Algorithms‎ > ‎Trees‎ > ‎

Inorder Tree Traversal without recursion and without stack!

April 5, 2010

Using Morris Traversal, we can traverse the tree without using stack and recursion. The idea of Morris Traversal is based on Threaded Binary TreeIn 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
```

Although the tree is modified through the traversal, it is reverted back to its original shape after the completion. Unlike Stack based traversal, no extra space is required for this traversal.

 `#include``#include` `/* A binary tree tNode has data, pointer to left child``   ``and a pointer to right child */``struct` `tNode``{``   ``int` `data;``   ``struct` `tNode* left;``   ``struct` `tNode* right;``};` `/* Function to traverse binary tree without recursion and ``   ``without stack */``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 */``}` `/* UTILITY FUNCTIONS */``/* Helper function that allocates a new tNode with the``   ``given data and NULL left and right pointers. */``struct` `tNode* newtNode(``int` `data)``{``  ``struct` `tNode* tNode = (``struct` `tNode*)``                       ``malloc``(``sizeof``(``struct` `tNode));``  ``tNode->data = data;``  ``tNode->left = NULL;``  ``tNode->right = NULL;` `  ``return``(tNode);``}` `/* Driver program to test above functions*/``int` `main()``{` `  ``/* Constructed binary tree is``            ``1``          ``/   \``        ``2      3``      ``/  \``    ``4     5``  ``*/``  ``struct` `tNode *root = newtNode(1);``  ``root->left        = newtNode(2);``  ``root->right       = newtNode(3);``  ``root->left->left  = newtNode(4);``  ``root->left->right = newtNode(5); ` `  ``MorrisTraversal(root);` `  ``getchar``();``  ``return` `0;``}`