# Iterative Postorder Traversal | Set 2 (Using One Stack)

• Difficulty Level : Hard
• Last Updated : 27 Jun, 2022

We have discussed a simple iterative postorder traversal using two stacks in the previous post. In this post, an approach with only one stack is discussed.

The idea is to move down to leftmost node using left pointer. While moving down, push root and root’s right child to stack. Once we reach leftmost node, print it if it doesn’t have a right child. If it has a right child, then change root so that the right child is processed before.

Following is detailed algorithm.

```1.1 Create an empty stack
2.1 Do following while root is not NULL
a) Push root's right child and then root to stack.
b) Set root as root's left child.
2.2 Pop an item from stack and set it as root.
a) If the popped item has a right child and the right child
is at top of stack, then remove the right child from stack,
push the root back and set root as root's right child.
b) Else print root's data and set root as NULL.
2.3 Repeat steps 2.1 and 2.2 while stack is not empty.```

Let us consider the following tree Following are the steps to print postorder traversal of the above tree using one stack.

```1. Right child of 1 exists.
Push 3 to stack. Push 1 to stack. Move to left child.
Stack: 3, 1

2. Right child of 2 exists.
Push 5 to stack. Push 2 to stack. Move to left child.
Stack: 3, 1, 5, 2

3. Right child of 4 doesn't exist. '
Push 4 to stack. Move to left child.
Stack: 3, 1, 5, 2, 4

4. Current node is NULL.
Pop 4 from stack. Right child of 4 doesn't exist.
Print 4. Set current node to NULL.
Stack: 3, 1, 5, 2

5. Current node is NULL.
Pop 2 from stack. Since right child of 2 equals stack top element,
pop 5 from stack. Now push 2 to stack.
Move current node to right child of 2 i.e. 5
Stack: 3, 1, 2

6. Right child of 5 doesn't exist. Push 5 to stack. Move to left child.
Stack: 3, 1, 2, 5

7. Current node is NULL. Pop 5 from stack. Right child of 5 doesn't exist.
Print 5. Set current node to NULL.
Stack: 3, 1, 2

8. Current node is NULL. Pop 2 from stack.
Right child of 2 is not equal to stack top element.
Print 2. Set current node to NULL.
Stack: 3, 1

9. Current node is NULL. Pop 1 from stack.
Since right child of 1 equals stack top element, pop 3 from stack.
Now push 1 to stack. Move current node to right child of 1 i.e. 3
Stack: 1

10. Repeat the same as above steps and Print 6, 7 and 3.
Pop 1 and Print 1.```

## C++

 `// C++ program for iterative postorder traversal using one``// stack``#include ``using` `namespace` `std;` `// A tree node``struct` `Node {``    ``int` `data;``    ``struct` `Node *left, *right;``};` `// A utility function to create a new tree node``struct` `Node* newNode(``int` `data)``{``    ``struct` `Node* node = ``new` `Node;``    ``node->data = data;``    ``node->left = node->right = NULL;``    ``return` `node;``}` `// An iterative function to do postorder traversal of a``// given binary tree``vector<``int``> postOrderIterative(``struct` `Node* root)``{``    ``vector<``int``> postOrderList;``    ``// Check for empty tree``    ``if` `(root == NULL)``        ``return` `postOrderList;``    ``stack S;``    ``S.push(root);``    ``Node* prev = NULL;``    ``while` `(!S.empty()) {``        ``auto` `current = S.top();``        ``/* go down the tree in search of a leaf an if so``           ``process it and pop stack otherwise move down */``        ``if` `(prev == NULL || prev->left == current``            ``|| prev->right == current) {``            ``if` `(current->left)``                ``S.push(current->left);``            ``else` `if` `(current->right)``                ``S.push(current->right);``            ``else` `{``                ``S.pop();``                ``postOrderList.push_back(current->data);``            ``}``            ``/* go up the tree from left node, if the child``               ``is right push it onto stack otherwise process``               ``parent and pop stack */``        ``}` `        ``else` `if` `(current->left == prev) {``            ``if` `(current->right)``                ``S.push(current->right);``            ``else` `{``                ``S.pop();``                ``postOrderList.push_back(current->data);``            ``}` `            ``/* go up the tree from right node and after``            ``coming back from right node process parent and``            ``pop stack */``        ``}``        ``else` `if` `(current->right == prev) {``            ``S.pop();``            ``postOrderList.push_back(current->data);``        ``}``        ``prev = current;``    ``}``    ``return` `postOrderList;``}` `// Driver program to test above functions``int` `main()``{``    ``// Let us construct the tree shown in above figure``    ``struct` `Node* root = NULL;``    ``root = newNode(1);``    ``root->left = newNode(2);``    ``root->right = newNode(3);``    ``root->left->left = newNode(4);``    ``root->left->right = newNode(5);``    ``root->right->left = newNode(6);``    ``root->right->right = newNode(7);``    ``printf``(``"Post order traversal of binary tree is :\n"``);``    ``printf``(``"["``);``    ``vector<``int``> postOrderList = postOrderIterative(root);``    ``for` `(``auto` `it : postOrderList)``        ``cout << it << ``" "``;``    ``printf``(``"]"``);``    ``return` `0;``}` `// This code is contributed by Aditya Kumar (adityakumar129)`

## C

 `// C program for iterative postorder traversal using one``// stack``#include ``#include ` `// Maximum stack size``#define MAX_SIZE 100` `// A tree node``struct` `Node {``    ``int` `data;``    ``struct` `Node *left, *right;``};` `// Stack type``struct` `Stack {``    ``int` `size;``    ``int` `top;``    ``struct` `Node** array;``};` `// A utility function to create a new tree node``struct` `Node* newNode(``int` `data)``{``    ``struct` `Node* node``        ``= (``struct` `Node*)``malloc``(``sizeof``(``struct` `Node));``    ``node->data = data;``    ``node->left = node->right = NULL;``    ``return` `node;``}` `// A utility function to create a stack of given size``struct` `Stack* createStack(``int` `size)``{``    ``struct` `Stack* stack``        ``= (``struct` `Stack*)``malloc``(``sizeof``(``struct` `Stack));``    ``stack->size = size;``    ``stack->top = -1;``    ``stack->array = (``struct` `Node**)``malloc``(``        ``stack->size * ``sizeof``(``struct` `Node*));``    ``return` `stack;``}` `// BASIC OPERATIONS OF STACK``int` `isFull(``struct` `Stack* stack)``{``    ``return` `stack->top - 1 == stack->size;``}` `int` `isEmpty(``struct` `Stack* stack)``{``    ``return` `stack->top == -1;``}` `void` `push(``struct` `Stack* stack, ``struct` `Node* node)``{``    ``if` `(isFull(stack))``        ``return``;``    ``stack->array[++stack->top] = node;``}` `struct` `Node* pop(``struct` `Stack* stack)``{``    ``if` `(isEmpty(stack))``        ``return` `NULL;``    ``return` `stack->array[stack->top--];``}` `struct` `Node* peek(``struct` `Stack* stack)``{``    ``if` `(isEmpty(stack))``        ``return` `NULL;``    ``return` `stack->array[stack->top];``}` `// An iterative function to do postorder traversal of a``// given binary tree``void` `postOrderIterative(``struct` `Node* root)``{``    ``// Check for empty tree``    ``if` `(root == NULL)``        ``return``;` `    ``struct` `Stack* stack = createStack(MAX_SIZE);``    ``do` `{``        ``// Move to leftmost node``        ``while` `(root) {``            ``// Push root's right child and then root to``            ``// stack.``            ``if` `(root->right)``                ``push(stack, root->right);``            ``push(stack, root);` `            ``// Set root as root's left child``            ``root = root->left;``        ``}` `        ``// Pop an item from stack and set it as root``        ``root = pop(stack);` `        ``// If the popped item has a right child and the``        ``// right child is not processed yet, then make sure``        ``// right child is processed before root``        ``if` `(root->right && peek(stack) == root->right) {``            ``pop(stack); ``// remove right child from stack``            ``push(stack, root); ``// push root back to stack``            ``root = root->right; ``// change root so that the``                                ``// right child is processed``                                ``// next``        ``}``        ``else` `// Else print root's data and set root as NULL``        ``{``            ``printf``(``"%d "``, root->data);``            ``root = NULL;``        ``}``    ``} ``while` `(!isEmpty(stack));``}` `// Driver program to test above functions``int` `main()``{``    ``// Let us construct the tree shown in above figure``    ``struct` `Node* root = NULL;``    ``root = newNode(1);``    ``root->left = newNode(2);``    ``root->right = newNode(3);``    ``root->left->left = newNode(4);``    ``root->left->right = newNode(5);``    ``root->right->left = newNode(6);``    ``root->right->right = newNode(7);``    ``printf``(``"Post order traversal of binary tree is :\n"``);``    ``printf``(``"["``);``    ``postOrderIterative(root);``    ``printf``(``"]"``);` `    ``return` `0;``}` `// This code is contributed by Aditya Kumar (adityakumar129)`

## Java

 `// A java program for iterative postorder traversal using``// stack` `import` `java.util.ArrayList;``import` `java.util.Stack;` `// A binary tree node``class` `Node {``    ``int` `data;``    ``Node left, right;` `    ``Node(``int` `item)``    ``{``        ``data = item;``        ``left = right;``    ``}``}` `class` `BinaryTree {``    ``Node root;``    ``ArrayList list = ``new` `ArrayList();` `    ``// An iterative function to do postorder traversal``    ``// of a given binary tree``    ``ArrayList postOrderIterative(Node node)``    ``{``        ``Stack S = ``new` `Stack();` `        ``// Check for empty tree``        ``if` `(node == ``null``)``            ``return` `list;``        ``S.push(node);``        ``Node prev = ``null``;``        ``while` `(!S.isEmpty()) {``            ``Node current = S.peek();` `            ``/* go down the tree in search of a leaf an if so``            ``process it and pop stack otherwise move down */``            ``if` `(prev == ``null` `|| prev.left == current || prev.right == current) {``                ``if` `(current.left != ``null``)``                    ``S.push(current.left);``                ``else` `if` `(current.right != ``null``)``                    ``S.push(current.right);``                ``else` `{``                    ``S.pop();``                    ``list.add(current.data);``                ``}` `                ``/* go up the tree from left node, if the``                ``child is right push it onto stack otherwise``                ``process parent and pop stack */``            ``}``            ``else` `if` `(current.left == prev) {``                ``if` `(current.right != ``null``)``                    ``S.push(current.right);``                ``else` `{``                    ``S.pop();``                    ``list.add(current.data);``                ``}` `                ``/* go up the tree from right node and after``                ``coming back from right node process parent``                ``and pop stack */``            ``}``            ``else` `if` `(current.right == prev) {``                ``S.pop();``                ``list.add(current.data);``            ``}` `            ``prev = current;``        ``}` `        ``return` `list;``    ``}` `    ``// Driver program to test above functions``    ``public` `static` `void` `main(String args[])``    ``{``        ``BinaryTree tree = ``new` `BinaryTree();` `        ``// Let us create trees shown in above diagram``        ``tree.root = ``new` `Node(``1``);``        ``tree.root.left = ``new` `Node(``2``);``        ``tree.root.right = ``new` `Node(``3``);``        ``tree.root.left.left = ``new` `Node(``4``);``        ``tree.root.left.right = ``new` `Node(``5``);``        ``tree.root.right.left = ``new` `Node(``6``);``        ``tree.root.right.right = ``new` `Node(``7``);` `        ``ArrayList mylist = tree.postOrderIterative(tree.root);` `        ``System.out.println(``            ``"Post order traversal of binary tree is :"``);``        ``System.out.println(mylist);``    ``}``}` `// This code is contributed by Aditya Kumar (adityakumar129)`

## Python3

 `# Python3 program for iterative postorder traversal``# using one stack` `# Stores the answer``ans ``=` `[]` `# A Binary tree node``class` `Node:``    ` `    ``# Constructor to create a new node``    ``def` `__init__(``self``, data):``        ``self``.data ``=` `data``        ``self``.left ``=` `None``        ``self``.right ``=` `None` `def` `peek(stack):``    ``if` `len``(stack) > ``0``:``        ``return` `stack[``-``1``]``    ``return` `None``# A iterative function to do postorder traversal of``# a given binary tree``def` `postOrderIterative(root):``        ` `    ``# Check for empty tree``    ``if` `root ``is` `None``:``        ``return` `    ``stack ``=` `[]``    ` `    ``while``(``True``):``        ` `        ``while` `(root):``            ``# Push root's right child and then root to stack``            ``if` `root.right ``is` `not` `None``:``                ``stack.append(root.right)``            ``stack.append(root)` `            ``# Set root as root's left child``            ``root ``=` `root.left``        ` `        ``# Pop an item from stack and set it as root``        ``root ``=` `stack.pop()` `        ``# If the popped item has a right child and the``        ``# right child is not processed yet, then make sure``        ``# right child is processed before root``        ``if` `(root.right ``is` `not` `None` `and``            ``peek(stack) ``=``=` `root.right):``            ``stack.pop() ``# Remove right child from stack``            ``stack.append(root) ``# Push root back to stack``            ``root ``=` `root.right ``# change root so that the``                            ``# right childis processed next` `        ``# Else print root's data and set root as None``        ``else``:``            ``ans.append(root.data)``            ``root ``=` `None` `        ``if` `(``len``(stack) <``=` `0``):``                ``break` `# Driver program to test above function``root ``=` `Node(``1``)``root.left ``=` `Node(``2``)``root.right ``=` `Node(``3``)``root.left.left ``=` `Node(``4``)``root.left.right ``=` `Node(``5``)``root.right.left ``=` `Node(``6``)``root.right.right ``=` `Node(``7``)` `print``(``"Post Order traversal of binary tree is"``)``postOrderIterative(root)``print``(ans)` `# This code is contributed by Nikhil Kumar Singh(nickzuck_007)`

## C#

 `// A C# program for iterative postorder traversal using stack``using` `System;``using` `System.Collections.Generic;` `// A binary tree node``class` `Node``{``  ``public` `int` `data;``  ``public` `Node left, right;` `  ``public` `Node(``int` `item)``  ``{``    ``data = item;``    ``left = right;``  ``}``}` `public` `class` `BinaryTree``{``  ``Node root;``  ``List<``int``> list = ``new` `List<``int``>();` `  ``// An iterative function to do postorder traversal``  ``// of a given binary tree``  ``List<``int``> postOrderIterative(Node node)``  ``{``    ``Stack S = ``new` `Stack();` `    ``// Check for empty tree``    ``if` `(node == ``null``)``      ``return` `list;``    ``S.Push(node);``    ``Node prev = ``null``;``    ``while` `(S.Count != 0)``    ``{``      ``Node current = S.Peek();` `      ``/* go down the tree in search of a leaf an if so process it``            ``and pop stack otherwise move down */``      ``if` `(prev == ``null` `|| prev.left == current ||``          ``prev.right == current)``      ``{``        ``if` `(current.left != ``null``)``          ``S.Push(current.left);``        ``else` `if` `(current.right != ``null``)``          ``S.Push(current.right);``        ``else``        ``{``          ``S.Pop();``          ``list.Add(current.data);``        ``}` `        ``/* go up the tree from left node, if the child is right``                ``push it onto stack otherwise process parent and pop``                ``stack */``      ``}``      ``else` `if` `(current.left == prev)``      ``{``        ``if` `(current.right != ``null``)``          ``S.Push(current.right);``        ``else``        ``{``          ``S.Pop();``          ``list.Add(current.data);``        ``}` `        ``/* go up the tree from right node and after coming back``                ``from right node process parent and pop stack */``      ``}``      ``else` `if` `(current.right == prev)``      ``{``        ``S.Pop();``        ``list.Add(current.data);``      ``}` `      ``prev = current;``    ``}` `    ``return` `list;``  ``}` `  ``// Driver code``  ``public` `static` `void` `Main(String []args)``  ``{``    ``BinaryTree tree = ``new` `BinaryTree();` `    ``// Let us create trees shown in above diagram``    ``tree.root = ``new` `Node(1);``    ``tree.root.left = ``new` `Node(2);``    ``tree.root.right = ``new` `Node(3);``    ``tree.root.left.left = ``new` `Node(4);``    ``tree.root.left.right = ``new` `Node(5);``    ``tree.root.right.left = ``new` `Node(6);``    ``tree.root.right.right = ``new` `Node(7);` `    ``List<``int``> mylist = tree.postOrderIterative(tree.root);` `    ``Console.WriteLine(``"Post order traversal of binary tree is :"``);``    ``foreach``(``int` `i ``in` `mylist)``      ``Console.Write(i+``" "``);``  ``}``}` `// This code contributed by shikhasingrajput`

## Javascript

 ``

Output

```Post order traversal of binary tree is :
[4 5 2 6 7 3 1 ]```

Time Complexity: O(n)

Auxiliary Space: O(n)

Method 2:
Push directly root node two times while traversing to the left. While popping if you find stack top() is same as root then go for root->right else print root.

## C++

 `// C++ program for iterative postorder traversal using one``// stack``#include ``using` `namespace` `std;` `// A tree node``struct` `Node {``    ``int` `data;``    ``struct` `Node *left, *right;``};` `// A utility function to create a new tree node``struct` `Node* newNode(``int` `data)``{``    ``struct` `Node* node = ``new` `Node;``    ``node->data = data;``    ``node->left = node->right = NULL;``    ``return` `node;``}` `// An iterative function to do postorder traversal of a``// given binary tree``vector<``int``> postOrderIterative(``struct` `Node* root)``{``    ``vector<``int``> postOrderList;``    ``stack st;``    ``while` `(``true``) {``        ``while` `(root) {``            ``st.push(root);``            ``st.push(root);``            ``root = root->left;``        ``}``        ``if` `(st.empty())``            ``return` `postOrderList;``        ``root = st.top();``        ``st.pop();``        ``if` `(!st.empty() && st.top() == root)``            ``root = root->right;``        ``else` `{``            ``postOrderList.push_back(root->data);``            ``root = NULL;``        ``}``    ``}``    ``return` `postOrderList;``}` `// Driver program to test above functions``int` `main()``{``    ``// Let us construct the tree shown in above figure``    ``struct` `Node* root = NULL;``    ``root = newNode(1);``    ``root->left = newNode(2);``    ``root->right = newNode(3);``    ``root->left->left = newNode(4);``    ``root->left->right = newNode(5);``    ``root->right->left = newNode(6);``    ``root->right->right = newNode(7);``    ``printf``(``"Post order traversal of binary tree is :\n"``);``    ``printf``(``"["``);``    ``vector<``int``> postOrderList = postOrderIterative(root);``    ``for` `(``auto` `it : postOrderList)``        ``cout << it << ``" "``;``    ``printf``(``"]"``);``    ``return` `0;``}` `// This code is contributed by Sania Kumari Gupta``// (kriSania804)`

## Java

 `// Simple Java program to print PostOrder Traversal(Iterative)``import` `java.util.Stack;` `// A binary tree node``class` `Node``{``    ``int` `data;``    ``Node left, right;` `    ``Node(``int` `item)``    ``{``        ``data = item;``        ``left = right;``    ``}``}` `// create a postorder class``class` `PostOrder``{``    ``Node root;``    ` `    ``// An iterative function to do postorder traversal``    ``// of a given binary tree``    ``private` `void` `postOrderIterative(Node root) {``        ``Stack stack = ``new` `Stack<>();``        ``while``(``true``) {``            ``while``(root != ``null``) {``                ``stack.push(root);``                ``stack.push(root);``                ``root = root.left;``            ``}``            ` `            ``// Check for empty stack``            ``if``(stack.empty()) ``return``;``            ``root = stack.pop();``            ` `            ``if``(!stack.empty() && stack.peek() == root) root = root.right;``            ` `            ``else` `{``                ` `                ``System.out.print(root.data + ``" "``); root = ``null``;``            ``}``        ``}``    ``}``    ` `    ``// Driver program to test above functions``    ``public` `static` `void` `main(String args[])``    ``{``    ``PostOrder tree = ``new` `PostOrder();``        ` `        ``// Let us create trees shown in above diagram``        ``tree.root = ``new` `Node(``1``);``        ``tree.root.left = ``new` `Node(``2``);``        ``tree.root.right = ``new` `Node(``3``);``        ``tree.root.left.left = ``new` `Node(``4``);``        ``tree.root.left.right = ``new` `Node(``5``);``        ``tree.root.right.left = ``new` `Node(``6``);``        ``tree.root.right.right = ``new` `Node(``7``);``        ``System.out.println(``"Post order traversal of binary tree is :"``);``        ``tree.postOrderIterative(tree.root);``    ``}``}`

## Python3

 `# Simple Python3 program to print``# PostOrder Traversal(Iterative)` `# A binary tree node``class` `Node:` `    ``def` `__init__(``self``, x):``        ` `        ``self``.data ``=` `x``        ``self``.right ``=` `None``        ``self``.left ``=` `None` `# Create a postorder class` `# An iterative function to do postorder``# traversal of a given binary tree``def` `postOrderIterative(root):``    ` `    ``stack ``=` `[]``    ` `    ``while``(``True``):``        ``while``(root !``=` `None``):``            ``stack.append(root)``            ``stack.append(root)``            ``root ``=` `root.left` `        ``# Check for empty stack``        ``if` `(``len``(stack) ``=``=` `0``):``            ``return``        ` `        ``root ``=` `stack.pop()` `        ``if` `(``len``(stack) > ``0` `and` `stack[``-``1``] ``=``=` `root):``            ``root ``=` `root.right``        ``else``:``            ``print``(root.data, end ``=` `" "``)``            ``root ``=` `None` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``# Let us create trees shown``    ``# in above diagram``    ``root ``=` `Node(``1``)``    ``root.left ``=` `Node(``2``)``    ``root.right ``=` `Node(``3``)``    ``root.left.left ``=` `Node(``4``)``    ``root.left.right ``=` `Node(``5``)``    ``root.right.left ``=` `Node(``6``)``    ``root.right.right ``=` `Node(``7``)``    ` `    ``print``(``"Post order traversal of binary tree is :"``)``    ` `    ``postOrderIterative(root)` `# This code is contributed by mohit kumar 29`

## C#

 `// Simple C# program to print PostOrder Traversal(Iterative)``using` `System;``using` `System.Collections.Generic;` `// A binary tree node``public``  ``class` `Node``  ``{``    ``public``      ``int` `data;``    ``public``      ``Node left, right;``    ``public``      ``Node(``int` `item)``    ``{``      ``data = item;``      ``left = right;``    ``}``  ``}` `// create a postorder class``public` `class` `PostOrder``{``  ``Node root;` `  ``// An iterative function to do postorder traversal``  ``// of a given binary tree``  ``private` `void` `postOrderIterative(Node root)``  ``{``    ``Stack stack = ``new` `Stack();``    ``while``(``true``)``    ``{``      ``while``(root != ``null``)``      ``{``        ``stack.Push(root);``        ``stack.Push(root);``        ``root = root.left;``      ``}` `      ``// Check for empty stack``      ``if``(stack.Count == 0) ``return``;``      ``root = stack.Pop();        ``      ``if``(stack.Count != 0 && stack.Peek() == root) root = root.right;           ``      ``else``      ``{              ``        ``Console.Write(root.data + ``" "``); root = ``null``;``      ``}``    ``}``  ``}` `  ``// Driver program to test above functions``  ``public` `static` `void` `Main(String []args)``  ``{``    ``PostOrder tree = ``new` `PostOrder();` `    ``// Let us create trees shown in above diagram``    ``tree.root = ``new` `Node(1);``    ``tree.root.left = ``new` `Node(2);``    ``tree.root.right = ``new` `Node(3);``    ``tree.root.left.left = ``new` `Node(4);``    ``tree.root.left.right = ``new` `Node(5);``    ``tree.root.right.left = ``new` `Node(6);``    ``tree.root.right.right = ``new` `Node(7);``    ``Console.WriteLine(``"Post order traversal of binary tree is :"``);``    ``tree.postOrderIterative(tree.root);``  ``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output

```Post order traversal of binary tree is :
4 5 2 6 7 3 1 ```

Time Complexity: O(n)

Auxiliary Space: O(n)

#### Method 3 (Iterative PostOrder Traversal Using Stack and Hashing) :

• Create a Stack for finding the postorder traversal and an unordered map for hashing to mark the visited nodes.
• Initially push the root node in the stack and follow the below steps until the stack is not empty. The stack will get empty when postorder traversal is stored in our answer container data structure.
• Mark the current node (node on the top of stack) as visited in our hashtable.
• If the left child of the current node is not NULL and not visited then push it into the stack.
• Otherwise, if the right child of the top node is not NULL and not visited push it into the stack
• If none of the above two conditions holds true then add the value of the current node to our answer and remove(pop) the current node from the stack.
• When the stack gets empty, we will have postorder traversal stored in our answer data structure (array or vector).

## C++

 `// A C++ program for iterative postorder traversal using``// stack``#include ``using` `namespace` `std;``#define MAX_HEIGHT 100000` `// Tree Node``struct` `Node {``    ``int` `data;``    ``Node* left;``    ``Node* right;``};` `// Utility function to create a new Tree Node``Node* newNode(``int` `val)``{``    ``Node* temp = ``new` `Node;``    ``temp->data = val;``    ``temp->left = NULL;``    ``temp->right = NULL;` `    ``return` `temp;``}` `// Function to Build Tree``Node* buildTree(string str)``{``    ``// Corner Case``    ``if` `(str.length() == 0 || str == ``'N'``)``        ``return` `NULL;` `    ``// Creating vector of strings from input``    ``// string after spliting by space``    ``vector ip;` `    ``istringstream iss(str);``    ``for` `(string str; iss >> str;)``        ``ip.push_back(str);` `    ``// Create the root of the tree``    ``Node* root = newNode(stoi(ip));` `    ``// Push the root to the queue``    ``queue queue;``    ``queue.push(root);` `    ``// Starting from the second element``    ``int` `i = 1;``    ``while` `(!queue.empty() && i < ip.size()) {` `        ``// Get and remove the front of the queue``        ``Node* currNode = queue.front();``        ``queue.pop();` `        ``// Get the current node's value from the string``        ``string currVal = ip[i];` `        ``// If the left child is not null``        ``if` `(currVal != ``"N"``) {` `            ``// Create the left child for the current node``            ``currNode->left = newNode(stoi(currVal));` `            ``// Push it to the queue``            ``queue.push(currNode->left);``        ``}` `        ``// For the right child``        ``i++;``        ``if` `(i >= ip.size())``            ``break``;``        ``currVal = ip[i];` `        ``// If the right child is not null``        ``if` `(currVal != ``"N"``) {` `            ``// Create the right child for the current node``            ``currNode->right = newNode(stoi(currVal));` `            ``// Push it to the queue``            ``queue.push(currNode->right);``        ``}``        ``i++;``    ``}` `    ``return` `root;``}` `// An iterative function to do postorder traversal``// of a given binary tree``vector<``int``> postOrder(Node* node)``{``    ``stack s;` `    ``// vector to store the postorder traversal``    ``vector<``int``> post;` `    ``// Using unordered map as hash table for hashing to mark``    ``// the visited nodes``    ``unordered_map vis;` `    ``// push the root node in the stack to traverse the tree``    ``s.push(node);` `    ``// stack will be empty when traversal is completed``    ``while` `(!s.empty()) {` `        ``// mark the node on the top of stack as visited``        ``vis[s.top()] = 1;` `        ``// if left child of the top node is not NULL and not``        ``// visited push it into the stack``        ``if` `(s.top()->left != 0) {``            ``if` `(!vis[s.top()->left]) {``                ``s.push(s.top()->left);``                ``continue``;``            ``}``        ``}` `        ``// Otherwise if the right child of the top node is``        ``// not NULL and not visited push it into the stack``        ``if` `(s.top()->right != 0) {``            ``if` `(!vis[s.top()->right]) {``                ``s.push(s.top()->right);``                ``continue``;``            ``}``        ``}` `        ``// Add the value of the top node in our postorder``        ``// traversal answer if none of the above two``        ``// conditions are met``        ``post.push_back(s.top()->data);` `        ``// Remove the top node from the stack``        ``s.pop();``    ``}` `    ``// post will now contain the postorder traversal of the``    ``// tree``    ``return` `post;``}` `int` `main()``{``    ``// Constructing the tree as shown in above diagram``    ``string s = ``"1 2 3 4 5 6 7"``;``    ``Node* root = buildTree(s);` `    ``vector<``int``> ans;` `    ``ans = postOrder(root);` `    ``cout << ``"Post order traversal of binary tree is :\n"``;``    ``for` `(``int` `i = 0; i < ans.size(); i++)``        ``cout << ans[i] << ``" "``;` `    ``cout << endl;` `    ``return` `0;``}` `// This code is contributed by Ishan Khandelwal`

Output

```Post order traversal of binary tree is :
4 5 2 6 7 3 1 ```

Time complexity: O(n) where n is no of nodes in a binary tree

Auxiliary Space: O(n)