Tuesday, June 18, 2013

Inorder Tree Traversal without recursion and without stack (Morris Traversal)

Problem:
Traverse a binary tree without using stack and recursion.

Solution:
Using Morris Traversal, we can traverse the tree without using stack and recursion. The idea of Morris Traversal is based on Threaded Binary Tree. In this traversal, we first create links to Inorder successor and print the data using these links, and finally revert the changes to restore original tree.

1. Initialize current as root 
2. While current is not NULL
   If current does not have left child
      a) Print current’s data
      b) Go to the right, i.e., current = current->right
   Else
      a) Make current as right child of the rightmost node in current's left subtree
      b) Go to this left child, i.e., current = current->left

void MorrisTraversal(struct tNode *root)
{
  struct tNode *current,*pre;
 
  if(root == NULL)
     return; 
 
  current = root;
  while(current != NULL)
  {                 
    if(current->left == NULL)
    {
      printf(" %d ", current->data);
      current = current->right;      
    }    
    else
    {
      /* Find the inorder predecessor of current */
      pre = current->left;
      while(pre->right != NULL && pre->right != current)
        pre = pre->right;
 
      /* Make current as right child of its inorder predecessor */
      if(pre->right == NULL)
      {
        pre->right = current;
        current = current->left;
      }
             
      /* Revert the changes made in if part to restore the original 
        tree i.e., fix the right child of predecssor */   
      else 
      {
        pre->right = NULL;
        printf(" %d ",current->data);
        current = current->right;      
      } /* End of if condition pre->right == NULL */
    } /* End of if condition current->left == NULL*/
  } /* End of while */
}


Complexity:
time - O(n)
space - O(1)
Links and credits:
http://www.geeksforgeeks.org/inorder-tree-traversal-without-recursion-and-without-stack/
http://www.careercup.com/question?id=6154593645887488

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