This document defines common tree data structure terminology and properties. It discusses different types of trees like binary trees and binary search trees. It covers tree traversal methods like pre-order, in-order and post-order traversal. It also describes how to construct expression trees from postfix and prefix expressions. Finally, it briefly mentions insertion and deletion operations in binary search trees.

2. INTRODUCTION
Tree is a non-linear data structure.
It is mainly used to represent data
containing a hierarchical
relationship between elements.
Eg: Government Subdivisions.

4. TREE TERMINOLOGIES
ROOT: Node at the top of the tree is called as root.
There is only one root in a tree.
PARENT: Any node(except the root) has exactly one
edge running upward to another node. The node
above the given node is called parent.
CHILD: Any node may have one or more lines running
downward to other nodes. The nodes below a given
node are called its children.

5. ANCESTOR: Parents, grandparents are called
ancestors
DESCENDANTS: Children, grandchildren are called
descendants.
SIBLINGS: Children of the same parent are called
siblings.
LEVEL: The level of a particular node refers to how
many generations the node is from the root. If the root
is assumed to be on level ‘0’ then its children are at
level ‘1’.
DEPTH: The Depth of a node ‘n’ is the length of the
unique path from root to node ‘n’. The root is at depth
‘0’.

6. LEAF NODE: Node having no children.
HEIGHT: Height of a node ‘n’ is the length of the
longest path from node ‘n’ to leaf.
Height of the tree= Height of the root.
DEGREE OF THE NODE: Degree of the node is the
number of children of the node.
The node with degree ‘0’ is a leaf or terminal
node.
Degree of tree= Maximum degree of any node in the
tree.

7. BINARY TREES
The Binary Tree is a tree in which no node
can have more than two children.
PROPERTIES:
Every Binary tree with ‘n’ elements,
n>0 has exactly n-1 edges.
A full binary tree of height ‘h’ has
exactly 2^(h+1) -1 nodes.

8. BINARY TREE TRAVERSAL METHOD:
Traversal is the process of visiting every
node in the tree exactly once. There are three methods
of Traversal.
Pre order.
In order.
Post order.

9. PRE ORDER:
Step 1: Visit the root.
Step 2: Traverse the left sub tree.
Step 3: Traverse the right sub tree.
IN ORDER:
Step 1: Traverse the left sub tree.
Step 2: Visit the root.
Step 3: Traverse the right sub tree.
POST ORDER:
Step 1: Traverse the left sub tree.
Step 2: Traverse the right sub tree.
Step 3: Visit the root.

10. EXPRESSION TREE
CONVERSION OF POSTFIX EXPRESSION INTO
EXPRESSION TREE:
Step 1: Read the postfix expression one symbol at a time
from left to right.
Step 2: If the symbol is an operand, we create a one node
tree and push a pointer to it on to a stack.
Step 3: If the symbol is an operator pop the last two sub
trees and forma new tree whose root is that operator.

11. Eg: ab+cde+**

13. CONVERSION OF PREFIX EXPRESSION TO
EXPRESSION TREE:
Step 1:Read the prefix expression from right to left.
Step 2: same as previous one.
Step 3: same as previous one. Additionally, the last
popped one should be on the left of the root.

14. Eg: ++a*bc*+*defg

18. BINARY SEARCH TREE
Binary Search Tree is a tree in which for every
node X, in the tree, the values of all the keys in its left
sub tree are smaller than the key value in X, and the
values of all the keys in its right sub tree are larger than
the key value in X.
Left Sub tree should have lesser value than its
corresponding root and also the main root. Whereas
Right Sub tree should have greater value than the root.

20. INSERTION:

21. DELETION:

23. THANK YOU!!