# 145. Binary Tree Postorder Traversal

## Description

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

Example 1:

Input: root = [1,null,2,3]
Output: [3,2,1]


Example 2:

Input: root = []
Output: []


Example 3:

Input: root = [1]
Output: [1]


Constraints:

• The number of the nodes in the tree is in the range [0, 100].
• -100 <= Node.val <= 100

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

## Solutions

1. Recusive Traversal

2. Non-recursive using Stack

3. Morris Traversal

• /**
* Definition for a binary tree node.
* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode() {}
*     TreeNode(int val) { this.val = val; }
*     TreeNode(int val, TreeNode left, TreeNode right) {
*         this.val = val;
*         this.left = left;
*         this.right = right;
*     }
* }
*/
class Solution {
public List<Integer> postorderTraversal(TreeNode root) {
while (root != null) {
if (root.right == null) {
root = root.left;
} else {
TreeNode next = root.right;
while (next.left != null && next.left != root) {
next = next.left;
}
if (next.left == null) {
next.left = root;
root = root.right;
} else {
next.left = null;
root = root.left;
}
}
}
return ans;
}
}

• /**
* Definition for a binary tree node.
* struct TreeNode {
*     int val;
*     TreeNode *left;
*     TreeNode *right;
*     TreeNode() : val(0), left(nullptr), right(nullptr) {}
*     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
*     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
vector<int> postorderTraversal(TreeNode* root) {
vector<int> ans;
while (root) {
if (!root->right) {
ans.push_back(root->val);
root = root->left;
} else {
TreeNode* next = root->right;
while (next->left && next->left != root) {
next = next->left;
}
if (!next->left) {
ans.push_back(root->val);
next->left = root;
root = root->right;
} else {
next->left = nullptr;
root = root->left;
}
}
}
reverse(ans.begin(), ans.end());
return ans;
}
};

• # Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
def postorderTraversal(self, root: Optional[TreeNode]) -> List[int]:
ans = []
while root:
if root.right is None:
ans.append(root.val)
root = root.left
else:
next = root.right
while next.left and next.left != root:
next = next.left
if next.left != root:
ans.append(root.val)
next.left = root
root = root.right
else:
next.left = None
root = root.left
return ans[::-1]


• /**
* Definition for a binary tree node.
* type TreeNode struct {
*     Val int
*     Left *TreeNode
*     Right *TreeNode
* }
*/
func postorderTraversal(root *TreeNode) []int {
var ans []int
for root != nil {
if root.Right == nil {
ans = append([]int{root.Val}, ans...)
root = root.Left
} else {
next := root.Right
for next.Left != nil && next.Left != root {
next = next.Left
}
if next.Left == nil {
ans = append([]int{root.Val}, ans...)
next.Left = root
root = root.Right
} else {
next.Left = nil
root = root.Left
}
}
}
return ans
}

• /**
* Definition for a binary tree node.
* class TreeNode {
*     val: number
*     left: TreeNode | null
*     right: TreeNode | null
*     constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
*         this.val = (val===undefined ? 0 : val)
*         this.left = (left===undefined ? null : left)
*         this.right = (right===undefined ? null : right)
*     }
* }
*/

function postorderTraversal(root: TreeNode | null): number[] {
if (root == null) return [];
let stack = [];
let ans = [];
let prev = null;
while (root || stack.length) {
while (root) {
stack.push(root);
root = root.left;
}
root = stack.pop();
if (!root.right || root.right == prev) {
ans.push(root.val);
prev = root;
root = null;
} else {
stack.push(root);
root = root.right;
}
}
return ans;
}


• // Definition for a binary tree node.
// #[derive(Debug, PartialEq, Eq)]
// pub struct TreeNode {
//   pub val: i32,
//   pub left: Option<Rc<RefCell<TreeNode>>>,
//   pub right: Option<Rc<RefCell<TreeNode>>>,
// }
//
// impl TreeNode {
//   #[inline]
//   pub fn new(val: i32) -> Self {
//     TreeNode {
//       val,
//       left: None,
//       right: None
//     }
//   }
// }
use std::rc::Rc;
use std::cell::RefCell;
impl Solution {
fn dfs(root: &Option<Rc<RefCell<TreeNode>>>, res: &mut Vec<i32>) {
if root.is_none() {
return;
}
let node = root.as_ref().unwrap().borrow();
Self::dfs(&node.left, res);
Self::dfs(&node.right, res);
res.push(node.val);
}

pub fn postorder_traversal(root: Option<Rc<RefCell<TreeNode>>>) -> Vec<i32> {
let mut res = vec![];
Self::dfs(&root, &mut res);
res
}
}