cur;
		cur = temp;
	}
}

void traversalReversal(TreeNode *begin, TreeNode *end) {
	reverse(begin, end);
	TreeNode *it = end;
	while (true) {
		cout << it->val << " ";
		if (it == begin)
			break;
		it = it->right;
	}
	reverse(end, begin);
}

void postorderMorris(TreeNode *root) {
	if (!root)
		return;
	TreeNode dump(0);
	dump.left = root;
	TreeNode *cur = &dump;
	TreeNode *pre = NULL;
	while (cur) {
		if (cur->left == NULL) {
			cur = cur->right;
		}
		else {
			pre = cur->left;
			while (pre->right != NULL && pre->right != cur)
				pre = pre->right;
			if (pre->right == NULL) {
				pre->right = cur;
				cur = cur->left;
			}
			else {
				traversalReversal(cur->left, pre);
				pre->right = NULL;
				cur = cur->right;
			}
		}
	}
}

int main(void)
{

	TreeNode* root = BuildTree();
	cout << "----------Preorder Recursive--------------" << endl;
	preorderRecursive(root);
	cout <<endl;
	cout << "----------Preorder Iterative---------------" << endl;
	preorderIterative(root);
	cout << endl;
	cout << "----------Preorder Morris---------------" << endl;
	preorderMorris(root);
	cout << endl;
	cout << endl;

	cout << "----------Inorder Recursive--------------" << endl;
	inorderRecursive(root);
	cout << endl;
	cout << "----------Inorder Iterative--------------" << endl;
	inorderIterative(root);
	cout << endl;
	cout << "----------Inorder Morris-----------------" << endl;
	inorderMorris(root);
	cout << endl;
	cout << endl;

	cout << "----------Postorder Recursive--------------" << endl;
	postorderRecursive(root);
	cout << endl;
	cout << "----------Postorder Iterative--------------" << endl;
	postorderIterative(root);
	cout << endl;
	cout << "----------Postorder Morris-----------------" << endl;
	postorderMorris(root);
	cout << endl;

}