Team-hawks_DSA_binary_tree[1] [Read-Only].pptx

BINARY TREE
AND ITS
OPERATIONS

TEAM Hawks
Muhammad Asfer Mahmood
Abdullah Shahid
Muhammad Zain
Hassan

Team Hawks
Muhammad Asfer Mahmood
Abdullah Shahid
Muhammad Zain
Hassan

Defination:
 A binary tree is a hierarchical
data structure,
 in which each node can have
at most two children: a left
child and a right child.
 It is called "binary" because
each node can have at most
two descendants .
9

10
Node: A basic unit of a
binary tree, containing data
and references to its
children.
Parent: A node that
has one or more
child nodes.
Root: The topmost node
of the tree, from which
all other nodes originate.
Leaf: A node with no
children (it is at the
bottom of the tree).

11
Child: A node that is
a descendant of
another node.
Sibling: Nodes
that share the
same parent.

12
Types
Full Binary Tree
each parent node
either has no
children or exactly
two children.
1
/
2 3
/ /
4 5 6 7
Perfect Binary Tree
every non-leaf node
has exactly two
children
1
/
2 3
/ /
4 5 6 7
Complete Binary
Tree almost like a
perfect binary tree
but the last level
might not be
completely filled
1
/
2 3
/ /
4 5 6
Balanced Binary
Tree The height
difference between
left and right
subtrees is at most
1.
1
/
2 3
/ /
4 5

Traversals
13
In binary tree traversal,
the goal is to visit all the
nodes in a specific order.

Traversals
⊷ Pre-order Traversal
(Root, Left, Right)
⊷ In-order Traversal
(Left, Root, Right)
⊷ Post-order Traversal
(Left, Right, Root)
14

Traversals
15
Root-Left-Right
Root

Traversals
16
Left-Root-Right
Root

Traversals
17
Left-Right-Root
Root

Binary Tree
Traversals
Pre-Order
R->l->r
1, 2, 4, 5, 3
In-Order
l->R->r
4, 2, 5, 1, 3
Post-Order
l->r->R
4, 5, 2, 3, 1
18
1
2 3
5
4

Pre-order
traversal is a
method
where we
visit the root
first, then the
left subtree,
and finally
the right
subtree
19
Binary Tree
Traversals
Pre-order
traversal:
⊷ Used in
file
explorers
because of
hierarchy
⊷* + 4 5
6
((4 + 5) * 6)

Post-order
traversal is
a method
where we
visit the left
subtree first,
then the
right
subtree, and
finally the
root.
In-order
traversal is
a method
where we
visit the left
subtree,
then the
root, and
then the
right
subtree.
20
Binary Tree
Traversals

Post-order
traversal:
⊷ Ensures
dependenci
es
⊷4 5 + 6 *
In-order
traversal:
⊷indexing
systems
⊷4 + 5 *
6
21
Binary Tree
Traversals
((4 + 5) * 6)

Operations:
22
D
e
l
e
t
i
o
n
Insertio
n
S
e
a
r
c
h

Operations:
D
e
l
e
t
i
o
n
Insertio
n
S
e
a
r
c
h

Insertion:
• Start at the root.
• Traverse the tree to find the first available position
• Insert the node at that position.
1
2 3
5
4
6

Deletion:
• Node is a leaf: Simply remove the node
• Node has one child: Replace the node with its child.
• Node has two children: Replace the node with the
in-order successor or in-order predecessor.
1
2 3
5
4
2

1
2 3
5
4
2
Deletion:

1
3
5
4
2
Deletion:

1
3
5
4
Search:
• Start at the root.
• Compare the value with the current node:
If equal, the node is found.
If less, search the left subtree.
If greater, search the right subtree.
3

Applications and Conclusion
32

⊷ Hierarchical Data
Representation:
• Binary trees are used to
represent hierarchical
structures like file
systems, organizational
charts, and decision trees.
33

⊷ Binary Search Trees
(BSTs):
• Efficient searching,
insertion, and deletion of
data.
• Example: Databases and
dictionaries
34

⊷ Expression Trees:
• Binary trees represent
algebraic expressions,
where operators are
internal nodes and
operands are leaves.
• Example: Compilers use
expression trees to
evaluate mathematical
expressions.
35

⊷ Routing and Networking:
• Used in network routing
algorithms like multicast
protocols to decide the
shortest path or
connectivity.
• Example:
• Routers use decision trees
to find the best route for
data packets.
36

Team-hawks_DSA_binary_tree[1] [Read-Only].pptx

More Related Content

Similar to Team-hawks_DSA_binary_tree[1] [Read-Only].pptx (20)

More from XEON14 (8)

Recently uploaded (20)

Team-hawks_DSA_binary_tree[1] [Read-Only].pptx