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

© 2006 Pearson Addison-Wesley. All rights reserved 8 A-1

CMPT 225

Midterm Review

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Topics Covered

• Java review• Software Engineering• Recursion

– (and a little algorithm efficiency)

• Abstract Data Types• Linked Lists• Stacks• Queues


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


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.


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…


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


Algorithm Efficiency

• Big-O notation:– What does O(n) mean?– What about O(n2)?

• Count the steps of an algorithm, translate to big-O


Abstract Data Types

• Difference:– ADT vs. data structure

• How do you specify ADTs?

• Designing the right ADT for a problem

• ADT List and SortedList


Linked Lists

• Object references

• Using nodes and references

• Programming with linked lists– inserting, deleting, traversing

• Variations– tail references, circular lists, doubly linked


Stacks

• ADT Stack– LIFO

• Implementations

• Problem solving with Stacks


Queues

• ADT Queue– FIFO

• Implementations

• Problem solving with Queues


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;

}


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!


Example 2

• What is wrong with this:

void printN(int n)

{

System.out.println(n);

printN(n-1);

}



• No base case!

• It will run forever


Example 3

• Write a recursive method that takes input n, and prints the numbers from n to 0.



void printUpToN(int n){if(n<0)

System.out.print(“”);else{

System.out.print(n);printUpToN(n-1);

}}


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



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);


Example 5

• Specify an abstract data type for a Bag... items can be inserted, contents dumped out, removed one by one



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


Example 6

• Write pseudocode to add the contents of one list to the end of another list



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


Example 7

• Same thing... using Queue ADT



append(Queue queue1, Queue queue2)

newQueue.createQueue();

while(!queue1.isEmpty())

newQueue.enQueue(queue1.deQueue());

while(!queue2.isEmpty())

newQueue.enQueue(queue2.deQueue());

return newQueue


Example 8

• Write a pseudocode method to count the number of items in a linked list.


Example 8 – Solution (Iterative)

numElements(LinkedList ll)

Node curr = head;int count = 0;

while(curr.getNext()!=null)count++;curr = curr.getNext();

return count;


Example 9

• Write a pseudocode method to find the largest element in a linked list of integers



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;


Example 10

• Given one possible explanation for a StackException that is thrown from a push operation



• Explanation:– The Stack ADT was implemented with a fixed

size array, and it has reached maximum capacity.


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);



• What are contents of aStack following this:aStack.createStack();if(aStack.isEmpty())aStack.push(4);

push(5);pop()popall();push(6);push(7);

7

6


Example 12

• Briefly explain/define these terms:– circular linked list– data structure– encapsulation


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


Example 13

• Given the following running times for input n, what is the big-O measure of efficiency– n + 6n steps– n2 + n(n2 + 5) steps– log n + n steps



• Given the following running times for input n, what is the big-O measure of efficiency– n + 6n steps ----------------------- O(n)– n2 + n(n2 + 5) steps -------------- O(n3)– log n + n steps -------------------- O(n)


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



• 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


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.



colour

shape

display( ) or draw( )

one end x,one end yother end xother end y

line

topleft xtopleft y bottomright xbottomright y

rectangle

center xcenter yradius

circle





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


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

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

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