Welcome to CIS 068 !

1. Welcome to CIS 068 ! Lesson 11: Data Structures 2 CIS 068

2. Overview • Description, Usage and Application of • Queues and Stacks CIS 068

3. Queues • FIFO (first in first out) Structure in 3 2 1 out CIS 068

4. Queues • Java Interface CIS 068

5. Queues: Implementation 1 • 1. Implementation as Linked List in out 3 2 1 (null) CIS 068

6. Adding an Element in out in out in out (null) 1 2 1 (null) (null) • Adding an element E: • If in == null: in = E, out = E, E.link = null • else in.link = E, in = E, E.link = null CIS 068

7. Removing an Element in out in out in out 2 1 2 (null) (null) (null) • Removing an element: • If out == null throw EmptyQueueException • else • E=out, out=out.link • If out = null: in = null • return E CIS 068

8. Queues: Implementation 2 2. Implementation as Circular Array Capacity = 6 Index ! 3 4 5 in --- out 1 2 size = 5 List-Size = 5 CIS 068

9. Circular Array: Adding an Element E in out out 9 9 10 10 11 11 12 12 13 13 E=14 in 14 --- size = 6 size = 5 If size == capacity return error (or increase capacity automatically) else array[in]=E size++ in = (in+1)%capacity CIS 068

10. Circular Array: Removing an Element out --- 9 out 10 10 11 11 12 12 13 13 in in --- --- size = 4 size = 5 If size == 0 throw EmptyQueueException else E = array[out] size -- out = (out+1)%capacity CIS 068

11. Stacks • LIFO (first in first out) Structure top 3 2 1 CIS 068

12. Stacks Java Interface CIS 068

13. Stack: Implementation 1 • 1. Implementation as Linked List top 1 2 3 (null) CIS 068

14. Adding an Element E 1 2 top (null) 1 2 E=3 top (null) Adding an Element E: E.link = top top = E CIS 068

15. Removing an Element 1 2 3 top (null) 1 2 top (null) return 3 Removing an Element E: if top==null throw EmptyQueueException else E=top top = top.link return E CIS 068

16. Stack: Implementation 2 • 2. Implementation as Array Capacity = 6 Index ! --- --- top 4 3 2 1 CIS 068

17. Adding / Removing --- --- top 4 3 2 1 Adding an Element E: If top == capacity return error (or increase capacity automatically) else array[top] = E top ++ Removing an Element: If top == 0 throw EmptyQueueException else top -- return array[top] CIS 068

18. Application 1 • Checking for Balanced Parantheses • Task: • Determine whether expression is balanced with respect to parantheses • Allow for different symbols of parentheses: • ( ) • [ ] • { } CIS 068

19. Algorithm CIS 068

20. Algorithm • Expression: • (a+{b-c}*[d+(a+b)) • Stack: • ( • ({ • ( • ([ • ([( • ([ Error ! CIS 068

21. Application 2 Evaluating a Postfix Expression Postfix expression: Why ? No brackets necessary ! CIS 068

22. PN / RPN • Prefix / Postfix Expression History • PREfix Notation (also called Polish Notation) invented in the 1920's by Polish mathematician Jan Lukasiewicz, • writing operators in front of their operands, instead of between them, makes brackets unnecessary • Postfix Expression = Reverse Polish Notation (RPN): operators appear behind their operands • Proposed in the late 1950's by the Australian philosopher and early computer scientist Charles L. Hamblin • Advantage: the operators appear in the order required for computation. CIS 068

23. HP9100A Engineers at the Hewlett-Packard company realised that RPN could be used to simplify the electronics of their calculators at the expense of a little learning by the user. The first "calculator" to use RPN was the HP9100A, which was introduced in 1968 Price: 4900$ CIS 068

24. Evaluation Algorithm • Evaluate Expression from left to right • If symbol read is operand: push onto the stack • If symbol read is operator: • pop two operators • Evaluate using operator • Push result on stack • Final value on stack is final result • (remark: works only on binary operators) CIS 068

25. Evaluation Algorithm Example CIS 068