threaded binary trees

7/30/2019 Threaded Binary Trees

1/18

Threaded Binary Trees


2/18

Demerits of Binary Trees

Binary trees have a lot of wasted space: the leaf

nodes each have 2 null pointers

We can use these pointers to help us in inordertraversals

We have the pointers reference the next node in

an inorder traversal; called threads

We need to know if a pointer is an actual link or a

thread, so we keep a boolean for each pointer


3/18

Need for Threaded Binary Tree

A binary tree with n nodes need 2n pointers out

of which (n+1) are null pointers

A.J. Perlis and C.Thomson devised a method toutilize these (n+1) null pointers as threads

Threads that take place of a left child pointer

indicate inorder predecessor and right child

pointer lead to inorder successor


4/18

Definition

Threaded binary tree is the left subtree of a root

node whose right child pointer points to itself.


5/18

Data Structures for Threaded BT

left_thread left_child data right_child right_t

TRUE FALSE

FALSE: childTRUE: thread


6/18

One Way Threading

Thread appears only on the RLINK of a node,

pointing to the inorder successor of the node

8

75

3

11

13

1

6

9


7/18

Two Way Threading

Thread appears in both LLINK and RLINK of a

node, pointing to the inorder predecessor and

inorder successor respectively.

8

75

3

11

13

1

6

9


8/18

8

Threaded Tree Traversal

We start at the leftmost node in the tree, print it, and

follow its right thread

If we follow a thread to the right, we output the node

and continue to its right

If we follow a link to the right, we go to the leftmost

node, print it, and continue


9/18

9


8

75

3

11

13

1

6

9

Start at leftmost node, print it

Output1


10/18

10


8

75

3

11

13

1

6

9

Follow thread to right, print node

Output1

3


11/18

11


8

75

3

11

13

1

6

9Follow link to right, go to

leftmost node and print

Output1

3

5


12/18

12


8

75

3

11

13

1

6

9


Output1

3

5

6


13/18

13


8

75

3

11

13

1

6



Output1

3

5

67


14/18

14


8

75

3

11

13

1

6

9


Output1

3

5

67

8


15/18

15


8

75

3

11

13

1

6



Output1

3

5

67

8

9


16/18

16


8

75

3

11

13

1

6

9


Output1

3

5

67

8

9

11


17/18

17


8

75

3

11

13

1

6



Output1

3

5

67

8

9

11

13


18/18

Inorder Traversal of Threaded Binary Tree

void threadedinorder(Root P)

{

do{

if P TRPOINT = = True then

P = P RLINK;

else

P = P RLINK;

while(P TLPOINT ! = TRUE)

P = P LLINK;

if(P!=ROOT)

print(p data)

}while(P = = ROOT);

}

threaded binary trees

Documents