2. Disclaimer: This presentation is prepared by trainees of
baabtra as a part of mentoring program. This is not official
document of baabtra –Mentoring Partner
Baabtra-Mentoring Partner is the mentoring division of baabte System Technologies Pvt .
Ltd

3. Binary Trees
ARUN KUMAR K A
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4. Tree Terminology
• A tree consists of a collection of elements or
nodes, with each node linked to its successors
• The node at the top of a tree is called its root
• The links from a node to its successors are
called branches
• The successors of a node are called its children
• The predecessor of a node is called its parent

5. Tree Terminology (continued)
• Each node in a tree has exactly one parent
except for the root node, which has no parent
• Nodes that have the same parent are siblings
• A node that has no children is called a leaf
node

6. Binary Trees
•A tree in which no node can have more than
two children.

7. Example: Expression Trees
• Leaves are operands (constants or variables)
• The other nodes (internal nodes) contain
operators
• Will not be a binary tree if some operators are
not binary

8. Example: Expression Trees
Expression tree for ( a + b * c ) + ( ( d * e + f ) * g

9. Binary Tree Traversal
• Traversal is the process of visiting every node
once
• 3 types of traversals
*Inorder
*Preorder
*Postorder

10. Preorder traversal
Expression tree for ( a + b * c ) + (( d * e + f ) * g
•root, left, right
•prefix expression
++a*bc*+*defg

11. Inorder traversal
Expression tree for ( a + b * c ) +( ( d * e + f ) * g
• left, root, right
•infix expression
a+b*c+d*e+f*g

12. Postorder traversal
Expression tree for ( a + b * c ) + (( d * e + f ) * g
• left, right, root
•postfix expression
abc*+de*f+g*+

13. Insert
Proceed down the tree as you would find a close match
If X is found, do nothing (or update something)
Otherwise, insert X at the last spot on the path traversed

14. Delete
Consider children of deleted node
Property of the search tree should be maintained.
Three cases:
(1) the node is a leaf
– Delete it immediately
(2) the node has one child
– Adjust a pointer from the parent to bypass that node

15. Delete
(3) the node has 2 children
– replace the key of that node with the minimum element at the
right subtree
– delete the minimum element
• Has either no child or only right child because if it has a left child, that
left child would be smaller and would have been chosen. So invoke
case 1 or 2.

16. Questions…..

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