Tree Data Structure & methods & operations

Trees
• So far we discussed mainly data structure - string, arrays, list
stacks, queues etc
• Now, we discuss about non-linear data structure called trees
• It is a data Structure that organizes data in a hierarchical model
with multiple levels
• Consider a parent-child relationship

Hierarchy Model
Sequence of Nodes like a family tree
structure
Starting from a Root node
Every node is parent of their belows
called childs
Nodes that are linked to both a parent
called siblings to each other

Main Terminology
Root
 Root
 Parent
 Siblings
 Child
 Descendents
 Ancestors
 Degree of Nodes
 Internal/External nodes
 Levels
 Height

Descendants
All nodes that can be reached from a node by following child
links.
Ancestors
All nodes along the path from a given node to the root.
Degree of Nodes
The number of children a node has

.
Internal/External Nodes
Internal nodes have children, while external nodes (leaves) do
not.
Levels
The distance from the root to a given node.
Height
The longest path from the root to a leaf node.

Types of Binary Trees
1. Full Binary Tree
A Binary Tree is a full binary tree if every node has 0 or 2
children. A full Binary tree is a special type of binary tree in
which every parent node/internal node has either two or no
children.

2. Perfect Binary Tree
 Internal have exactly 2 children
 All leaf nodes are on same level

3. Complete Binary Tree
A complete binary tree is just like a full binary tree, but with two
major differences:
Every level except the last level must be completely filled.
All the leaf elements must lean towards the left.
The last leaf element might not have a right sibling i.e. a
complete binary tree doesn’t have to be a full binary tree.

4. Skewed Binary Tree
A skewed binary tree is a pathological/degenerate tree and there
are two types of skewed binary tree: left-skewed binary tree and
right-skewed binary tree.

5. Binary Search Tree
Binary Search Tree is a node-based binary tree data structure that
has the following properties:
The left subtree of a node contains only nodes with keys lesser
than the node’s key.
The right subtree of a node contains only nodes with keys
greater than the node’s key.
The left and right subtree each must also be a binary search
tree.

Tree Traversals
Traversals means ‘VISITING’ their elements.
Preorder: visit(node), preorder(LNSubtree), preorder(RNSubtree)
Inorder: inorder(left), visit(node), inorder(right)
Postorder: postorder(left), postorder(right), visit(node)
Levelorder: Level by level

Tree Traversals Easy Method ‘I’
Preorder Inorder Postorder
A
C
G
B
F
E
D
C
B
A
G
F
E
D
C
B
G
F
E
A
D
A,B,D,E,C,F,G D,B,E,A,F,C,G D,E,B,F,G,C,A

Tree Traversals Easy Method ‘II’
PostOrder InOrder PreOrder

Level Order of Traversal
Tree traversal method that visits nodes level
by level, starting from the root and moving
downwards to each successive level, from
left to right. It’s often referred to as a
Breadth-First Search (BFS) for trees because
it explores each level entirely before moving
to the next.
C
B
F
E
A
G
D
A,B,C,D,E,F,G

Tree Operations
Insertion
Deletion
Searching
Root

1. Insertion:
Inserting a new element (node) into the tree, typically by
following a certain rule to place it in the correct position.
Example:
Imagine a family tree. When a new child is born, they are added
as a child under their parents. The tree grows, but the family
structure remains intact with the new addition.

2. Searching
Finding a specific node within the tree based on a given value.
Example:
In an organizational chart, if you’re trying to locate an employee,
you might start at the top (CEO) and search down through
departments until you find them.

3. Deletion
When removing from a binary search tree, we are concerned
with keeping the rest of the tree in the correct order.
This means removing is different depending on whether the
node we are removing has children.
There are three cases for deleting a node:
1.Leaf Node
2.Single Child
3.Having two children

Tree Data Structure & methods & operations

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