Here is an algorithm to traverse a threaded binary tree 2. Set currentNode to the left child of the in inorder sequence: header node 1. Set currentNode to the left child of the header node 3. While currentNode is not equal to the header node 2. While currentNode is not equal to the header node a. Print currentNode a. Print currentNode b. If the right child of currentNode is b. If the right child of currentNode is a thread a thread i. Set currentNode to the right child of i. Set currentNode to the right currentNode child of currentNode ii. Go

1. Data Structures and Algorithms
Objectives
In this session, you will learn to:
Apply trees to solve programming problems
Implement a threaded binary tree
Ver. 1.0 Session 14

2. Data Structures and Algorithms
Indexing
The on disk is an usually of an index.
Datafollowingfiles isexampleorganized as records containing
several fields, one of which is often used as a key field.
The key field is used to uniquely identify each record in a
Key field Offset
file. 36 0
52 200
Indexing is one of the data access methods for accessing
24 400
records from the disk files.
44 600
Indexing is implemented through a table called index.
40 800
Index consists of two entries: 1000
68
59 1200
Key fields of all the records
55 1400
Offset position of each record
72 1600
35 1800
43 2000
Ver. 1.0 Session 14

3. Data Structures and Algorithms
Indexing (Contd.)
To access the record with key field 59, search the index for
You can implement a binary search tree to store these
this key value to retrieve its corresponding offset value,
index values.
which is 1200. enables faster search for a key value.
This approach
Read the record from the file starting from this offset
Key field Offset 52
36
position. 0
52 200
36 68
24 400
44 600
40 800 24 44 59 72
68 1000
59 1200 40 55
55 1400
72 1600
35 43
35 1800
43 2000
Index Key Fields Stored in a Binary Search Tree
Ver. 1.0 Session 14

4. Data Structures and Algorithms
Implementing a Threaded Binary Trees
One of the common operations on a binary tree is traversal.
In a linked representation of a binary tree, traversal is
usually implemented through recursion.
As a result, a stack is maintained in the memory.
If the tree is huge, implementing recursion to traverse the
tree would require a lot of memory space.
In the absence of sufficient memory space, implementing
recursion can lead to a memory leak.
Ver. 1.0 Session 14

5. Data Structures and Algorithms
Defining Threaded Binary Trees
In such a case, it would be good if you have some
mechanism by which you can traverse the tree without
implementing recursion.
You can solve this problem by implementing a threaded
binary tree.
In a binary search tree, there are many nodes that have an
empty left child or empty right child or both.
You can utilize these fields in such a way so that the empty
left child of a node points to its inorder predecessor and
empty right child of the node points to its inorder successor.
Ver. 1.0 Session 14

6. Data Structures and Algorithms
Defining Threaded Binary Trees (Contd.)
Consider theitfollowing binary search tree. fields are
In this case, would be good if these NULL
utilized for some other useful purpose.
Most of the nodes in this tree hold a NULL value in their left
or right child fields.
. 65 .
. 40 . . 72 .
30 . 50 . 69 80
60
Ver. 1.0 Session 14

7. Data Structures and Algorithms
Defining Threaded Binary Trees (Contd.)
Such a type of binary tree is node as be used to point tree.
The empty left child field of aknowncan a threaded binaryto
itsfield thatpredecessor.
A inorder holds the address of its inorder successor or
predecessor empty right thread.
Similarly, the is known as child field of a node can be used to
point to its inorder successor.
. 65 .
. 40 . . 72 .
30 50 . 69 80
60
Ver. 1.0 Session 14

8. Data Structures and Algorithms
Defining Threaded Binary Trees (Contd.)
Node 30 does not have an inorder predecessor because it
is the first node to be traversed in inorder sequence.
Similarly, node 80 does not have an inorder successor.
. 65 .
. 40 . . 72 .
30 50 . 69 80
60
Ver. 1.0 Session 14

9. Data Structures and Algorithms
Defining Threaded Binary Trees (Contd.)
Therefore, you of theaheader node always points to itself.
The right child take dummy node called the header node.
Header Node
. 65 .
. 40 . . 72 .
30 50 . 69 80
60
Ver. 1.0 Session 14

10. Data Structures and Algorithms
Defining Threaded Binary Trees (Contd.)
The threaded binary tree is represented as the left child of
the header node. Header Node
. 65 .
. 40 . . 72 .
30 50 . 69 80
60
Ver. 1.0 Session 14

11. Data Structures and Algorithms
Defining Threaded Binary Trees (Contd.)
The left thread of node 30 and the right thread of node 80
point to the header node. Header Node
. 65 .
. 40 . . 72 .
. 30 50 . 69 80 .
60
Ver. 1.0 Session 14

12. Data Structures and Algorithms
Just a minute
In a threaded binary tree, the right thread of a node points to
its inorder ___________, and the left thread points to its
inorder ____________.
Answer:
successor, predecessor
Ver. 1.0 Session 14

13. Data Structures and Algorithms
Representing a Threaded Binary Tree
The left and right threadin a threaded binary tree istwo
structure of a node fields of a node can have a bit
values: from that of a normal binary tree.
different
– 1: a normal normal link to the child node
UnlikeIndicates a binary tree, each node of a threaded binary
tree 0: Indicates a thread pointing of the inorder predecessor or
– contains two extra pieces to information, namely left
thread and successor
inorder right thread.
4631 Information 2389
Left Address of Data Address of Right
Thread Left Child Right Child Thread
Ver. 1.0 Session 14

14. Data Structures and Algorithms
Representing a Threaded Binary Tree (Contd.)
Various operations in a threaded binary tree are as follows:
Traversal
Search
Insert
Delete
Ver. 1.0 Session 14

15. Data Structures and Algorithms
Just a minute
How do you identify a root node in a threaded binary tree?
Answer:
In a threaded binary tree, the root node is identified as the left
child of the header node. If the tree is empty, the left child of
the header node becomes a thread pointing to itself.
Ver. 1.0 Session 14

16. Data Structures and Algorithms
Just a minute
How is the structure of a node of a threaded binary tree
different from that of a normal binary tree?
Answer:
Each node in a threaded binary tree holds two extra pieces of
information known as left thread and right thread. The value of
these two fields indicates whether the left/right child field of a
node contains a link to a child node or a thread to its inorder
predecessor/successor.
Ver. 1.0 Session 14

17. Data Structures and Algorithms
Traversing a Threaded Binary Tree
To traverse a threaded binary tree in inorder sequence, you
need to determine the inorder successor of a node at each
step.
Ver. 1.0 Session 14

18. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. Identify the node for which you want
to locate the inorder successor, and
Write an algorithm toinorder the inorder successor of a node
Algorithm to find the locate mark it as currentNode.
in a threaded a node tree. threaded 3. If the right child of currentNode is a
successor of binary in a
thread:
binary tree. a. Mark the right child of
currentNode as successor.
b. Exit.
4. Make currentNode point to its right
child.
6. Repeat step 5 until left child of
currentNode becomes a thread.
8. Make currentNode point to its left
child.
10. Mark currentNode as successor.
Ver. 1.0 Session 14

19. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. Identify the node for which you want
Header Node to locate the inorder successor, and
mark it as currentNode.
3. If the right child of currentNode is a
thread:
a. Mark the right child of
currentNode as successor.
. 65 . b. Exit.
4. Make currentNode point to its right
child.
. 40 . . 72 . 6. Repeat step 5 until left child of
currentNode becomes a thread.
8. Make currentNode point to its left
child.
30 . 50 . 69 80 10. Mark currentNode as successor.
60 Let us find the inorder successor of node 65
Ver. 1.0 Session 14

20. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
• Identify the node for which you want
Header Node to locate the inorder successor, and
mark it as currentNode.
• If the right child of currentNode is a
thread:
a. Mark the right child of
currentNode as successor.
currentNode . 65 . b. Exit.
4. Make currentNode point to its right
child.
. 40 . . 72 . 6. Repeat step 5 until left child of
currentNode becomes a thread.
8. Make currentNode point to its left
child.
30 . 50 . 69 80 10. Mark currentNode as successor.
60 Let us find the inorder successor of node 65.
Ver. 1.0 Session 14

21. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
• Identify the node for which you want
Header Node to locate the inorder successor, and
mark it as currentNode.
• If the right child of currentNode is a
thread:
a. Mark the right child of
currentNode as successor.
currentNode . 65 . b. Exit.
4. Make currentNode point to its right
child.
. 40 . . 72 . 6. Repeat step 5 until left child of
currentNode becomes a thread.
8. Make currentNode point to its left
child.
30 . 50 . 69 80 10. Mark currentNode as successor.
60 Let us find the inorder successor of node 65.
Ver. 1.0 Session 14

22. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. Identify the node for which you want
Header Node to locate the inorder successor, and
mark it as currentNode.
3. If the right child of currentNode is a
thread:
a. Mark the right child of
currentNode as successor.
currentNode . 65 . b. Exit.
currentNode • Make currentNode point to its right
child.
. 40 . . 72 . • Repeat step 5 until left child of
currentNode becomes a thread.
• Make currentNode point to its left
child.
30 . 50 . 69 80 • Mark currentNode as successor.
60 Let us find the inorder successor of node 65.
Ver. 1.0 Session 14

23. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. Identify the node for which you want
Header Node to locate the inorder successor, and
mark it as currentNode.
3. If the right child of currentNode is a
thread:
a. Mark the right child of
currentNode as successor.
. 65 . b. Exit.
currentNode • Make currentNode point to its right
child.
. 40 . . 72 . • Repeat step 5 until left child of
currentNode becomes a thread.
• Make currentNode point to its left
child.
30 . 50 . 69 80 • Mark currentNode as successor.
60 Let us find the inorder successor of node 65.
Ver. 1.0 Session 14

24. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. Identify the node for which you want
Header Node to locate the inorder successor, and
mark it as currentNode.
3. If the right child of currentNode is a
thread:
a. Mark the right child of
currentNode as successor.
. 65 . b. Exit.
currentNode • Make currentNode point to its right
child.
. 40 . . 72 . • Repeat step 5 until left child of
currentNode becomes a thread.
• Make currentNode point to its left
child.
30 . 50 . 69 80 • Mark currentNode as successor.
currentNode
60 Let us find the inorder successor of node 65.
Ver. 1.0 Session 14

25. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. Identify the node for which you want
Header Node to locate the inorder successor, and
mark it as currentNode.
3. If the right child of currentNode is a
thread:
a. Mark the right child of
currentNode as successor.
. 65 . b. Exit.
• Make currentNode point to its right
child.
. 40 . . 72 . • Repeat step 5 until left child of
currentNode becomes a thread.
• Make currentNode point to its left
child.
30 . 50 . 69 80 • Mark currentNode as successor.
currentNode
60 Let us find the inorder successor of node 65.
Ver. 1.0 Session 14

26. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
Inorder successor 1. Identify the node for which you want
Header Node to locate the inorder successor, and
located mark it as currentNode.
3. If the right child of currentNode is a
thread:
a. Mark the right child of
currentNode as successor.
. 65 . b. Exit.
• Make currentNode point to its right
child.
. 40 . . 72 . • Repeat step 5 until left child of
successor
currentNode becomes a thread.
• Make currentNode point to its left
child.
30 . 50 . 69 80 • Mark currentNode as successor.
currentNode
60 Let us find the inorder successor of node 65.
Ver. 1.0 Session 14

27. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
Write an algorithm to traverse a threaded binary tree in
inorder sequence.
Ver. 1.0 Session 14

28. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
Algorithm to traverse a threaded b. Exit.
binary tree in inorder sequence. 2. Mark the left child of the header
node as currentNode.
4. Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
6. Make currentNode point to its left
child.
. 40 . . 72 . 8. Display the information held by
currentNode.
10. Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
12. Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
14. Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

29. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
2. Mark the left child of the header
node as currentNode.
4. Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
6. Make currentNode point to its left
child.
. 40 . . 72 . 8. Display the information held by
currentNode.
10. Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
12. Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
14. Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

30. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
currentNode . 65 . currentNode becomes a thread.
• Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

31. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
currentNode . 65 . currentNode becomes a thread.
• Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

32. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
• If the left child of the header node
is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
currentNode . 65 . currentNode becomes a thread.
currentNode • Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

33. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
currentNode • Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

34. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
currentNode • Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
currentNode successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

35. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
• Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
currentNode successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

36. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
• Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
currentNode successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

37. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
• Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
currentNode successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

38. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
currentNode • Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
currentNode successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

39. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 40 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
currentNode • Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

40. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 40 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
currentNode • Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
currentNode
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

41. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 40 50 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
• Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
currentNode
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

42. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 40 50 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
• Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
currentNode
• Display the information held by
the currentNode.
60 currentNode
Ver. 1.0 Session 14

43. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 40 50 60 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
• Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
• Display the information held by
the currentNode.
60 currentNode
Ver. 1.0 Session 14

44. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 40 50 60 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
currentNode . 65 . currentNode becomes a thread.
• Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
• Display the information held by
the currentNode.
60 currentNode
Ver. 1.0 Session 14

45. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 40 50 60 65 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
currentNode . 65 . currentNode becomes a thread.
• Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

46. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 40 50 60 65 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
currentNode . 65 . currentNode becomes a thread.
• Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
currentNode
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

47. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 40 50 60 65 69 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
• Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
currentNode
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

48. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 40 50 60 65 69 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
currentNode • Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
currentNode
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

49. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 40 50 60 65 69 72 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
currentNode • Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

50. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 40 50 60 65 69 72 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
. 65 . currentNode becomes a thread.
currentNode • Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
currentNode successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

51. Data Structures and Algorithms
Traversing a Threaded Binary Tree (Contd.)
1. If the left child of the header node
30 40 50 60 65 69 72 80 is a thread pointing to itself:
Header Node a. Display “Tree is empty”.
b. Exit.
• Mark the left child of the header
node as currentNode.
• Repeat step 4 until the left child of
Traversal complete . 65 . currentNode becomes a thread.
• Make currentNode point to its left
child.
. 40 . . 72 . • Display the information held by
currentNode.
• Repeat steps 7 and 8 until right
child of currentNode points to the
30 . 50 . 69 80
header node.
• Find the inorder successor of
currentNode, and mark the inorder
currentNode successor as currentNode.
• Display the information held by
the currentNode.
60
Ver. 1.0 Session 14

52. Data Structures and Algorithms
Inserting Nodes in a Threaded Binary Tree
Insert an algorithm to locate the position inserting a newto be
Write operation refers to the process of of a new node
node at its appropriatebinary tree.
inserted in a threaded position.
To implement an insert operation in a threaded binary tree,
you first need to locate the position for the new node to be
inserted.
For this, you first need to implement a search operation.
Ver. 1.0 Session 14

53. Data Structures and Algorithms
Inserting Nodes in a Threaded Binary Tree (Contd.)
1. If the left child of the header node is a thread
Insert node 35 pointing to itself:
a. Mark head as parent.
AlgorithmHeader Node the
to locate b. Exit.
position of a new node in 2. Mark the left child of head as currentNode.
.
a threaded binary tree.
3.
4.
Mark head as parent.
Repeat steps a, b, c, d, and e until currentNode
becomes NULL:
a. Mark currentNode as parent.
. 65 . b. If the value of the new node is less than
that of currentNode and the left child of
currentNode is a normal link:
i. Make currentNode point to its left
child and go to step 4.
. 40 . . 72 . c. If the value of the new node is less than
that of currentNode and the left child of
currentNode is a thread:
i. Mark currentNode as NULL and go
to step 4.
d. If the value of the new node is greater than
30 . 50 . 69 80 that of currentNode and the right child of
currentNode is a normal link:
i. Make currentNode point to its right
child and go to step 4.
e. If the value of the new node is greater than
that of currentNode and the right child of
currentNode is a thread:
60 i. Mark currentNode as NULL and go
to step 4.
Ver. 1.0 Session 14

54. Data Structures and Algorithms
Inserting Nodes in a Threaded Binary Tree (Contd.)
1. If the left child of the header node is a thread
Insert node 35 pointing to itself:
a. Mark head as parent.
Header Node
b. Exit.
2. Mark the left child of head as currentNode.
. 3.
4.
Mark head as parent.
Repeat steps a, b, c, d, and e until currentNode
becomes NULL:
a. Mark currentNode as parent.
. 65 . b. If the value of the new node is less than
that of currentNode and the left child of
currentNode is a normal link:
i. Make currentNode point to its left
child and go to step 4.
. 40 . . 72 . c. If the value of the new node is less than
that of currentNode and the left child of
currentNode is a thread:
i. Mark currentNode as NULL and go
to step 4.
d. If the value of the new node is greater than
30 . 50 . 69 80 that of currentNode and the right child of
currentNode is a normal link:
i. Make currentNode point to its right
child and go to step 4.
e. If the value of the new node is greater than
that of currentNode and the right child of
currentNode is a thread:
60 i. Mark currentNode as NULL and go
to step 4.
Ver. 1.0 Session 14

55. Data Structures and Algorithms
Inserting Nodes in a Threaded Binary Tree (Contd.)
1. If the left child of the header node is a thread
Insert node 35 pointing to itself:
a. Mark head as parent.
Header Node
b. Exit.
• Mark the left child of head as currentNode.
. •
•
Mark head as parent.
Repeat steps a, b, c, d, and e until currentNode
becomes NULL:
a. Mark currentNode as parent.
currentNode . 65 . b. If the value of the new node is less than
that of currentNode and the left child of
currentNode is a normal link:
i. Make currentNode point to its left
child and go to step 4.
. 40 . . 72 . c. If the value of the new node is less than
that of currentNode and the left child of
currentNode is a thread:
i. Mark currentNode as NULL and go
to step 4.
d. If the value of the new node is greater than
30 . 50 . 69 80 that of currentNode and the right child of
currentNode is a normal link:
i. Make currentNode point to its right
child and go to step 4.
e. If the value of the new node is greater than
that of currentNode and the right child of
currentNode is a thread:
60 i. Mark currentNode as NULL and go
to step 4.
Ver. 1.0 Session 14

56. Data Structures and Algorithms
Inserting Nodes in a Threaded Binary Tree (Contd.)
1. If the left child of the header node is a thread
Insert node 35 pointing to itself:
a. Mark head as parent.
Header Node
b. Exit.
• Mark the left child of head as currentNode.
parent
. •
•
Mark head as parent.
Repeat steps a, b, c, d, and e until currentNode
becomes NULL:
a. Mark currentNode as parent.
currentNode . 65 . b. If the value of the new node is less than
that of currentNode and the left child of
currentNode is a normal link:
i. Make currentNode point to its left
child and go to step 4.
. 40 . . 72 . c. If the value of the new node is less than
that of currentNode and the left child of
currentNode is a thread:
i. Mark currentNode as NULL and go
to step 4.
d. If the value of the new node is greater than
30 . 50 . 69 80 that of currentNode and the right child of
currentNode is a normal link:
i. Make currentNode point to its right
child and go to step 4.
e. If the value of the new node is greater than
that of currentNode and the right child of
currentNode is a thread:
60 i. Mark currentNode as NULL and go
to step 4.
Ver. 1.0 Session 14