Converting Infix to
Postfix Notation
Lecture Slides prepared by Absar Moeen ROOTS
SCHOOL ISLAMABAD
1
Hierarchy of Operators
This is the hierarchy of the operators
– () brackets first
– * or / that comes first from the left hand
side is done first, precedence level is
same
– + or - that comes first from the left hand
side is done first, precedence level is
same
Lecture Slides prepared by Absar Moeen ROOTS
SCHOOL ISLAMABAD
2
Example
X = (A + B) / (( C - D) * ( E + F))
Lecture Slides prepared by Absar Moeen ROOTS
SCHOOL ISLAMABAD
3
•
Number the operators according to the
precedence of the equation
1.
2.
3.
4.
5.
6.
–
+
+
*
/
=
This is the hierarchy of the operators for this
equation
Lecture Slides prepared by Absar Moeen ROOTS
SCHOOL ISLAMABAD
4
6
1
5
2
4
3
• X = (A + B) / (( C - D) * ( E + F))
Lecture Slides prepared by Absar Moeen ROOTS
SCHOOL ISLAMABAD
5
• Now we will put them in a binary tree, by
following the rule
– The last operator goes in the tree first (ROOT)
– Then the left hand side of the operator goes
on the left side of the root node and the right
side of the operator goes on the right side of
the node
• If there is an operand then write it directly
• If there is an expression then follow the same
principal of insertion
Lecture Slides prepared by Absar Moeen ROOTS
SCHOOL ISLAMABAD
6
=
X
/
+
*
A
B
-
C
+
D
E
Lecture Slides prepared by Absar Moeen ROOTS
SCHOOL ISLAMABAD
F
7
6
X
=
1
A
+
5
B
/
2
C
-
4
D
*
3
E
Lecture Slides prepared by Absar Moeen ROOTS
SCHOOL ISLAMABAD
+
F
8
• Now to get the post fix notation we are
going to perform a post order traversal on
the binary tree
• Visit the left node
• Visit the right node
• Print the root node
Lecture Slides prepared by Absar Moeen ROOTS
SCHOOL ISLAMABAD
9
=
X
XAB+CD–EF+*/=
/
+
A
*
B
C
+
D
E
F
Lecture Slides prepared by Absar Moeen ROOTS
SCHOOL ISLAMABAD
10