Stacks & Queues Infix Calculator CSC 172 SPRING 2002 LECTURE 5

Workshop sign-up Still time : Dave Feil-Seifer Ross Carmara

Infix to postfix * 3 == 7 (because multiplication has higher precidence) 10 – 4 – 3 == 3 (because subtraction proceeds left to right)

Infix to postfix 4 ^ 3 ^ 2 == != 4096 Generally, Rather than:

Precidence A few simple rules: () > ^ > * / > + - Subtraction associates left-to-right Exponentiation associates right to left

Infix Evaluation 1 – 2 – 4 ^ 5 * 3 * 6 / 7 ^ 2 ^ 2 == -8 (1 – 2) – ( ( ( ( 4 ^ 5) * 3) * 6) / (7 ^ ( 2 ^ 2 ) ) ) Could you write a program to evaluate stuff like this?

Postfix  If we expressed (1 – 2) – ( ( ( ( 4 ^ 5) * 3) * 6) / (7 ^ ( 2 ^ 2 ) ) ) As 1 2 – 4 5 ^ 3 * 6 * ^ ^ / - Then, we could use the postfix stack evaluator

Postfix evaluation using a stack 1. Make an empty stack 2. Read tokens until EOF a. If operand push onto stack b. If operator i. Pop two stack values ii. Perform binary operation iii. Push result 3. At EOF, pop final result

1 2 – 4 5 ^ 3 * 6 * ^ ^ / -

1

2121

1 2 – 4 5 ^ 3 * 6 * ^ ^ / - 4

1 2 – 4 5 ^ 3 * 6 * ^ ^ / - 5 4

1 2 – 4 5 ^ 3 * 6 * ^ ^ /

1 2 – 4 5 ^ 3 * 6 * ^ ^ /

1 2 – 4 5 ^ 3 * 6 * ^ ^ /

1 2 – 4 5 ^ 3 * 6 * ^ ^ /

1 2 – 4 5 ^ 3 * 6 * ^ ^ /

1 2 – 4 5 ^ 3 * 6 * ^ ^ /

1 2 – 4 5 ^ 3 * 6 * ^ ^ /

1 2 – 4 5 ^ 3 * 6 * ^ ^ /

1 2 – 4 5 ^ 3 * 6 * ^ ^ /

1 2 – 4 5 ^ 3 * 6 * ^ ^ /

1 2 – 4 5 ^ 3 * 6 * ^ ^ / - 7

1 2 – 4 5 ^ 3 * 6 * ^ ^ / - -8

But how to go from infix to postfix?  Could you write a program to do it?  What data structures would you use  Stack  Queue  How about a simple case just using “+”    Operands send on to output?  Operator push on stack?  Pop ‘em all at the end?

More complex 2 ^ 5 – 1 == 2 5 ^ 1 – Modify the simple rule? If you are an operator, pop first, then push yourself? ok

Even more complex 3 * 2 ^ ^ * 1 – If you are an operator: Pop if the top of the stack is higher precedence than

Infix to postfix Stack Algorithm Operands : Immediately output Close parenthesis: Pop stack until open parenthesis Operators: 1. Pop all stack symbols until a symbol of lower precedence (or a right-associative symbol of equal precedence) appears. 2. Push operator EOF: pop all remaining stack symbols

1 – 2 ^ 3 ^ 3 – ( * 6) * 7

1

- 1

- 1 2

1 – 2 ^ 3 ^ 3 – ( * 6) * 7 ^- ^- 1 2

1 – 2 ^ 3 ^ 3 – ( * 6) * 7 ^- ^

1 – 2 ^ 3 ^ 3 – ( * 6) * 7 ^^- ^^

1 – 2 ^ 3 ^ 3 – ( * 6) * 7 ^^- ^^

1 – 2 ^ 3 ^ 3 – ( * 6) * ^ ^ -

1 – 2 ^ 3 ^ 3 – ( * 6) * 7 (- ( ^ ^ -

1 – 2 ^ 3 ^ 3 – ( * 6) * 7 (- ( ^ ^ - 4

1 – 2 ^ 3 ^ 3 – ( * 6) * 7 +(- +( ^ ^ - 4

1 – 2 ^ 3 ^ 3 – ( * 6) * 7 +(- +( ^ ^ - 4 5

1 – 2 ^ 3 ^ 3 – ( * 6) * 7 *+(- *+( ^ ^ - 4 5

1 – 2 ^ 3 ^ 3 – ( * 6) * 7 *+(- *+( ^ ^

1 – 2 ^ 3 ^ 3 – ( * 6) * ^ ^ * +

1 – 2 ^ 3 ^ 3 – ( * 6) * 7 *- * ^ ^ * +

1 – 2 ^ 3 ^ 3 – ( * 6) * 7 *- * ^ ^ * + 7

1 – 2 ^ 3 ^ 3 – ( * 6) * ^ ^ * + 7 * -

1 – 2 ^ 3 ^ 3 – ( * 6) * ^ ^ * + 7 * - ((1 – (2 ^ (3 ^ 3))) – (( 4 + (5 * 6)) * 7)) Input To evaluation stack