# 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++

 `// 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

 `// 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[])` `{` `    ``// 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);` `}` `}`   `// This code is contributed by Arnab Kundu`

## Python3

 `# 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`   `# Construct 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#

 `// 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)` `{` `    ``// 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);` `}` `}`   `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output:

`4 5 2 3 1`

Time Complexity: O(N)
Auxiliary Space: O(N)

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