1. Data Structures and Algorithms
Objectives
In this session, you will learn to:
Implement a threaded binary tree
Implement a height balanced binary tree
Store data in a graph
Ver. 1.0 Session 16

2. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree
Write an algorithm to locate thebinary to berefers to in a
Delete operation in a threaded node tree deleted the
threadedof removing the specified node from the threaded
process binary tree.
binary tree.
Before implementing a delete operation, you first need to
locate the node to be deleted.
This requires you to implement a search operation.
After the search operation, the node to be deleted is marked
as the currentNode and its parent as parent.
Ver. 1.0 Session 16

3. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Mark the left child of the header node as
currentNode.
Delete 80 2. Mark the header node as parent.
Algorithm header node
to locate the
node 3. Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
to be deleted and its parent in becomes NULL:
a. Mark currentNode as parent.
a threaded binary tree. b. If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
. 65 . i. Make currentNode point to its
left child and go to step 3.
c. If the value to be searched is less
than that of currentNode, and the left
. 40 . . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

4. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
• Mark the left child of the header node as
currentNode.
• Mark the header node as parent.
Delete 80
header node • Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
a. Mark currentNode as parent.
b. If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
currentNode . 65 . i. Make currentNode point to its
left child and go to step 3.
c. If the value to be searched is less
than that of currentNode, and the left
. 40 . . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

5. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
• Mark the left child of the header node as
currentNode.
• Mark the header node as parent.
Delete 80
parent header node
• Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
a. Mark currentNode as parent.
b. If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
currentNode . 65 . i. Make currentNode point to its
left child and go to step 3.
c. If the value to be searched is less
than that of currentNode, and the left
. 40 . . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

6. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
• Mark the left child of the header node as
currentNode.
• Mark the header node as parent.
Delete 80
parent header node
• Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
a. Mark currentNode as parent.
b. If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
currentNode . 65 . i. Make currentNode point to its
left child and go to step 3.
c. If the value to be searched is less
than that of currentNode, and the left
. 40 . . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

7. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Mark the left child of the header node as
currentNode.
Delete 80 2. Mark the header node as parent.
parent header node 3. Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
• Mark currentNode as parent.
• If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
currentNode . 65 . parent i. Make currentNode point to its
left child and go to step 3.
c. If the value to be searched is less
than that of currentNode, and the left
. 40 . . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

8. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Mark the left child of the header node as
currentNode.
Delete 80 2. Mark the header node as parent.
header node 3. Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
• Mark currentNode as parent.
• If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
currentNode . 65 . parent i. Make currentNode point to its
left child and go to step 3.
c. If the value to be searched is less
than that of currentNode, and the left
. 40 . . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

9. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Mark the left child of the header node as
currentNode.
Delete 80 2. Mark the header node as parent.
header node 3. Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
a. Mark currentNode as parent.
b. If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
currentNode . 65 . parent i. Make currentNode point to its
left child and go to step 3.
c. If the value to be searched is less
than that of currentNode, and the left
. 40 . . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

10. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
• Mark the left child of the header node as
currentNode.
• Mark the header node as parent.
Delete 80
header node • Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
a. Mark currentNode as parent.
b. If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
currentNode . 65 . parent i. Make currentNode point to its
left child and go to step 3.
c. If the value to be searched is less
than that of currentNode, and the left
. 40 . . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

11. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Mark the left child of the header node as
currentNode.
Delete 80 2. Mark the header node as parent.
header node 3. Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
a. Mark currentNode as parent.
b. If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
currentNode . 65 . parent i. Make currentNode point to its
left child and go to step 3.
currentNode c. If the value to be searched is less
than that of currentNode, and the left
. 40 . . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

12. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
• Mark the left child of the header node as
currentNode.
• Mark the header node as parent.
Delete 80
header node • Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
a. Mark currentNode as parent.
b. If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
. 65 . parent i. Make currentNode point to its
left child and go to step 3.
currentNode c. If the value to be searched is less
than that of currentNode, and the left
. 40 . . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

13. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Mark the left child of the header node as
currentNode.
Delete 80 2. Mark the header node as parent.
header node 3. Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
• Mark currentNode as parent.
• If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
. 65 . parent i. Make currentNode point to its
left child and go to step 3.
currentNode c. If the value to be searched is less
than that of currentNode, and the left
. 40 . parent . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

14. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Mark the left child of the header node as
currentNode.
Delete 80 2. Mark the header node as parent.
header node 3. Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
• Mark currentNode as parent.
• If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
. 65 . i. Make currentNode point to its
left child and go to step 3.
currentNode c. If the value to be searched is less
than that of currentNode, and the left
. 40 . parent . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

15. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Mark the left child of the header node as
currentNode.
Delete 80 2. Mark the header node as parent.
header node 3. Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
a. Mark currentNode as parent.
b. If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
. 65 . i. Make currentNode point to its
left child and go to step 3.
currentNode c. If the value to be searched is less
than that of currentNode, and the left
. 40 . parent . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

16. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Mark the left child of the header node as
currentNode.
Delete 80 2. Mark the header node as parent.
header node 3. Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
a. Mark currentNode as parent.
b. If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
. 65 . i. Make currentNode point to its
left child and go to step 3.
currentNode c. If the value to be searched is less
than that of currentNode, and the left
. 40 . parent . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

17. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1.
Mark the left child of the header node as
currentNode.
Delete 80 2. Mark the header node as parent.
header node 3. Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
a. Mark currentNode as parent.
b. If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
. 65 . i. Make currentNode point to its
left child and go to step 3.
currentNode c. If the value to be searched is less
than that of currentNode, and the left
. 40 . parent .
72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
currentNode right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

18. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
•Mark the left child of the header node as
currentNode.
Nodes located • Mark the header node as parent.
Delete 80
header node • Repeat steps a, b, c, d, and e until the node
to be searched is found or currentNode
becomes NULL:
a. Mark currentNode as parent.
b. If the value to be searched is less
than that of currentNode, and the left
child of the currentNode is a link:
. 65 . i. Make currentNode point to its
left child and go to step 3.
c. If the value to be searched is less
than that of currentNode, and the left
. 40 . parent . 72 . child of the currentNode is a thread:
i. Make currentNode as NULL
and go to step 3.
d. If the value to be searched is greater
than that of currentNode, and the
right child of the currentNode is a link:
30 . 50 . 69 80
i. Make currentNode point to its
right child and go to step 3.
e. If the value to be searched is greater
than that of currentNode, and the
currentNode right child of the currentNode is a
thread:
i. Mark currentNode as NULL
60 and go to step 3.
Ver. 1.0 Session 16

19. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
Once you if the tree is not empty, there can be three cases:
Before implementingnode to be deleted and its parent, to
However, locate the a delete operation, you first need you
can Node to be deleted is isof the node to be deleted after
release the memory empty or
check whether the tree a leaf node not.
adjustingis empty if thethreads appropriately. node is a
tree the links and left child of the header
The Node to be deleted has one child (left or right)
thread pointingdeleted has two children
Node to be to itself.
If the tree is empty, an error message is shown.
header node
Ver. 1.0 Session 16

20. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
Let us first consider a case in which the node to be deleted
is the leaf node.
In this case, you first need to check if there is only one node
present in the tree.
header node
65
new node
Ver. 1.0 Session 16

21. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
To delete this node, make the left child of the header node
as a thread pointing to itself.
header node
65
new node
Ver. 1.0 Session 16

22. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
To delete this node, make the left child of the header node
as a thread pointing to itself.
Now release the memory of the node to be deleted.
header node
Delete operation complete
65
new node
Ver. 1.0 Session 16

23. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
header node 1. Locate the position of the node to
Delete node 60 be deleted. Mark it as
However, if there are more than currentNode and its parent as
parent.
one nodes in the tree, you need
3. If currentNode is the left child of
another algorithm to delete a leaf
node. . 65 . parent:
a. Set the left thread field of
parent as zero.
b. Make the left child field of
parent as a thread pointing
. 40 . . 72 . to the inorder predecessor
of currentNode.
c. Go to step 4.
4. If currentNode is the right child of
parent:
30 . 50 . 69 80 a. Set the right thread field of
parent as zero.
b. Make the right child field of
parent as a thread pointing
to the inorder successor of
currentNode.
60 5. Release the memory for
currentNode.
Ver. 1.0 Session 16

24. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
header node • Locate the position of the node to
Delete node 60 be deleted. Mark it as
currentNode and its parent as
parent.
• If currentNode is the left child of
. 65 . parent:
a. Set the left thread field of
parent as zero.
b. Make the left child field of
parent as a thread pointing
. 40 . . 72 . to the inorder predecessor
of currentNode.
c. Go to step 4.
4. If currentNode is the right child of
parent:
30 . 50 . 69 80 a. Set the right thread field of
parent as zero.
b. Make the right child field of
parent parent as a thread pointing
to the inorder successor of
currentNode.
60 5. Release the memory for
currentNode.
currentNode
Ver. 1.0 Session 16

25. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
header node • Locate the position of the node to
Delete node 60 be deleted. Mark it as
currentNode and its parent as
parent.
• If currentNode is the left child of
. 65 . parent:
a. Set the left thread field of
parent as zero.
b. Make the left child field of
parent as a thread pointing
. 40 . . 72 . to the inorder predecessor
of currentNode.
c. Go to step 4.
4. If currentNode is the right child of
parent:
30 . 50 . 69 80 a. Set the right thread field of
parent as zero.
b. Make the right child field of
parent parent as a thread pointing
to the inorder successor of
currentNode.
60 5. Release the memory for
currentNode.
currentNode
Ver. 1.0 Session 16

26. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
header node 1. Locate the position of the node to
Delete node 60 be deleted. Mark it as
currentNode and its parent as
parent.
3. If currentNode is the left child of
. 65 . parent:
a. Set the left thread field of
parent as zero.
b. Make the left child field of
parent as a thread pointing
. 40 . . 72 . to the inorder predecessor
of currentNode.
c. Go to step 4.
4. If currentNode is the right child of
parent:
30 . 50 . 69 80 a. Set the right thread field of
parent as zero.
b. Make the right child field of
parent parent as a thread pointing
to the inorder successor of
currentNode.
60 5. Release the memory for
currentNode.
currentNode
Ver. 1.0 Session 16

27. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
header node 1. Locate the position of the node to
Delete node 60 be deleted. Mark it as
currentNode and its parent as
parent.
3. If currentNode is the left child of
. 65 . parent:
a. Set the left thread field of
parent as zero.
b. Make the left child field of
parent as a thread pointing
. 40 . . 72 . to the inorder predecessor
of currentNode.
c. Go to step 4.
4. If currentNode is the right child of
parent:
30 . 50 . 69 80 • Set the right thread field of
parent as zero.
• Make the right child field of
parent parent as a thread pointing
to the inorder successor of
currentNode.
60 5. Release the memory for
currentNode.
currentNode
Ver. 1.0 Session 16

28. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
header node 1. Locate the position of the node to
Delete node 60 be deleted. Mark it as
currentNode and its parent as
parent.
3. If currentNode is the left child of
. 65 . parent:
a. Set the left thread field of
parent as zero.
b. Make the left child field of
parent as a thread pointing
. 40 . . 72 . to the inorder predecessor
of currentNode.
c. Go to step 4.
4. If currentNode is the right child of
parent:
30 . 50 . 69 80 • Set the right thread field of
parent as zero.
• Make the right child field of
parent parent as a thread pointing
to the inorder successor of
currentNode.
60 5. Release the memory for
currentNode.
currentNode
Ver. 1.0 Session 16

29. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
header node 1. Locate the position of the node to
Delete node 60 be deleted. Mark it as
currentNode and its parent as
parent.
3. If currentNode is the left child of
. 65 . parent:
a. Set the left thread field of
parent as zero.
b. Make the left child field of
parent as a thread pointing
. 40 . . 72 . to the inorder predecessor
of currentNode.
c. Go to step 4.
4. If currentNode is the right child of
parent:
30 . 50 69 80 • Set the right thread field of
parent as zero.
• Make the right child field of
parent parent as a thread pointing
to the inorder successor of
Deletion complete currentNode.
60 5. Release the memory for
currentNode.
currentNode
Ver. 1.0 Session 16

30. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
Write an algorithm to delete a node, which has one child in
a threaded binary tree.
Ver. 1.0 Session 16

31. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Locate the node to be deleted. Mark it as
header node
Delete node 50 currentNode and its parent as parent.
2. If currentNode has a left subtree:
Algorithm to delete aa case in
Let us now consider node a. Mark the left child of current node as
child.
with one child from a deleted
which the node to be b. Go to step 4.
3. If currentNode has a right subtree:
threadedchild (left or right).
has one binary tree. • Mark the right child of currentNode as
. 65 . •
child.
Go to step 4.
4. If currentNode is the left child of parent:
a. Make the left child of parent point to
child.
. 40 . . 72 . 5.
b. Go to step 6.
If currentNode is the right child of parent:
a. Make the right child of parent point to
child.
b. Go to step 6.
6. Find the inorder successor and inorder
30 . 50 . 69 80
predecessor of currentNode. Mark them as
successor and predecessor, respectively.
7. If currentNode has a right child:
a. Make the left child field of its successor
point to its predecessor and set the left
thread of successor to zero.
b. Go to step 9.
8. If currentNode has a left child:
60 a. Make the right child of its predecessor
point to its successor and set the right
thread of predecessor to zero.
9. Release the memory for currentNode.
Ver. 1.0 Session 16

32. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
• Locate the node to be deleted. Mark it as
header node
Delete node 50 currentNode and its parent as parent.
• If currentNode has a left subtree:
a. Mark the left child of current node as
child.
b. Go to step 4.
3. If currentNode has a right subtree:
a. Mark the right child of currentNode as
. 65 . b.
child.
Go to step 4.
parent 4. If currentNode is the left child of parent:
a. Make the left child of parent point to
child.
. 40 . . 72 . 5.
b. Go to step 6.
If currentNode is the right child of parent:
a. Make the right child of parent point to
child.
b. Go to step 6.
6. Find the inorder successor and inorder
30 . 50 . 69 80
predecessor of currentNode. Mark them as
successor and predecessor, respectively.
7. If currentNode has a right child:
a. Make the left child field of its successor
point to its predecessor and set the left
currentNode thread of successor to zero.
b. Go to step 9.
8. If currentNode has a left child:
60 a. Make the right child of its predecessor
point to its successor and set the right
thread of predecessor to zero.
9. Release the memory for currentNode.
Ver. 1.0 Session 16

33. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
• Locate the node to be deleted. Mark it as
header node
Delete node 50 currentNode and its parent as parent.
• If currentNode has a left subtree:
a. Mark the left child of current node as
child.
b. Go to step 4.
3. If currentNode has a right subtree:
a. Mark the right child of currentNode as
. 65 . b.
child.
Go to step 4.
parent 4. If currentNode is the left child of parent:
a. Make the left child of parent point to
child.
. 40 . . 72 . 5.
b. Go to step 6.
If currentNode is the right child of parent:
a. Make the right child of parent point to
child.
b. Go to step 6.
6. Find the inorder successor and inorder
30 . 50 . 69 80
predecessor of currentNode. Mark them as
successor and predecessor, respectively.
7. If currentNode has a right child:
a. Make the left child field of its successor
point to its predecessor and set the left
currentNode thread of successor to zero.
b. Go to step 9.
8. If currentNode has a left child:
60 a. Make the right child of its predecessor
point to its successor and set the right
thread of predecessor to zero.
9. Release the memory for currentNode.
Ver. 1.0 Session 16

34. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Locate the node to be deleted. Mark it as
header node
Delete node 50 currentNode and its parent as parent.
2. If currentNode has a left subtree:
a. Mark the left child of current node as
child.
b. Go to step 4.
3. If currentNode has a right subtree:
a. Mark the right child of currentNode as
. 65 . b.
child.
Go to step 4.
parent 4. If currentNode is the left child of parent:
a. Make the left child of parent point to
child.
. 40 . . 72 . 5.
b. Go to step 6.
If currentNode is the right child of parent:
a. Make the right child of parent point to
child.
b. Go to step 6.
6. Find the inorder successor and inorder
30 . 50 . 69 80
predecessor of currentNode. Mark them as
successor and predecessor, respectively.
7. If currentNode has a right child:
a. Make the left child field of its successor
point to its predecessor and set the left
currentNode thread of successor to zero.
b. Go to step 9.
8. If currentNode has a left child:
60 a. Make the right child of its predecessor
point to its successor and set the right
thread of predecessor to zero.
9. Release the memory for currentNode.
Ver. 1.0 Session 16

35. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Locate the node to be deleted. Mark it as
header node
Delete node 50 currentNode and its parent as parent.
2. If currentNode has a left subtree:
a. Mark the left child of current node as
child.
b. Go to step 4.
3. If currentNode has a right subtree:
• Mark the right child of currentNode as
. 65 . •
child.
Go to step 4.
parent 4. If currentNode is the left child of parent:
a. Make the left child of parent point to
child.
. 40 . . 72 . 5.
b. Go to step 6.
If currentNode is the right child of parent:
a. Make the right child of parent point to
child.
b. Go to step 6.
6. Find the inorder successor and inorder
30 . 50 . 69 80
predecessor of currentNode. Mark them as
successor and predecessor, respectively.
7. If currentNode has a right child:
a. Make the left child field of its successor
point to its predecessor and set the left
currentNode thread of successor to zero.
b. Go to step 9.
8. If currentNode has a left child:
60 a. Make the right child of its predecessor
point to its successor and set the right
thread of predecessor to zero.
child 9. Release the memory for currentNode.
Ver. 1.0 Session 16

36. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Locate the node to be deleted. Mark it as
header node
Delete node 50 currentNode and its parent as parent.
2. If currentNode has a left subtree:
a. Mark the left child of current node as
child.
b. Go to step 4.
3. If currentNode has a right subtree:
• Mark the right child of currentNode as
. 65 . •
child.
Go to step 4.
parent 4. If currentNode is the left child of parent:
a. Make the left child of parent point to
child.
. 40 . . 72 . 5.
b. Go to step 6.
If currentNode is the right child of parent:
a. Make the right child of parent point to
child.
b. Go to step 6.
6. Find the inorder successor and inorder
30 . 50 . 69 80
predecessor of currentNode. Mark them as
successor and predecessor, respectively.
7. If currentNode has a right child:
a. Make the left child field of its successor
point to its predecessor and set the left
currentNode thread of successor to zero.
b. Go to step 9.
8. If currentNode has a left child:
60 a. Make the right child of its predecessor
point to its successor and set the right
thread of predecessor to zero.
child 9. Release the memory for currentNode.
Ver. 1.0 Session 16

37. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Locate the node to be deleted. Mark it as
header node
Delete node 50 currentNode and its parent as parent.
2. If currentNode has a left subtree:
a. Mark the left child of current node as
child.
b. Go to step 4.
3. If currentNode has a right subtree:
a. Mark the right child of currentNode as
. 65 . b.
child.
Go to step 4.
parent 4. If currentNode is the left child of parent:
a. Make the left child of parent point to
child.
. 40 . . 72 . 5.
b. Go to step 6.
If currentNode is the right child of parent:
a. Make the right child of parent point to
child.
b. Go to step 6.
6. Find the inorder successor and inorder
30 . 50 . 69 80
predecessor of currentNode. Mark them as
successor and predecessor, respectively.
7. If currentNode has a right child:
a. Make the left child field of its successor
point to its predecessor and set the left
currentNode thread of successor to zero.
b. Go to step 9.
8. If currentNode has a left child:
60 a. Make the right child of its predecessor
point to its successor and set the right
thread of predecessor to zero.
child 9. Release the memory for currentNode.
Ver. 1.0 Session 16

38. Data Structures and Algorithms
Deleting a Node from a Threaded Binary Tree (Contd.)
1. Locate the node to be deleted. Mark it as
header node
Delete node 50 currentNode and its parent as parent.
2. If currentNode has a left subtree:
a. Mark the left child of current node as
child.
b. Go to step 4.
3. If currentNode has a right subtree:
a. Mark the right child of currentNode as
. 65 . b.
child.
Go to step 4.
parent 4. If currentNode is the left child of parent:
a. Make the left child of parent point to
child.
. 40 . . 72 . 5.
b. Go to step 6.
If currentNode is the right child of parent:
a. Make the right child of parent point to
child.
b. Go to step 6.
6. Find the inorder successor and inorder
30 . 50 . 69 80
predecessor of currentNode. Mark them as
successor and predecessor, respectively.
7. If currentNode has a right child:
a. Make the left child field of its successor
point to its predecessor and set the left
currentNode thread of successor to zero.
b. Go to step 9.
8. If currentNode has a left child:
60 a. Make the right child of its predecessor
point to its successor and set the right
thread of predecessor to zero.
child 9. Release the memory for currentNode.
Ver. 1.0 Session 16