1. Trees
Tree traversal
By : Dana Dia’a
Data structure and algorithms

2. Tree (ADT)
 What is a tree ?
 A set of nodes.
 Each node can have one or more children .
 Each node can have at most one parent.
Root
( no parent)
Leaves
( no child)
Node level
1
2
3
4

3. Binary tree
 In binary tree , each node has at most two children .
 In other word , it can have zero children ( empty ) , one or
two children but not more than two children .
 Examples of a binary trees :

4. binary search tree ( BSTree)
 Every node entry has a unique key ( keys are not the
same in the tree ) .
 All the keys in the left of a node are less than the key of
a node
 All the keys in the right of a node are greater than the
key of a node .
 Example of a BStree :
Left
Less than 8
Right
Greater than 8

5. A binary tree but NOT binary search
tree

6. Search a node
 A binary search tree provide an excellent structure for
searching a node .
 For example : find the node with value 6 .
 We compare: 6 is <or > 8( the root) ?
 6 is less than 8 so we go to the left of node .
 Then we compare : 6 is <or > 3 ?
 6 is greater than 3 so we go right to
The right of node .
 6 is found .

7. Tree traversal
 The process of visiting all nodes in a tree only
one time .
 Two classes :
 1 . Breadth – first traversal .
 2 . Depth –first traversal .

8. Breadth – first traversal
 We can go with two methods :
1. Visiting each node starting from the lowest level (
root ) and moving down level by level , visiting
each node from left to right . ( top – down – from
left – to right ) .
Output : 8 , 3 , 10 ,1 ,6 ,14 ,4 ,7
,13
Starts

9. Breadth – first traversal (cont.)
 The other method is :
1. Visiting each node starting from the highest level (
leaves ) and moving up level by level , visiting each
node from right to left . ( bottom – up – from right –
to left ) .
Starts
Output : 13 , 7 ,4 , 14 ,6 ,1 ,10 ,3 ,8

10. Depth – first traversal
 We have to consider three tasks in this type .
 V – visiting a node .
 L – traversing the left sub-tree if any .
 R – traversing the right sub-tree if any .
 There are six types of depth –first traversal , but
we will consider three of them :
 VLR ( Preorder )
 LVR ( Inorder )
 LRV ( Postorder)

11. VLR ( Preorder )
VLR
VLR VLR
VLRVLR VLR
VLR
VLR
VLR
Output : 8 ,3 ,1 ,6 ,4 ,7 ,10 ,14 ,13
Assuming that the
visit(v) is to output
the value

12. LVR ( Ineorder )
LVR
Output : 1 , 3 , 4 , 6 , 7 , 8 ,10 ,13 ,14
Assuming that the
visit() is to output
the valueLVR
LVR
LVR
LVR
LVR
LVR
LVRLVR

13. LRV ( Posteorder )
LRV
Output : 1 , 4 , 7 ,6 ,3 , 13 , 14 , 10 , 8
Assuming that the
visit() is to output
the value
LRV
LRV LRV
LRV
LRV
LRVLRVLRV