1. Basic Data Structures Stacks

2. A collection of objects Objects can be inserted into or removed from the collection at one end (top) First-in-last-out

3. Stack Applications: Reversing a Word RAIL  LIAR

4. Empty Stack Start from an empty stack Insert the word RAIL into the stack

5. R A I L R

6. A R

7. I A R

8. L I A R

9. The Word is now in the stack. Now empty the Stack. L I A R

10. L L I A R

11. L I I A R

12. L I A A R

13. L I A R R

14. Stack Operations push : push a new item on the top of the stack pop : if the stack is not empty, remove the top item of the stack; not defined if the stack is empty top : if the stack is not empty, read the value of the top item of the stack; not defined if the stack is empty

15. Practice What’s remained in the stack after the following operations, assuming that at the beginning the stack is empty? push(3); push(5); pop(); top(); push(9);

16. Evaluate Postfix Expressions Operator comes after the operands PostfixInfix 5 4 +5 + 4 5 4 + 3 *(5 + 4) * 3 5 4 + 9 6 - *(5 + 4) * (9 - 6)

17. Evaluate Postfix: Keep Intermediate Results E.g. the result of (5 + 4) while we calculate (9 - 6) stacks do this! Assumptions: –binary operators only –we can split the expression string into tokens (pieces)

18. Evaluate Postfix: the Algorithm while there are more tokens in the input string: –if next token is a number, push it onto the stack –if next token is an operand pop two elements off the stack perform the operation stack the result pop final element as answer

19. Evaluate 5 4 + 9 6 - * 5 is a number, place it on the stack 5

20. Evaluate 5 4 + 9 6 - * 4 is a number, place it on the stack 4 5

21. Evaluate 5 4 + 9 6 - * + is an operand Pop two numbers Apply Operand 4 5 4 5 + = 9

22. Evaluate 5 4 + 9 6 - * Put the result back onto the stack 9 5 4 + = 9

23. Evaluate 5 4 + 9 6 - * 9 is a number, place it on the stack 9 9

24. Evaluate 5 4 + 9 6 - * 6 is a number, place it on the stack 6 9 9

25. Evaluate 5 4 + 9 6 - * - is an operand Pop two numbers Apply Operand 9 6 9 6 9 - = 3

26. Evaluate 5 4 + 9 6 - * - is an operand Put the result back onto the stack 9 6 9 - = 3 3

27. Evaluate 5 4 + 9 6 - * 9 3 * is an operand  Pop two numbers  Apply Operand 3 9 * = 27

28. Evaluate 5 4 + 9 6 - * 27 * is an operand  Pop two numbers  Apply Operand 3 9 * = 27

29. Evaluate 5 4 + 9 6 - * No more tokens in the string Pop the final answer 27 5 4 + 9 6 - * = (5 + 4) * (9 - 6) = 27