1. 2018, Fall Pusan National University Ki-Joune Li
Threaded Binary Tree
2018, Fall
Pusan National University
Ki-Joune Li

2. Threaded Binary Tree – Basic Concept
Limitations of Binary Tree
Next node to visit (e.g. in-order traversal)
Need an additional data structure: stack
Some pointers to left and right children are NULL (not used)
 Use empty (null) left and/or right children a b c d e ? f ? ? ? ? ? ?

3. Threaded Binary Tree – single threaded binary treec d e f g h

4. Threaded Binary Tree – single threaded binary tree
Convert a binary tree to threaded binary tree a b c d e f g h
Use in-order traversal: d b g e a c h f The right child pointer of rightmost node is null. If right child pointer is null, replace it with the pointer to successor of in-order traversal.

5. Threaded Binary Tree – single threaded binary treec
thread node f d e g
null
thread
class Node {
T data;
Node *left, *right;
bool rightThread;
// true when right is a // thread };
class ThreadedBinaryTree {
Node *root;
public:
void inOrder(); };

6. Threaded Binary Tree – single threaded binary tree: traversalc p d e
Thread node f
null
Print: d g h
null
void ThreadedBinaryTree::inOrder() {
Node *p=leftmost(root);
while (p != NULL) {
cout<< p->data <<“ “;
if (p->rightThread) p=p->right;
else p=leftmost(p->right); }
Node* leftMost(Node *n) {
if(n==NULL) return NULL;
while (n->left != NULL) n=n->left;
return n; }

7. Threaded Binary Tree – single threaded binary tree: traversalc p d e
Thread node f
null
Print: d g h
null
void ThreadedBinaryTree::inOrder() {
Node *p=leftmost(root);
while (p != NULL) {
cout<< p->data <<“ “;
if (p->rightThread) p=p->right;
else p=leftmost(p->right); }
Node* leftMost(Node *n) {
if(n==NULL) return NULL;
while (n->left != NULL) n=n->left;
return n; }

8. Threaded Binary Tree – single threaded binary tree: traversalp b c d e f
null
Print: d g h
null
void ThreadedBinaryTree::inOrder() {
Node *p=leftmost(root);
while (p != NULL) {
cout<< p->data <<“ “;
if (p->rightThread) p=p->right;
else p=leftmost(p->right); }
Node* leftMost(Node *n) {
if(n==NULL) return NULL;
while (n->left != NULL) n=n->left;
return n; }

9. Threaded Binary Tree – single threaded binary tree: traversalp b c
Not thread node d e f
null
Print: d b g h
null
void ThreadedBinaryTree::inOrder() {
Node *p=leftmost(root);
while (p != NULL) {
cout<< p->data <<“ “;
if (p->rightThread) p=p->right;
else p=leftmost(p->right); }
Node* leftMost(Node *n) {
if(n==NULL) return NULL;
while (n->left != NULL) n=n->left;
return n; }

10. Threaded Binary Tree – single threaded binary tree: traversalc d e f
null
Print: d b g g h
null p
thread node
void ThreadedBinaryTree::inOrder() {
Node *p=leftmost(root);
while (p != NULL) {
cout<< p->data <<“ “;
if (p->rightThread) p=p->right;
else p=leftmost(p->right); }
Node* leftMost(Node *n) {
if(n==NULL) return NULL;
while (n->left != NULL) n=n->left;
return n; }

11. Threaded Binary Tree – single threaded binary tree: traversalc d e f
null p
Print: d b g e g h
null
void ThreadedBinaryTree::inOrder() {
Node *p=leftmost(root);
while (p != NULL) {
cout<< p->data <<“ “;
if (p->rightThread) p=p->right;
else p=leftmost(p->right); }
Node* leftMost(Node *n) {
if(n==NULL) return NULL;
while (n->left != NULL) n=n->left;
return n; }

12. Threaded Binary Tree – single threaded binary tree: traversal
Advantage of TBT:
Not a recursive algorithm  no stack is needed
void ThreadedBinaryTree::inOrder() {
Node *p=leftmost(root);
while (p != NULL) {
cout<< p->data <<“ “;
if (p->rightThread) p=p->right;
else p=leftmost(p->right); }
Node* leftMost(Node *n) {
if(n==NULL) return NULL;
while (n->left != NULL) n=n->left;
return n; }

13. Threaded Binary Tree – single threaded binary tree: traversalc d e f
null g h
null
void ThreadedBinaryTree::inOrder() {
Node *p=leftmost(root);
while (p != NULL) {
cout<< p->data <<“ “;
if (p->rightThread) p=p->right;
else p=leftmost(p->right); }
How to modify it for preorder() ?

14. Threaded Binary Tree – double (full) threaded binary treec d e f
null h
null g
Use in-order traversal: (null) d b g e a c h f (null) The left child of leftmost node and right child pointer of rightmost node are null. If right child pointer is null, replace it with the pointer to successor of in-order traversal.