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Disclaimer: This presentation is prepared by trainees of baabtra as a part of mentoring program. This is not official document of baabtra –Mentoring PartnerBaabtra-Mentoring Partner is the mentoring division of baabte System Technologies Pvt . Ltd
Binary Trees
ARUN KUMAR K [email protected]/
arunkumar3040twitter.com/arunkumar3040in.linkedin.com/in/
arunkumar3040+919496349799
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
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
Binary Trees
•A tree in which no node can have more than two children.
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
Example: Expression Trees
Expression tree for ( a + b * c ) + ( ( d * e + f ) * g
Binary Tree Traversal
• Traversal is the process of visiting every node once
• 3 types of traversals*Inorder*Preorder*Postorder
Preorder traversal
Expression tree for ( a + b * c ) + (( d * e + f ) * g
• root, left, right• prefix expression
++a*bc*+*defg
Inorder traversal
Expression tree for ( a + b * c ) +( ( d * e + f ) * g
• left, root, right• infix expression
a+b*c+d*e+f*g
Postorder traversal
Expression tree for ( a + b * c ) + (( d * e + f ) * g
• left, right, root• postfix expression
abc*+de*f+g*+
InsertProceed down the tree as you would find a close matchIf X is found, do nothing (or update something)Otherwise, insert X at the last spot on the path traversed
DeleteConsider children of deleted nodeProperty 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
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.
Questions…..
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