Triple order traversal of a binary tree

The problem focuses on performing a triple-order traversal of a binary tree, which involves visiting each node in the tree three times: first in a preorder traversal, then in an inorder traversal, and finally in a postorder traversal. The goal is to print the nodes during each traversal, resulting in a sequence of nodes that appears three times in the specified order.

Problem Statement

Given a binary tree, the task is to perform a triple-order traversal. During the traversal, each node is visited three times: first in a preorder fashion, then in an inorder fashion, and finally in a postorder fashion. The program should print the nodes during each traversal.

Example

Consider the binary tree illustrated in the code:

         4    
        / \                         
       /   \    
     -4     7    
     / \     \               
    2   3     1
       / \   / 
      6   8 5
     /       
    9

The triple-order traversal output for this tree will be:

4 -4 2 2 2 -4 3 6 9 9 9 6 6 3 8 8 8 3 -4 4 7 7 1 5 5 5 1 1 7 4

Idea to Solve

The problem can be solved using a recursive approach. During the traversal, at each node, we perform the following steps:

1. Print the node value during the preorder traversal.
2. Recursively traverse the left subtree.
3. Print the node value during the inorder traversal.
4. Recursively traverse the right subtree.
5. Print the node value during the postorder traversal.

By following these steps, we ensure that each node is visited three times in the specified order.

Pseudocode

function tripleOrder(node):
    if node is not null:
        print node.data during preorder
        tripleOrder(node.left)
        print node.data during inorder
        tripleOrder(node.right)
        print node.data during postorder

main:
    create binary tree
    construct tree as shown
    call tripleOrder with root node

Algorithm Explanation

1. The tripleOrder function recursively traverses the binary tree and performs the specified actions during each traversal type (preorder, inorder, and postorder).
2. In the main function, a binary tree is constructed, and the tripleOrder function is called with the root node.

Code Solution

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Time Complexity

The time complexity of the solution is proportional to the number of nodes in the binary tree since each node is visited once during the traversal. In the worst case, the time complexity is O(n), where n is the number of nodes in the binary tree.