Convert a Binary Tree to Threaded binary tree | Set 2 (Efficient)

Idea of Threaded Binary Tree is to make inorder traversal faster and do it without stack and without recursion. In a simple threaded binary tree, the NULL right pointers are used to store inorder successor. Where-ever a right pointer is NULL, it is used to store inorder successor.

Following diagram shows an example Single Threaded Binary Tree. The dotted lines represent threads.

Following is structure of single threaded binary tree.

```struct Node
{
int key;
Node *left, *right;

// Used to indicate whether the right pointer is a normal right
// pointer or a pointer to inorder successor.
};```

How to convert a Given Binary Tree to Threaded Binary Tree?
We have discussed a Queue based solution here. In this post, a space efficient solution is discussed that doesn’t require queue.

The idea is based on the fact that we link from inorder predecessor to a node. We link those inorder predecessor which lie in subtree of node. So we find inorder predecessor of a node if its left is not NULL. Inorder predecessor of a node (whose left is NULL) is rightmost node in left child. Once we find the predecessor, we link a thread from it to current node.
Following is the implementation of the above idea.

```/* C++ program to convert a Binary Tree to
#include <iostream>
#include <queue>
using namespace std;

/* Structure of a node in threaded binary tree */
struct Node
{
int key;
Node *left, *right;

// Used to indicate whether the right pointer
// is a normal right pointer or a pointer
// to inorder successor.
};

// Converts tree with given root to threaded
// binary tree.
// This function returns rightmost child of
// root.
{
// Base cases : Tree is empty or has single
//              node
if (root == NULL)
return NULL;
if (root->left == NULL &&
root->right == NULL)
return root;

// Find predecessor if it exists
if (root->left != NULL)
{
// Find predecessor of root (Rightmost
// child in left subtree)

// root.
l->right = root;
}

// If current node is rightmost child
if (root->right == NULL)
return root;

// Recur for right subtree.
}

// A utility function to find leftmost node
// in a binary tree rooted with 'root'.
// This function is used in inOrder()
Node *leftMost(Node *root)
{
while (root != NULL && root->left != NULL)
root = root->left;
return root;
}

// Function to do inorder traversal of a threadded
// binary tree
void inOrder(Node *root)
{
if (root == NULL) return;

// Find the leftmost node in Binary Tree
Node *cur = leftMost(root);

while (cur != NULL)
{
cout << cur->key << " ";

// If this Node is a thread Node, then go to
// inorder successor
cur = cur->right;

else // Else go to the leftmost child in right subtree
cur = leftMost(cur->right);
}
}

// A utility function to create a new node
Node *newNode(int key)
{
Node *temp = new Node;
temp->left = temp->right = NULL;
temp->key = key;
return temp;
}

// Driver program to test above functions
int main()
{
/*       1
/ \
2   3
/ \ / \
4  5 6  7   */
Node *root = newNode(1);
root->left = newNode(2);
root->right = newNode(3);
root->left->left = newNode(4);
root->left->right = newNode(5);
root->right->left = newNode(6);
root->right->right = newNode(7);

cout << "Inorder traversal of creeated "
inOrder(root);
return 0;
}
```

Output:

```Inorder traversal of creeated threaded tree is
4 2 5 1 6 3 7```

This algorithm works in O(n) time complexity and O(1) space other than function call stack.

This article is contributed by Gopal Agarwal. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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