Question

Convert the following infix expression to A) postfix B) prefix

3 * 4 / ( 5 - 6 * 7 )

Answer 1

Move	Current Token	Stack	Output
1	3	empty	3
2	*	*	3
3.	4	*	3 4
4	/	/	3 4 *
5	(	(/	3 4 *
6	5	(/	3 4 * 5
7	-	-(/	3 4 * 5
8	6	-(/	3 4 * 5 6
9	*	*-(/	3 4 * 5 6
10	7	*-(/	3 4 * 5 6 7
11	)	/	3 4 * 5 6 7 * -
12		empty	3 4 * 5 6 7 * - /

So,

a) Postfix

3 4 * 5 6 7 * - /

b) Prefix

For converting to prefix, reverse infix expression, then convert to postfix and reverse postfix.

Reversed infix

(7* 6 - 5 ) / 4 * 3

Convert to postfix

Move	Current Token	Stack	Output
1	(	(
2	7	(	7
3.	*	*(	7
4	6	*(	7 6
5	-	-(	7 6 *
6	5	-(	7 6 * 5
7	)		7 6 * 5 -
8	/	/	7 6 * 5 -
9	4	/	7 6 * 5 - 4
10	*	*/	7 6 * 5 - 4
11	3	*/	7 6 * 5 - 4 3
12		empty	7 6 * 5 - 4 3 * /

Reverse postfix

/ * 3 4 - 5 * 6 7

So, the prefix is

/ * 3 4 - 5 * 6 7