tree traversal

4.  In-order
 Post-order
 Pre-order

5.  Tree
 Binary tree
 Recursive
 Traversal
 Traversal in trees and types
Conclusion
1. In-order
2. Post-order
3. Pre-order

6. A tree T is a set of nodes storing
elements such that the nodes have a
parent-child relationship
 Root : The top node in the tree.
 Leaves : Nodes having no children.
 Height of a tree : length of the
longest path from the root to a
leaf.
height of this tree= 3
RL
N Root

7. Binary Trees
(Full Binary Trees)
 Full Binary Tree: A full binary tree is a binary
tree where all the leaves are on the same
level and every non-leaf has two children.
 The first four full binary trees are:
7

8. Binary Tree
A
B
D
H
C
E F
G I
Left subtree
Root/Parent
Right subtree

9. Binary Tree
 Recursive
That repeat itself again and again.
A
B
D
H
C
E F
G ILeft subtree
parent
Right subtree

10. A
B
D
H
C
E F
G I
Left sub tree
parent
Recursive

11. A
B
D
H
C
E F
G I
parent
Recursive

12. A
B
D
H
C
E F
G I
parent
Right subtree
Recursive

13. A
B
D
H
C
E F
G I
parent
Right subtreeLeft subtree
Recursive

15. Traversal is the process of visiting every
node once in a tree.
Three techniques are used for traversing in trees
 In-order
 Post-order
 Pre-order

16. 16
In-order Traversal:
1. Traverse left sub tree(LST)
2. Visit the root
3. Traverse right sub tree(RST)
Post-order Traversal:
1. Traverse left sub tree(LST)
2. Traverse right sub tree(RST)
3. Visit the root
Pre-order Traversal:
1. Visit the root
2. Traverse left sub tree (LST)
3. Traverse right sub tree(RST)

17. Node
Pre-order: (N,L,R)
In-order: (L,N,R)
Post-order: (L,R,N)
left
subtree
right
subtreeL
N
R

18. Traversing in Binary Tree
Ways to print a 3 node tree
= 23 = 6 A
CB
(A,B,C) , (A,C,B)
(B,A,C) , (B,C,A)
(C,B,A) , (C,A,B)

19.  Assume: visiting a node (traversal)
 Pre-order:
1, 3 ,5, 4, 6, 7, 8, 9, 10, 11, 12
 In-order:
4 ,5 ,6 ,3 ,1 ,8 ,7 ,9 ,11, 10 ,12
 Post-order:
4, 6, 5, 3, 8, 11, 12, 10, 9 ,7 ,1
19
1
3
11
98
4 6
5
7
12
10

20. Preorder: 14 4 3 9 7 5 15 18 16 17 20
14
154
9
7
183
5
16 20
17
Traversing a Binary Tree
pre-order???

21. In-order: 3 4 5 7 9 14 15 16 17 18 20
14
154
9
7
183
5
16 20
17
Traversing a Binary Tree
In-order???

22. Post-order: 3 5 7 9 4 17 16 20 18 15 14
14
154
9
7
183
5
16 20
17
Traversing a Binary Tree
post-order???

23. 23
void preOrder(Tree *tree)
{
if (tree->isEmpty( ))
return;
visit(tree->getRoot( ));
preOrder(tree->getLeftSubtree());
preOrder(tree->getRightSubtree());
}
Code for the Traversal

24. Code for the Traversal
void postOrder(Tree *tree)
{
if (tree->isEmpty( ))
return;
postOrder(tree->getLeftSubtree( ));
postOrder(tree->getRightSubtree( ));
visit(tree->getRoot( ));
}

25. void inOrder(Tree *tree)
{
if (tree->isEmpty( ))
return;
inOrder(tree->getLeftSubtree( ));
visit(tree->getRoot( ));
inOrder(tree->getRightSubtree( ));
}
Code for the Traversal

26. Traversal: In tree s a technique in which we search
elements “once”.
 Three types of traversal used in trees are:
1. Post-order (root, Left sub tree, Right sub tree)
2. In-Order ( Left sub tree, Root, Right sub tree)
3. Pre-order(Left sub tree, Right sub tree, Root)