145. Binary Tree Postorder Traversal

题目：

Given a binary tree, return the postorder traversal of its nodes' values.

For example:
Given binary tree {1,#,2,3},

   1
    \
     2
    /
   3

return [3,2,1].

Note: Recursive solution is trivial, could you do it iteratively?

链接： http://leetcode.com/problems/binary-tree-postorder-traversal/

题解：

二叉树后序遍历。 刚接触leetcode时也做过这道题，用了很蠢笨的方法。现在学习discuss里大神们的版本，真的进步很多。下面这个版本是基于上道题目 - 二叉树先序遍历的。由于后序遍历是left -> right -> root，  先序是root -> left -> right， 所以我们改变的只是如何插入结果到 list里，以及被压入栈的先后顺序而已。在这里，pop出的结果要插入到list前部，而且要先把左子树压入栈，其次是右子树。

Time Complexity - O(n)，Space Complexity - O(n)。

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<Integer> postorderTraversal(TreeNode root) {
        List<Integer> res = new LinkedList<>();
        if(root == null)
            return res;
        Stack<TreeNode> stack = new Stack<>();
        stack.push(root);

        while(!stack.isEmpty()) {
            TreeNode node = stack.pop();
            if(node != null) {
                res.add(0, node.val);           // insert at the front of list
                stack.push(node.left);          // opposite push
                stack.push(node.right);
            }
        }

        return res;
    }
}

二刷:

Java:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<Integer> postorderTraversal(TreeNode root) {
        List<Integer> res = new LinkedList<>();
        if (root == null) return res;
        Stack<TreeNode> stack = new Stack<>();
        stack.push(root);

        while (!stack.isEmpty()) {
            TreeNode node = stack.pop();
            if (node != null) {
                res.add(0, node.val);
                stack.push(node.left);
                stack.push(node.right);
            }
        }
        return res;
    }
}

Recursive:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<Integer> postorderTraversal(TreeNode root) {
        List<Integer> res = new ArrayList<>();
        postorderTraversal(res, root);
        return res;
    }

    private void postorderTraversal(List<Integer> res, TreeNode root) {
        if (root == null) return;
        postorderTraversal(res, root.left);
        postorderTraversal(res, root.right);
        res.add(root.val);
    }
}

三刷:

Java:

Reversed preorder traversal with LinkedList and Stack:

主要使用一个LinkedList和一个stack来辅助我们的遍历。其实顺序和pre-order并没有区别，只是把遍历过的节点值不断从链表头部插入，也就形成了我们的后续遍历。注意处理节点的左节点和右节点时，对栈先压入左节点再压入右节点，之后pop时我们就会先处理右节点。

Time Complexity - O(n)，Space Complexity - O(n)。

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<Integer> postorderTraversal(TreeNode root) {
        List<Integer> res = new LinkedList<>();
        if (root == null) return res;
        Stack<TreeNode> stack = new Stack<>();
        TreeNode node = root;
        stack.push(node);
        while (!stack.isEmpty()) {
            node = stack.pop();
            res.add(0, node.val);
            if (node.left != null) stack.push(node.left);
            if (node.right != null) stack.push(node.right);
        }
        return res;
    }
}

Recursive:

Time Complexity - O(n)，Space Complexity - O(n)。

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<Integer> postorderTraversal(TreeNode root) {
        List<Integer> res = new ArrayList<>();
        postorderTraversal(res, root);
        return res;
    }

    private void postorderTraversal(List<Integer> res, TreeNode root) {
        if (root == null) return;
        postorderTraversal(res, root.left);
        postorderTraversal(res, root.right);
        res.add(root.val);
    }
}

Morris Traversal:

三刷终于学习了Morris Traversal。这里的Morris Traversal也使用的是Reversed Preorder traversal with LinkedList。也就是使用类似与Preorder traversal类似的代码，以及一个LinkedList，每次从表头插入结果。

因为Postorder和Preorder的对应关系，这里与Preorder Morris Traversal不同的就是，我们要找的不是左子树的predecessor，而是右子树中当前节点的successor，也就是当前节点右子树中最左边的元素。下面我们详述一下步骤。

1. 依然先做一个root的reference - node，在node非空的情况对树进行遍历。当node.right为空的时候，我们将node.val从链表res头部插入，然后向左遍历左子树
2. 假如右子树非空，则我们要找到当前节点在右子树中的succesor，简称succ，一样是两种情况:
   1. 首次访问succ，此时succ.left = null，我们把succ和当前node连接起来，进行succ.left = node。之后讲node.val从链表res头部插入，向右遍历node.right
   2. 否则，我们二次访问succ，这时succ.left = node，我们做一个还原操作，设succ.left = null，然后向左遍历node.left。因为node.val已经处理过，所以不要重复处理node.val.

Time Complexity - O(n)，Space Complexity - O(1)。

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<Integer> postorderTraversal(TreeNode root) {
        List<Integer> res = new LinkedList<>();
        TreeNode node = root, succ = null;
        while (node != null) {
            if (node.right == null) {
                res.add(0, node.val);
                node = node.left;
            } else {
                succ = node.right;
                while (succ.left != null && succ.left != node) {
                    succ = succ.left;
                }
                if (succ.left == null) {
                    succ.left = node;
                    res.add(0, node.val);
                    node = node.right;
                } else {
                    succ.left = null;
                    node = node.left;
                }
            }
        }
        return res;
    }
}

Reference：

144. Binary Tree Preorder Traversal

https://leetcode.com/discuss/9736/accepted-code-with-explaination-does-anyone-have-better-idea

https://leetcode.com/discuss/71943/preorder-inorder-and-postorder-iteratively-summarization

https://leetcode.com/discuss/21995/a-very-concise-solution

https://leetcode.com/discuss/36711/solutions-iterative-recursive-traversal-different-solutions