# Iterative Postorder traversal | Set 3

We have seen different ways of performing postorder traversal on Binary Trees.

Here is another way of performing the postorder traversal on a Binary Tree iteratively using a single stack.

Consider the Below Terminologies:

```0 -  Left element
1 -  Right element
2 -  Node element
```

Following is the detailed algorithm:

```Take a Stack and perform the below operations:

1) Insert a pair of the root node as (node, 0).
2) Pop the top element to get the pair
(Let a = node and b be the variable)
If b is equal to 0:
Push another pair as (node, 1) and
Push the left child as (node->left, 0)
Repeat Step 2
Else If b is equal to 1:
Push another pair as (node, 2) and
Push right child of node as (node->right, 0)
Repeat Step 2
Else If b is equal to 2:
Print(node->data)
3) Repeat the above steps while stack is not empty
```

Consider the Below Binary Tree with just 3 nodes:

Illustration:

```1) Push(a, 0)
Stack - (a, 0)

2) top = (a, 0)
Push(a, 1)
Push(b, 0)
Stack - (b, 0)
(a, 1)

3) top = (b, 0)
Push(b, 1)
Stack - (b, 1)
(a, 1)

4) top = (b, 1)
Push(b, 2)
Stack - (b, 2)
(a, 1)

5) top = (b, 2)
print(b)
Stack -(a, 1)

6) top = (a, 1)
push(a, 2)
push(c, 0)
Stack -  (c, 0)
(a, 2)

7) top = (c, 0)
push(c, 1)
Stack - (c, 1)
(a, 2)

8) top = (c, 1)
push(c, 2)
Stack - (c, 2)
(a, 2)

9) top = (c, 2)
print(c)
Stack - (a, 2)

10) top = (a, 2)
print(a)
Stack - empty()
```

Below is the implementation of the above approach:

 `// C++ program to print postorder traversal ` `// iteratively ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Binary Tree Node ` `struct` `Node { ` `    ``int` `data; ` `    ``struct` `Node* left; ` `    ``struct` `Node* right; ` `}; ` ` `  `// Helper function to create a ` `// new Binary Tree node ` `struct` `Node* newNode(``int` `data) ` `{ ` `    ``struct` `Node* node = ``new` `Node; ` `    ``node->data = data; ` `    ``node->left = NULL; ` `    ``node->right = NULL; ` `    ``return` `(node); ` `} ` ` `  `// Function to perform postorder ` `// traversal iteratively ` `void` `iterativePostorder(Node* root) ` `{ ` `    ``stack > st; ` `    ``st.push(make_pair(root, 0)); ` ` `  `    ``while` `(!st.empty()) { ` `        ``struct` `Node* temp = st.top().first; ` `        ``int` `b = st.top().second; ` `        ``st.pop(); ` ` `  `        ``if` `(temp == NULL) ` `            ``continue``; ` ` `  `        ``if` `(b == 0) { ` `            ``st.push(make_pair(temp, 1)); ` ` `  `            ``if` `(temp->left != NULL) ` `                ``st.push(make_pair(temp->left, 0)); ` `        ``} ` `        ``else` `if` `(b == 1) { ` `            ``st.push(make_pair(temp, 2)); ` ` `  `            ``if` `(temp->right != NULL) ` `                ``st.push(make_pair(temp->right, 0)); ` `        ``} ` `        ``else` `            ``cout << temp->data << ``" "``; ` `    ``} ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``// Construct the below Binary Tree ` `    ``//        1 ` `    ``//       / \ ` `    ``//      2   3 ` `    ``//    /   \ ` `    ``//   4     5 ` `    ``Node* root = newNode(1); ` `    ``root->left = newNode(2); ` `    ``root->right = newNode(3); ` `    ``root->left->left = newNode(4); ` `    ``root->left->right = newNode(5); ` ` `  `    ``iterativePostorder(root); ` ` `  `    ``return` `0; ` `} `

 `// Java program to print postorder traversal ` `// iteratively ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `//pair class ` `static` `class` `Pair ` `{ ` `    ``Node first; ` `    ``int` `second; ` `    ``Pair(Node a,``int` `b) ` `    ``{ ` `        ``first = a; ` `        ``second = b; ` `    ``} ` `} ` ` `  `// Binary Tree Node ` `static` `class` `Node  ` `{ ` `    ``int` `data; ` `    ``Node left; ` `    ``Node right; ` `}; ` ` `  `// Helper function to create a ` `// new Binary Tree node ` `static` `Node newNode(``int` `data) ` `{ ` `    ``Node node = ``new` `Node(); ` `    ``node.data = data; ` `    ``node.left = ``null``; ` `    ``node.right = ``null``; ` `    ``return` `(node); ` `} ` ` `  `// Function to perform postorder ` `// traversal iteratively ` `static` `void` `iterativePostorder(Node root) ` `{ ` `    ``Stack st = ``new` `Stack(); ` `    ``st.add(``new` `Pair(root, ``0``)); ` ` `  `    ``while` `(st.size() > ``0``) ` `    ``{ ` `        ``Node temp = st.peek().first; ` `        ``int` `b = st.peek().second; ` `        ``st.pop(); ` ` `  `        ``if` `(temp == ``null``) ` `            ``continue``; ` ` `  `        ``if` `(b == ``0``)  ` `        ``{ ` `            ``st.add(``new` `Pair(temp, ``1``)); ` ` `  `            ``if` `(temp.left != ``null``) ` `                ``st.add(``new` `Pair(temp.left, ``0``)); ` `        ``} ` `        ``else` `if` `(b == ``1``) ` `        ``{ ` `            ``st.add(``new` `Pair(temp, ``2``)); ` ` `  `            ``if` `(temp.right != ``null``) ` `                ``st.add(``new` `Pair(temp.right, ``0``)); ` `        ``} ` `        ``else` `            ``System.out.print( temp.data + ``" "``); ` `    ``} ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``// Con the below Binary Tree ` `    ``//     1 ` `    ``//     / \ ` `    ``//     2 3 ` `    ``// / \ ` `    ``// 4     5 ` `    ``Node root = newNode(``1``); ` `    ``root.left = newNode(``2``); ` `    ``root.right = newNode(``3``); ` `    ``root.left.left = newNode(``4``); ` `    ``root.left.right = newNode(``5``); ` ` `  `    ``iterativePostorder(root); ` `} ` `} ` ` `  `// This code is contributed by Arnab Kundu `

 `# Python program to print postorder traversal ` `# iteratively ` ` `  `# pair class ` `class` `Pair: ` `    ``def` `__init__(``self``, a, b): ` `        ``self``.first ``=` `a ` `        ``self``.second ``=` `b ` `     `  `# Binary Tree Node ` `class` `Node : ` `    ``def` `__init__(``self``): ` `        ``self``.data ``=` `0` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None` ` `  `# Helper function to create a ` `# new Binary Tree node ` `def` `newNode(data): ` ` `  `    ``node ``=` `Node() ` `    ``node.data ``=` `data ` `    ``node.left ``=` `None` `    ``node.right ``=` `None` `    ``return` `(node) ` ` `  `# Function to perform postorder ` `# traversal iteratively ` `def` `iterativePostorder( root): ` ` `  `    ``st ``=` `[] ` `    ``st.append(Pair(root, ``0``)) ` ` `  `    ``while` `(``len``(st)> ``0``): ` `     `  `        ``temp ``=` `st[``-``1``].first ` `        ``b ``=` `st[``-``1``].second ` `        ``st.pop() ` ` `  `        ``if` `(temp ``=``=` `None``): ` `            ``continue` ` `  `        ``if` `(b ``=``=` `0``) : ` `            ``st.append(Pair(temp, ``1``)) ` ` `  `            ``if` `(temp.left !``=` `None``): ` `                ``st.append(Pair(temp.left, ``0``)) ` `         `  `        ``elif` `(b ``=``=` `1``): ` `            ``st.append(Pair(temp, ``2``)) ` ` `  `            ``if` `(temp.right !``=` `None``): ` `                ``st.append(Pair(temp.right, ``0``)) ` `         `  `        ``else``: ` `            ``print``( temp.data ,end``=` `" "``) ` `     `  `# Driver Code ` ` `  `# Con the below Binary Tree ` `#     1 ` `#     / \ ` `# 2 3 ` `# / \ ` `# 4 5 ` `root ``=` `newNode(``1``) ` `root.left ``=` `newNode(``2``) ` `root.right ``=` `newNode(``3``) ` `root.left.left ``=` `newNode(``4``) ` `root.left.right ``=` `newNode(``5``) ` ` `  `iterativePostorder(root) ` ` `  `# This code is contributed by Arnab Kundu `

 `// C# program to print postorder traversal ` `// iteratively ` `using` `System;  ` `using` `System.Collections.Generic;  ` `class` `GFG ` `{ ` ` `  `//pair class ` `public` `class` `Pair ` `{ ` `    ``public` `Node first; ` `    ``public` `int` `second; ` `    ``public` `Pair(Node a,``int` `b) ` `    ``{ ` `        ``first = a; ` `        ``second = b; ` `    ``} ` `} ` ` `  `// Binary Tree Node ` `public` `class` `Node  ` `{ ` `    ``public` `int` `data; ` `    ``public` `Node left; ` `    ``public` `Node right; ` `}; ` ` `  `// Helper function to create a ` `// new Binary Tree node ` `static` `Node newNode(``int` `data) ` `{ ` `    ``Node node = ``new` `Node(); ` `    ``node.data = data; ` `    ``node.left = ``null``; ` `    ``node.right = ``null``; ` `    ``return` `(node); ` `} ` ` `  `// Function to perform postorder ` `// traversal iteratively ` `static` `void` `iterativePostorder(Node root) ` `{ ` `    ``Stack st = ``new` `Stack(); ` `    ``st.Push(``new` `Pair(root, 0)); ` ` `  `    ``while` `(st.Count > 0) ` `    ``{ ` `        ``Node temp = st.Peek().first; ` `        ``int` `b = st.Peek().second; ` `        ``st.Pop(); ` ` `  `        ``if` `(temp == ``null``) ` `            ``continue``; ` ` `  `        ``if` `(b == 0)  ` `        ``{ ` `            ``st.Push(``new` `Pair(temp, 1)); ` ` `  `            ``if` `(temp.left != ``null``) ` `                ``st.Push(``new` `Pair(temp.left, 0)); ` `        ``} ` `        ``else` `if` `(b == 1) ` `        ``{ ` `            ``st.Push(``new` `Pair(temp, 2)); ` ` `  `            ``if` `(temp.right != ``null``) ` `                ``st.Push(``new` `Pair(temp.right, 0)); ` `        ``} ` `        ``else` `            ``Console.Write(temp.data + ``" "``); ` `    ``} ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main(String []args) ` `{ ` `    ``// Con the below Binary Tree ` `    ``//     1 ` `    ``//     / \ ` `    ``//     2 3 ` `    ``// / \ ` `    ``// 4     5 ` `    ``Node root = newNode(1); ` `    ``root.left = newNode(2); ` `    ``root.right = newNode(3); ` `    ``root.left.left = newNode(4); ` `    ``root.left.right = newNode(5); ` ` `  `    ``iterativePostorder(root); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:
```4 5 2 3 1
```

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