Iterative postorder traversal

The given problem is to perform an iterative postorder traversal of a binary tree using a stack. Postorder traversal is a way of visiting all the nodes of a binary tree in a specific order. In postorder traversal, the left subtree is visited first, followed by the right subtree, and finally, the root node is visited.

Problem Statement

We are given a binary tree, and we need to perform an iterative postorder traversal on it using a stack and print the node values in the postorder sequence.

Explanation with Suitable Example

Let's consider the binary tree provided in the code comments:

      10
    /    \
   2      5
  / \    /  \
 1   3  7    2
    /    \      
   9       8

The iterative postorder traversal for this tree will be: 1 9 3 2 8 7 2 5 10

Pseudocode

The following is the pseudocode for performing an iterative postorder traversal of a binary tree:

function iterativePostorder()
    Initialize an empty stack
    Push the root node onto the stack

    while stack is not empty
        Peek the top node from the stack (without removing it)
        if the top node has not been visited (visit = 0)
            Increment the visit count for the top node (visit = 1)
            if the top node has a left child
                Push the left child onto the stack
            else if the top node has a right child
                Push the right child onto the stack
            else
                Print the top node's data (this is the postorder visit)
                Pop the top node from the stack
        else
            Print the top node's data (this is the postorder visit)
            Pop the top node from the stack

Algorithm Explanation

1. Initialize an empty stack.
2. Push the root node onto the stack.
3. Repeat the following steps while the stack is not empty:
   • Peek the top node from the stack (without removing it).
   • If the top node has not been visited yet (visit = 0):
     • Increment the visit count for the top node (visit = 1).
     • If the top node has a left child, push the left child onto the stack.
     • Else if the top node has a right child, push the right child onto the stack.
     • Else, print the top node's data (this is the postorder visit), and pop the top node from the stack.
   • If the top node has been visited (visit = 1):
     • Print the top node's data (this is the postorder visit).
     • Pop the top node from the stack.

Code Solution

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Time Complexity

The time complexity of the iterative postorder traversal algorithm is O(n), where n is the number of nodes in the binary tree. In each iteration, we either push a node onto the stack or pop a node from the stack, and each node is processed exactly once.

Resultant Output Explanation

For the given binary tree, the postorder traversal is:

1 9 3 2 8 7 2 5 10

The output is the same for both the recursive and iterative methods, as both methods traverse the tree in the same order. The iterative postorder traversal is achieved using a stack, which allows us to simulate the function call stack used in the recursive approach.