Binary Tree
A Tree
Binary Trees
The Binary tree means that the
node can have maximum two
children. Here, binary name itself
suggests that 'two'; therefore,
each node can have either 0, 1 or 2
children.
Example of Binary Tree
Binary Search Tree
A binary tree which has the
following properties:
-The left subtree of a node contains
only nodes with keys less than the
node's key.
-The right subtree of a node
contains only nodes with keys
greater than or equal to the node's
key.
-Both the left and right subtrees
must also be binary search trees.
Example of Binary Search Tree
20
10
20
15
15
5
30
15
4
5
3
1
14
8
18
13
18
8
25
35
7
15
17
10
24
8
20
11
4
19
18
21
Example of Not Binary Search Tree
2
5
10
25
22
35
25
39
15
20
51
34
13
33
Answer:
20
10
5
25
2
33
25
22
15
39
13
35
34
51
Tree Traversal
Tree traversal also known
as tree search and walking
the tree is a form of graph
traversal and refers to the
process of visiting
retrieving, updating, or
deleting each node in a tree
data structure, exactly once.
Tree Traversal Strategies
• Breadth First
Starting at either the highest or
lowest node and visiting each level
until the other end is reached.
-Lowest to Highest
-Highest to Lowest
• Depth First
Proceeding as far as possible to the
right (or left), and then returning one
level, stepping over and stepping
down.
Left to Right
Right to Left
Breadth First Traversal
Traverse through one level of children
nodes, then traverse the level of
grandchildren's nodes. Consider Top
Down, left to right traversal.
Example:
Level 0
A
B
D
Level 1
C
E
F
G
Level order : A, B, C, D, E, F, G
Level 2
Depth First Traversal
Traverse through left subtrees first, then
traverse through the right subtrees.
V = visiting a node
L = traversing the left subtree
R = traversing the right subtree
Options
-VLR (Pre Order Tree Traversal)
-LVR (In order Tree Traversal)
-LRV (Post order Tree Traversal)
Example Depth First Traversal
START
Level 0
1
2
4
8
VLR
PRE-ORDER:
Level 1
3
5
9
1, 2, 4, 8, 9, 5, 3, 6, 7, 10
LRV
POST-ORDER: 8, 9, 4, 5, 2, 6, 10, 7, 3, 1
6
7
10
Level 2
Level 3
LVR
IN-ORDER: 8, 4, 9, 2, 5, 1, 6, 3, 10, 7
LEVEL-ORDER: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Code for Depth First Traversal
45
10
7
90
12