1. © 2006 Pearson Addison-Wesley. All rights reserved8 A-1 CMPT 225 Midterm Review

2. © 2006 Pearson Addison-Wesley. All rights reserved8 A-2 Topics Covered Java review Software Engineering Recursion –(and a little algorithm efficiency) Abstract Data Types Linked Lists Stacks Queues

3. © 2006 Pearson Addison-Wesley. All rights reserved8 A-3 Topics Covered Roughly: chapters 1-8 Minus chapter 6... though we did some of it in class We didn’t read the second half of ch. 7, but we covered it in class The algorithm efficiency was not in any of these chapters

4. © 2006 Pearson Addison-Wesley. All rights reserved8 A-4 Java Review You should be able to read Java code –You don’t need to memorize a bunch of java.util classes You should be able to write Java code –Defining your own classes, interfaces, methods, etc.

5. © 2006 Pearson Addison-Wesley. All rights reserved8 A-5 Software Engineering What is a good solution to a problem? Object oriented design –Read a UML diagram –Write a UML diagram Modularity, modifiability, readability, ease of use, fail-safe programming…

6. © 2006 Pearson Addison-Wesley. All rights reserved8 A-6 Recursion Write recurrence relations –e.g. rabbits(n) = rabbits(n-1) + rabbits(n-2) Write recursive (Java) methods Solve problems with simple recursive solutions Backtracking Relation with induction

7. © 2006 Pearson Addison-Wesley. All rights reserved8 A-7 Algorithm Efficiency Big-O notation: –What does O(n) mean? –What about O(n 2 )? Count the steps of an algorithm, translate to big-O

8. © 2006 Pearson Addison-Wesley. All rights reserved8 A-8 Abstract Data Types Difference: –ADT vs. data structure How do you specify ADTs? Designing the right ADT for a problem ADT List and SortedList

9. © 2006 Pearson Addison-Wesley. All rights reserved8 A-9 Linked Lists Object references Using nodes and references Programming with linked lists –inserting, deleting, traversing Variations –tail references, circular lists, doubly linked

10. © 2006 Pearson Addison-Wesley. All rights reserved8 A-10 Stacks ADT Stack –LIFO Implementations Problem solving with Stacks

11. © 2006 Pearson Addison-Wesley. All rights reserved8 A-11 Queues ADT Queue –FIFO Implementations Problem solving with Queues

12. © 2006 Pearson Addison-Wesley. All rights reserved8 A-12 Example 1 Write a pre-condition, post-condition, and loop invariant for the following: public int Factorial(int n) { int val = 1; for(int i=1; i<=n; i++) val = val*i; return val; }

13. © 2006 Pearson Addison-Wesley. All rights reserved8 A-13 Example 1 - Solution Pre-condition: –n is an integer greater than or equal to 1 Post-condition: –returned value is n! Loop invariant: –after iteration i of the for loop, val is equal to i!

14. © 2006 Pearson Addison-Wesley. All rights reserved8 A-14 Example 2 What is wrong with this: void printN(int n) { System.out.println(n); printN(n-1); }

15. © 2006 Pearson Addison-Wesley. All rights reserved8 A-15 Example 2 - Solution No base case! It will run forever

16. © 2006 Pearson Addison-Wesley. All rights reserved8 A-16 Example 3 Write a recursive method that takes input n, and prints the numbers from n to 0.

17. © 2006 Pearson Addison-Wesley. All rights reserved8 A-17 Example 3 - Solution void printUpToN(int n) { if(n<0) System.out.print(“”); else { System.out.print(n); printUpToN(n-1); }

18. © 2006 Pearson Addison-Wesley. All rights reserved8 A-18 Example 4 Using only the List ADT operations, write a pseudocode method swap(List list, int i, int j) that exchanges positions i and j in List

19. © 2006 Pearson Addison-Wesley. All rights reserved8 A-19 Example 4 - Solution swap(List list, int i, int j): int temp = list.retrieve(i); list.add(j+1,temp); temp = list.retrieve(j); list.remove(j); list.add(i+1,temp); list.remove(i);

20. © 2006 Pearson Addison-Wesley. All rights reserved8 A-20 Example 5 Specify an abstract data type for a Bag... items can be inserted, contents dumped out, removed one by one

21. © 2006 Pearson Addison-Wesley. All rights reserved8 A-21 Example 5 - Solution ADT Bag +createBag() //Creates an empty bag +isEmpty():boolean{query} //Determines if the Bag is empty +add(in newItem:BagItemType) //Adds newItem to the Bag +removeAll() //Removes all items from the Bag +pickRandom() //Removes a random item from the Bag

22. © 2006 Pearson Addison-Wesley. All rights reserved8 A-22 Example 6 Write pseudocode to add the contents of one list to the end of another list

23. © 2006 Pearson Addison-Wesley. All rights reserved8 A-23 Example 6 - Solution append(List list1, List list2) newList.createList(); while(!list1.isEmpty()) newList.add(newList.size()+1,list1.get(1)); list1.remove(1); while(!list2.isEmpty()) newList.add(newList.size()+1,list2.get(1)); list2.remove(1); return newList

24. © 2006 Pearson Addison-Wesley. All rights reserved8 A-24 Example 7 Same thing... using Queue ADT

25. © 2006 Pearson Addison-Wesley. All rights reserved8 A-25 Example 7 - Solution append(Queue queue1, Queue queue2) newQueue.createQueue(); while(!queue1.isEmpty()) newQueue.enQueue(queue1.deQueue()); while(!queue2.isEmpty()) newQueue.enQueue(queue2.deQueue()); return newQueue

26. © 2006 Pearson Addison-Wesley. All rights reserved8 A-26 Example 8 Write a pseudocode method to count the number of items in a linked list.

27. © 2006 Pearson Addison-Wesley. All rights reserved8 A-27 Example 8 – Solution (Iterative) numElements(LinkedList ll) Node curr = head; int count = 0; while(curr.getNext()!=null) count++; curr = curr.getNext(); return count;

28. © 2006 Pearson Addison-Wesley. All rights reserved8 A-28 Example 9 Write a pseudocode method to find the largest element in a linked list of integers

29. © 2006 Pearson Addison-Wesley. All rights reserved8 A-29 Example 9 - Solution largestElement(LinkedList ll) if(head==null) throw exception Node curr = head; int largest = head.getItem(); while(curr.getItem()!=null) if(largest<curr.getItem()) largest = curr.getItem() curr=curr.getNext(); return largest;

30. © 2006 Pearson Addison-Wesley. All rights reserved8 A-30 Example 10 Given one possible explanation for a StackException that is thrown from a push operation

31. © 2006 Pearson Addison-Wesley. All rights reserved8 A-31 Example 10- Solution Explanation: –The Stack ADT was implemented with a fixed size array, and it has reached maximum capacity.

32. © 2006 Pearson Addison-Wesley. All rights reserved8 A-32 Example 11 What are contents of aStack following this: aStack.createStack(); if(aStack.isEmpty()) aStack.push(4); push(5); pop() popall(); push(6); push(7);

33. © 2006 Pearson Addison-Wesley. All rights reserved8 A-33 Example 11 - Solution What are contents of aStack following this: aStack.createStack(); if(aStack.isEmpty()) aStack.push(4); push(5); pop() popall(); push(6); push(7); 7676

34. © 2006 Pearson Addison-Wesley. All rights reserved8 A-34 Example 12 Briefly explain/define these terms: –circular linked list –data structure –encapsulation

35. © 2006 Pearson Addison-Wesley. All rights reserved8 A-35 Example 12 Briefly explain/define these terms: –circular linked list a linked list where tail node references the head –data structure a construct in a programming language that stores data –encapsulation objects keep internal data enclosed internally, hiding it from view and preventing it from being accessed

36. © 2006 Pearson Addison-Wesley. All rights reserved8 A-36 Example 13 Given the following running times for input n, what is the big-O measure of efficiency –n + 6n steps –n2 + n(n 2 + 5) steps –log n + n steps

37. © 2006 Pearson Addison-Wesley. All rights reserved8 A-37 Example 13 - Solution Given the following running times for input n, what is the big-O measure of efficiency –n + 6n steps ----------------------- O(n) –n2 + n(n 2 + 5) steps -------------- O(n 3 ) –log n + n steps -------------------- O(n)

38. © 2006 Pearson Addison-Wesley. All rights reserved8 A-38 Example 14 Which ADT is appropriate for each type of data: –An alphabetic list of names –Airplanes that stack above a busy airport waiting to land –An employer that is laying off employees, starting with the most recent hires

39. © 2006 Pearson Addison-Wesley. All rights reserved8 A-39 Example 14 - Solution Which ADT is appropriate for each type of data: –An alphabetic list of names LIST –Airplanes that stack above a busy airport waiting to land QUEUE –An employer that is laying off employees, starting with the most recent hires STACK

40. © 2006 Pearson Addison-Wesley. All rights reserved8 A-40 Example 15 Give UML diagram from requirements: –A drawing program is to allow kids to draw all sorts of shapes: lines, rectangles, and circles. While using this program, kids select the shape they wish to draw, the colour of the shape and they indicate the shape's position on the canvas (a canvas is a drawing area on a window created by the drawing program). –The position of a line is indicated by the x and y coordinates of its end points. –The position of a rectangle is indicated by the x and y coordinates of its top left corner and the x and y coordinates of its bottom right corner. –The position of a circle is indicated by the x and y coordinates of its center and the length of its radius.

41. © 2006 Pearson Addison-Wesley. All rights reserved8 A-41 Example 15 - Solution colour shape display( ) or draw( ) one end x, one end y other end x other end y line topleft x topleft y bottomright x bottomright y rectangle center x center y radius circle display( ) or draw( )

42. © 2006 Pearson Addison-Wesley. All rights reserved8 A-42 More types of examples Predict the output of Java code.... Recursive methods for traversal... for recognizing classes of strings (e.g. all ‘a’) Defining ADT’s from description... bank account, rectangle Merging sorted lists

43. © 2006 Pearson Addison-Wesley. All rights reserved8 A-43 More types of examples Displaying contents of a Queue or Stack Writing data structure for an ADT... say the Bag from earlier... need to decide data members Inserting nodes in doubly linked/circular linked lists