A tree is not a linear structure and hence, can be traversed in many ways. To traverse a tree, we need to go through all its nodes in some order, which can be —  inorder, preorder, or postorder depth-first traversal and level order, breadth-first traversal, or some hybrid scheme. In this article, we discuss inorder tree traversal without the use of recursion or stack.

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In this article, we’ll discuss:

• What Is Inorder Tree Traversal?
• Inorder Tree Traversal Without Recursion and Stack Example
• Time Complexity
• Advantages and Disadvantages of Inorder Tree Traversal Using Morris Traversal
• Problems and Interview Questions on Inorder Tree Traversal
• FAQs on Inorder Tree Traversal Without Recursion and Stack
  

What Is Inorder Tree Traversal?

The process of traversing a tree that involves visiting the left child and its entire subtree first, then visiting the node, and lastly, visiting the right child and its entire subtree similarly is called inorder traversal. 

This traversal method can be especially useful in the case of binary search trees, where it helps output all the node values in ascending order.

To learn more about other types of tree travels, read Tree Traversal: Inorder, Preorder, Postorder, and Level-order.

Inorder Tree Traversal Without Recursion and Stack Example

Since a tree is not a linear data structure, and nodes can have multiple child nodes, there can be many possible nodes to visit after a node is visited. Nodes that need to be visited later need to, in some manner, be stored for a future visit. 

This could be achieved by storing the nodes in a stack for future visits or using recursion, where the nodes are implicitly stored in a stack for future visits. This article, however, is not about these two methods. It’s about how we can do inorder tree traversal without involving recursion or stack using Morris Traversal.

Problem Statement

Achieve inorder tree traversal without using recursion and without using stack.

Solution: Morris Traversal

Morris Traversal is a method based on the idea of a threaded binary tree and can be used to traverse a tree without using recursion or stack. Morris traversal involves:

• Step 1: Creating links to inorder successors
• Step 2: Printing the information using the created links (the tree is altered during the traversal)
• Step 3: Once the traversal has been completed, reverting the changes and restoring the original tree
  

Note that unlike when we use the stack for traversal, we don’t need any additional space in this method.

Look at the pseudocode, and code below to understand this process better:

Morris Traversal Pseudocode

Initialize the variable “current” node as the root 

While the “current” node is not NULL

   If the current node lacks a left child

      Print the information in the current node

      Visit the right child, current = current->right

   Else

In the current left subtree, find the rightmost node or find the node whose right child == current.

If the node’s right child == current

Update the node’s right child as NULL

Print the information in current

Visit the right child, current = current->right

         Else

Set the current variable as the right child of that rightmost node found; and 

Visit the left child, current = current->left

Code for Inorder Traversal Using Morris Traversal

#include <stdio.h>

#include <stdlib.h>

/* Each treeNode holds some value, a pointer to left child (leftChild)

   and a pointer to right child (rightChild) */

struct treeNode 

{

    int value;

    struct treeNode* leftChild;

    struct treeNode* rightChild;

};

/* A method to traverse a tree using Morris traversal, hence without using recursion or stack */

void MorrisTraversal(struct treeNode* root)

{

    struct treeNode *current, *predecessorofCurrent;

    if (root == NULL)

        return;

    current = root;

    //The while loop continues till our current root is not NULL

    while (current != NULL) 

    {

        if (current->leftChild == NULL) 

        {

            printf("%d ", current->value);

            current = current->rightChild;

        }

        else 

        {

            //Getting the inorder predecessor of the current node

            predecessorofCurrent = current->leftChild;

            while (predecessorofCurrent->rightChild != NULL

                   && predecessorofCurrent->rightChild != current)

                predecessorofCurrent = predecessorofCurrent->rightChild;

            /* Setting the right child of predecessorofCurrent as current, and update current to the value of the leftChild of the current */

            if (predecessorofCurrent->rightChild == NULL) 

            {

                predecessorofCurrent->rightChild = current;

                current = current->leftChild;

            }

            /* Reverting the changes made due to the if block to

               restore the tree to its original state by fixing the right

               child of the predecessor. Printing the result of traversal */

            else 

            {

                predecessorofCurrent->rightChild = NULL;

                printf("%d ", current->value);

                current = current->rightChild;

            } 

        } 

    } 

}

/* A utility/helper function to allocate a new treeNode with the

   given value, along with NULL leftChild and NULL rightChild pointers. */

struct treeNode* newtreeNode(int value)

{

    struct treeNode* node = new treeNode;

    node->value = value;

    node->leftChild = NULL;

    node->rightChild = NULL;

    return (node);

}

int main()

{

    /* The tree created:

            4

          /   \

         2     5

       /   \

      1     3

  */

    struct treeNode* root = newtreeNode(4);

    root->leftChild = newtreeNode(2);

    root->rightChild = newtreeNode(5);

    root->leftChild->leftChild = newtreeNode(1);

    root->leftChild->rightChild = newtreeNode(3);

  /* Morris Traversal for the created tree */

    MorrisTraversal(root);

    return 0;

}

Output

1 2 3 4 5

Time Complexity

When it comes to time complexity, we can note the following about Morris traversal:

• The number of times an edge is visited is constant in Morris traversal. For example, for a binary tree, one edge is visited at most thrice:
  1) The first visit aims to locate a node
  2) The second visit aims to find the predecessor of a node
  3) The third visit is for restoring the right child of the predecessor to NULL
• Since the number of times the node will be traversed is constant, the time complexity is O(n).
• At worst, a predecessor has to be found for each node. In that case, the number of additional edges created and removed will be equal to the number of edges in the input tree.

Advantages and Disadvantages of Inorder Tree Traversal Using Morris Traversal

Some advantages of using the Morris Traversal method for inorder tree traversal include:

• Allows inorder tree traversal without using recursion and stack
• Does not require additional space, unlike when a stack is used for the purpose.
• Does not require as much memory and time as recursion.
• The node keeps track of its parent.

Some disadvantages of using the Morris Traversal method for inorder tree traversal include:

• Makes for a more complex tree.
• Only one traversal can be done at a time.
• Can be error-prone in cases where both the children are absent from a binary tree, and both values of the nodes point to their ancestors.

Problems and Interview Questions on Inorder Tree Traversal 

1. Implement inorder tree traversal using stack
2. Implement inorder tree traversal using recursion
3. Implement inorder tree traversal without using recursion or stack
4. What is the Morris Traversal method for inorder traversal? Can you use it for preorder traversal?
5. What are some advantages and disadvantages of using Morris Traversal? 

FAQs on Inorder Tree Traversal Without Recursion and Stack

1.  How do you implement inorder traversal without recursion?

You can implement inorder traversal without using recursion using a stack and using Morris Traversal.

2. Which method of tree traversal does not use a stack?

The recursion method implicitly uses a stack, so out of the three tree traversal methods — stack, recursion, and Morris Traversal — Morris Traversal is the traversal method that does not use a stack.

3. What is a threaded binary tree?

A binary tree in which every node that does not have a right child has a link (or thread) to its inorder successor is called a threaded binary tree. This helps us in avoiding the use of recursion during traversal, saving memory and time consumption.

4. How many ways can we use to traverse a tree?

Broadly, we commonly traverse trees using breadth-first or depth-first algorithms. There are sub-parts to both, and there are hybrid ways as well. But commonly, breadth- and depth-first are the two broad categories used most often for tree traversal.

5. In how many ways can we traverse a tree in depth-first order?

There are three ways to traverse a tree in depth-first order: Inorder, Preorder, and Postorder.

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