Convert the following infix expression to A) postfix B) prefix
3 * 4 / ( 5 - 6 * 7 )
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
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