MINISTRY OF EDUCATION & HIGHER EDUCATION
COLLEGE OF SCIENCE AND TECHNOLOGY
KHANYOUNIS- PALESTINE
DATA STRUCTURE
Information Technology , 3’rd Semester
Using C#
Lecture 14:
Trees Operations
Presented By: Mahmoud Rafeek Alfarra
Outline
Implementation of binary Search tree.
 Add new Item.
 Traversing a Binary Search Tree
 Emank X Mezank !!

Implementation of BST
3

A binary search tree is made up of nodes, so
we need a Node class that is similar to the
Node class we used in the linked list
implementation.
Presented & Prepared by: Mahmoud R. Alfarra
Build the Basic Node
Implementation of BST
4
Let’s look at the code for the Node class first:
Presented & Prepared by: Mahmoud R. Alfarra
Build a Binary Search Tree
Implementation of BST
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 Next we’re ready to build a Binary Search Tree (BST)
class.
 The class consists of just one data member—a Node
object that represents the root node of the BST.
Presented & Prepared by: Mahmoud R. Alfarra
Build a Binary Search Tree
Insert method
6
 We next need an Insert method to add new nodes to our tree:
1. Create a Node object and assign the data the Node holds to the Data
variable.
2. See If our BST has a root node.
•
If not, then this is a new BST and the node we are inserting is
the root node. If this is the case, then the method is finished.
•
Otherwise, the method moves on to the next step.
3. Find the proper insertion point.
Presented & Prepared by: Mahmoud R. Alfarra
Build a Binary Search Tree
Determining the proper position for a node
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1. Set the parent node to be the current node, which is the root node.
2. If the data value in the new node is less than the data value in the current
node, set the current node to be the left child of the current node.
3. If the data value in the new node is greater than the data value in the
current node, skip to Step 4. If the value of the left child of the current
node is null, insert the new node here and exit the loop. Otherwise, skip to
the next iteration of the While loop.
4. Set the current node to the right child node of the current node.
5. If the value of the right child of the current node is null, insert the new
node here and exit the loop. Otherwise, skip to the next iteration of the
While loop.
Presented & Prepared by: Mahmoud R. Alfarra
Build a Binary Search Tree
Determining the proper position for a node
8
1. Current = Root
2. Parent = current
3. If (new.data <current.data)
 Current = Current.left
 If left.data = null

insert the new node here and exit the loop
 Else

skip to the next iteration of the While loop.
 else

Skip to step 4
Presented & Prepared by: Mahmoud R. Alfarra
Build a Binary Search Tree
Determining the proper position for a node
9
4. If (new.data <current.data)
4. Current = Current.right
5. If right.data = null
4. insert the new node here and exit the loop
6. Else
4. skip to the next iteration of the While loop.
Presented & Prepared by: Mahmoud R. Alfarra
Terminology of Tree
10
Insert
method
Presented & Prepared by: Mahmoud R. Alfarra
Traversing a Binary Search Tree
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 We need to be able to traverse the BST so that we can
visit the different nodes in several different orders:
 There are three traversal methods used with BSTs:
1. Inorder: visits all the nodes in a BST in ascending
order of the node key values.
2. Preorder: visits the root node first, followed by the
nodes in the subtrees under the left child of the root,
followed by the nodes in the subtrees under the
right child of the root.
3. Postorder.
Presented & Prepared by: Mahmoud R. Alfarra
Traversing a Binary Search Tree
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Inorder Traversal Order
Presented & Prepared by: Mahmoud R. Alfarra
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Traversing a Binary Search Tree
Inorder Traversal Order
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Presented & Prepared by: Mahmoud R. Alfarra
Traversing a Binary Search Tree
Preorder Traversal Order
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 The only difference between the preOrder method and
the inOrder method is where the three lines of code
are placed.
 The call to the displayNode method was sandwiched
between the two recursive calls in the inOrder method
and it is the first line of the preOrder method.
Presented & Prepared by: Mahmoud R. Alfarra
Traversing a Binary Search Tree
Preorder Traversal Order
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Presented & Prepared by: Mahmoud R. Alfarra
Traversing a Binary Search Tree
Postorder Traversal Order
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 The difference between this method and the other two
traversal methods is where the recursive calls and the
call to displayNode are placed.
 In a postorder traversal, the method first recurses over
the left subtrees and then over the right subtrees.
Presented & Prepared by: Mahmoud R. Alfarra
Traversing a Binary Search Tree
Postorder Traversal Order
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Presented & Prepared by: Mahmoud R. Alfarra
‫!! ‪Emank X Mezank‬‬
‫يقول النيب صلى هللا عليه وسلم‪:‬‬
‫كفى ابملرء كذبـًا أن‬
‫حيدث بكل ما مسـع‬
‫َ‬
Next Lecture
Finding a Node and
Minimum/Maximum Values
in a Binary Search Tree