Category Archives: Lesson

Elevens lab: Activity 4

Lab

The Elevens Game
Screen Shot 2015-02-23 at 11.00.25 PM

Adding a Shuffle Method to the Deck Class

Introduction:
You implemented a Deck class in Activity 2. This class should be complete except for the shuffle method. You also implemented a DeckTester class that you used to test your incomplete Deck class.

In Activity 3, you implemented methods in the Shuffler class, which shuffled integers.

Now you will use what you learned about shuffling in Activity 3 to implement the Deck shuffle
method.

Exercises:
1.The file Deck.java, found in the Activity 4 Starter Code folder, is a correct solution from Activity 2. Complete the Deck class by implementing the shuffle method. Use the efficient selection shuffle algorithm from Activity 3.

Note that the Deck constructor creates the deck and then calls the shuffle method. The shuffle method also needs to reset the value of size to indicate that all of the cards can be dealt again.

2.The DeckTester.java file, found in the Activity4 Starter Code folder, provides a basic set of Deck tests. It is similar to the DeckTester class you might have written in Activity 2. Add additional code at the bottom of the main method to create a standard deck of 52 cards and test the shuffle method. You can use the Deck toString method to “see” the cards after every shuffle.

Teacher’s Comments:

Elevens lab: Activity 3 Ex 1 and 2

Lab

The Elevens Game
Screen Shot 2015-02-23 at 11.00.25 PM

Activity 3: Exercise 1
Use the file Shuffler.java, found in the Activity3 Starter Code, to implement the perfect shuffle and the efficient selection shuffle methods as described in the Exploration section of this activity. You will be shuffling arrays of integers.

Activity 3: Exercise 2
Shuffle.java also provides a main method that calls the shuffling methods. Execute the main method and inspect the output to see how well each shuffle method actually randomizes the array elements. You should execute main with different values of SHUFFLE_COUNT and VALUE_COUNT.

Teacher’s Comments:
1. If you run the two methods with VALUE_COUNT = 10, how often would there be duplicate results?
2. Can the number of duplicate results show the efficiency of the two different shuffles?

https://www.youtube.com/watch?v=hPNRtbbf-Jg

Elevens lab: Activity 3 Questions

Lab

The Elevens Game
Screen Shot 2015-02-23 at 11.00.25 PM

Activity 3: Shuffling the Cards in a Deck

Introduction:
Think about how you shuffle a deck of cards by hand. How well do you think it randomizes the cards in the deck?

Exploration:
We now consider the shuffling of a deck, that is, the permutation of its cards into a random-looking sequence. A requirement of the shuffling procedure is that any particular permutation has just as much chance of occurring as any other. We will be using the Math.random method to generate random numbers to produce these permutations.

Several ideas for designing a shuffling method come to mind. We will consider two:

Perfect Shuffle
Card players often shuffle by splitting the deck in half and then interleaving the two half-decks, as shown below.

vendingmachines

This procedure is called a perfect shuffle if the interleaving alternates between the two half-decks. Unfortunately, the perfect shuffle comes nowhere near generating all possible deck permutations. In fact, eight shuffles of a 52-card deck return the deck to its original state!

Consider the following “perfect shuffle” algorithm that starts with an array named cards that contains 52 cards and creates an array named shuffled.

Initialize shuffled to contain 52 “empty” elements. Set k to 0.

For j = 0 to 25,
−– Copy cards[j] to shuffled[k];
−– Set k to k+2. Set k to 1.

For j = 26 to 51,
−– Copy cards[j] to shuffled[k];
–− Set k to k+2.

This approach moves the first half of cards to the even index positions of shuffled, and it moves the second half of cards to the odd index positions of shuffled.

The above algorithm shuffles 52 cards. If an odd number of cards is shuffled, the array shuffled has one more even-indexed position than odd-indexed positions. Therefore, the first loop must copy one more card than the second loop does. This requires rounding up when calculating the index of the middle of the deck. In other words, in the first loop j must go up to (cards.length + 1) / 2, exclusive, and in the second loop j most begin at (cards.length + 1) / 2.

Selection Shuffle
Consider the following algorithm that starts with an array named cards that contains 52 cards and creates an array named shuffled. We will call this algorithm the “selection shuffle.”

Initialize shuffled to contain 52 “empty” elements.
Then for k = 0 to 51,
−– Repeatedly generate a random integer j between 0 and 51, inclusive until cards[j] contains a card (not marked as empty);
−– Copy cards[j] to shuffled[k];
−– Set cards[j] to empty.

This approach finds a suitable card for the kth position of the deck. Unsuitable candidates are any cards that have already been placed in the deck.

While this is a more promising approach than the perfect shuffle, its big defect is that it runs too slowly. Every time an empty element is selected, it has to loop again. To determine the last element of shuffled requires an average of 52 calls to the random number generator.

A better version, the “efficient selection shuffle,” works as follows:

For k = 51 down to 1,
−– Generate a random integer r between 0 and k, inclusive;
−– Exchange cards[k] and cards[r].

This has the same structure as selection sort:
For k = 51 down to 1,
−– Find r, the position of the largest value among cards[0] through cards[k];
−– Exchange cards[k] and cards[r].

This way, the “efficient” selection shuffle algorithm does not require a loop to find the largest (or smallest) value to swap, so it works quicker than the selection shuffle seen above.

Questions:

  1. Write a static method named flip that simulates a flip of a weighted coin by returning either “heads” or “tails” each time it is called. The coin is twice as likely to turn up heads as tails. Thus, flip should return “heads” about twice as often as it returns “tails.”
  2. Write a static method named “arePermutations” that, given two int arrays of the same length but with no duplicate elements, returns true if one array is a permutation of the other (i.e., the arrays differ only in how their contents are arranged). Otherwise, it should return false.
  3. Suppose that the initial contents of the values array in Shuffler.java are {1, 2, 3, 4}. For what sequence of random integers would the efficient selection shuffle change values to contain {4, 3, 2, 1}?

Teacher’s Comments:
1. If you run the two methods with VALUE_COUNT = 10, how often would there be duplicate results?
2. Can the number of duplicate results show the efficiency of the two different shuffles?

https://www.youtube.com/watch?v=hPNRtbbf-Jg

Elevens lab: Activities 9 and 11

March 22nd, 2016

Lab

The Elevens Game
Screen Shot 2015-02-23 at 11.00.25 PM

Classwork:
Activity 9: Questions 3 short discussion

Quick Interfaces Review:
• All methods in an interface type are abstract; that is, they have a name, parameters, and a return type, but they don’t have an implementation.
• All methods in an interface type are automatically public.
• An interface type does not have instance variables, but it is legal to specify constants.

How is the correct method executed when the interface method is invoked?
How did the correct method get called if the caller didn’t even know the exact class to which meas belongs?

The Java virtual machine locates the correct method by first looking at the class of the actual object, and then calling the method with the given name in that class.

This means that one method call can invoke different methods depending on the momentary contents of an interface variable. This mechanism for locating the appropriate method is called dynamic method look-up.

Dynamic method look-up enables a programming technique called polymorphism. The term polymorphism comes from the Greek words for “many shapes”. The same computation works for objects of many shapes, and adapts itself to the nature of the objects.

Activity 11 – Simulation of Elevens: Exercises 1, 2 and 3

Homework:
Activity 11: Simulation of Elevens
Exercise 4, and 5
AP Exam 2012 Question 4

Elevens lab: Activities 1 and 2

Lab

The Elevens Game
Screen Shot 2015-02-23 at 11.00.25 PM

Classwork:
Screen Shot 2015-02-25 at 1.14.50 PM

Activity 1

Introduction:

In this activity, you will complete a Card class that will be used to create card objects.

Think about card games you’ve played. What kinds of information do these games require a card object to “know”? What kinds of operations do these games require a card object to provide?

Exploration:

Now think about implementing a class to represent a playing card. What instance variables should it have? What methods should it provide? Discuss your ideas for this Card class with classmates.

Read the partial implementation of the Card class available in the Activity1 Starter Code folder. As you read through this class, you will notice the use of the @Override annotation before the toString method. The Java @Override annotation can be used to indicate that a method is intended to override a method in a superclass.

In this example, the Object class’s toString method is being overridden in the Card class. If the indicated method doesn’t override a method, then the Java compiler will give an error message.

Here’s a situation where this facility comes in handy. Programmers new to Java often encounter problems matching headings of overridden methods to the superclass’s original method heading. For example, in the Weight class below, the tostring method is intended to be invoked when toString is called for a Weight object.

public class Weight {
private int pounds;
private int ounces;
…
public String tostring(String str) {
return this.pounds + ” lb. ” + this.ounces + ” oz.”;
}
…
}

Unfortunately, this doesn’t work; the tostring method given above has a different name and a different signature from the Object class’s toString method. The correct version below has the correct name toString and no parameter:

public String toString() {
return this.pounds + ” lb. ” + this.ounces + ” oz.”;
}

Activity 1: Design and Create a Card Class

The @Override annotation would cause an error message for the first tostring version to alert the programmer of the errors.

Exercises:
1. Complete the implementation of the provided Card class. You will be required to complete:

a. a constructor that takes two String parameters that represent the card’s rank and suit, and an int parameter that represents the point value of the card;

b. accessor methods for the card’s rank, suit, and point value;

c. a method to test equality between two card objects; and

d. the toString method to create a String that contains the rank, suit, and point value of the card object.

The string should be in the following format:

rank of suit (point value = pointValue)

  1. Once you have completed the Card class, find the CardTester.java file in the Activity1 Starter Code folder. Create three Card objects and test each method for each Card object.

/** Sample Output:

The rank of the first card is: Queen
The suit of the first card is: Hearts
The point value of the first card is: 12
In summary, the first card is the Queen of Hearts (12)

The rank of the second card is: Five
The suit of the second card is: Spades
The point value of the second card is: 5
In summary, the second card is the Five of Spades (5)

The rank of the third card is: Five
The suit of the third card is: Spades
The point value of the third card is: 5
In summary, the third card is the Five of Spades (5)

The first card and the second card are not equivalent.
The second card and the third card are equivalent.
The first card and the third card are not equivalent.

*/

Activity 2: Initial Design of a Deck Class

Introduction:
Think about a deck of cards. How would you describe a deck of cards? When you play card games, what kinds of operations do these games require a deck to provide?

Exploration:
Now consider implementing a class to represent a deck of cards. Describe its instance variables and methods, and discuss your design with a classmate.

Read the partial implementation of the Deck class available in the Activity 2 Starter Code folder. This file contains the instance variables, constructor header, and method headers for a Deck class general enough to be useful for a variety of card games.

Discuss the Deck class with your classmates; in particular, make sure you understand the role of each of the parameters to the Deck constructor, and of each of the private instance variables in the Deck class.

Exercises:
1. Complete the implementation of the Deck class by coding each of the following:
• Deck constructor — This constructor receives three arrays as parameters. The arrays contain the ranks, suits, and point values for each card in the deck. The constructor creates an ArrayList, and then creates the specified cards and adds them to the list.

For example, if ranks = {“A”, “B”, “C”}, suits = {“Giraffes”, “Lions”}, and values = {2,1,6}, the constructor would create the following cards:

[“A”, “Giraffes”, 2], [“B”, “Giraffes”, 1], [“C”, “Giraffes”, 6], [“A”, “Lions”, 2], [“B”, “Lions”, 1], [“C”, “Lions”, 6]
and would add each of them to cards. The parameter size would then be set to the size of cards, which in this example is 6.

Finally, the constructor should shuffle the deck by calling the shuffle method. Note that you will not be implementing the shuffle method until Activity 4.

• isEmpty — This method should return true when the size of the deck is 0; false otherwise.

• size — This method returns the number of cards in the deck that are left to be dealt.

• deal — This method “deals” a card by removing a card from the deck and returning it, if there are any cards in the deck left to be dealt. It returns null if the deck is empty. There are several ways of accomplishing this task. Here are two possible algorithms:

Algorithm 1: Because the cards are being held in an ArrayList, it would be easy to simply call the List method that removes an object at a specified index, and return that object. Removing the object from the end of the list would be more efficient than removing it from the beginning of the list. Note that the use of this algorithm also requires a separate “discard” list to keep track of the dealt cards. This is necessary so that the dealt cards can be reshuffled and dealt again.

Algorithm 2: It would be more efficient to leave the cards in the list. Instead of removing the card, simply decrement the size instance variable and then return the card at size. In this algorithm, the size instance variable does double duty; it determines which card to “deal” and it also represents how many cards in the deck are left to be dealt. This is the algorithm that you should implement.

  1. Once you have completed the Deck class, find DeckTester.java file in the Activity2 Starter Code folder. Add code in the main method to create three Deck objects and test each method for each Deck object.

Questions:
1. Explain in your own words the relationship between a deck and a card.

  1. Consider the deck initialized with the statements below. How many cards does the deck contain?

String[] ranks = {“jack”, “queen”, “king”};
String[] suits = {“blue”, “red”};
int[] pointValues = {11, 12, 13};
Deck d = new Deck(ranks, suits, pointValues);

  1. The game of Twenty-One is played with a deck of 52 cards. Ranks run from ace (highest) down to 2 (lowest). Suits are spades, hearts, diamonds, and clubs as in many other games. A face card has point value 10; an ace has point value 11; point values for 2, …, 10 are 2, …, 10, respectively. Specify the contents of the ranks, suits, and pointValues arrays so that the statement

Deck d = new Deck(ranks, suits, pointValues);

initializes a deck for a Twenty-One game.

  1. Does the order of elements of the ranks, suits, and pointValues arrays matter?

/** TESTING
Testing deck1
deck1 size: 3
deck1 deal: three of hearts (point value = 3)
deck1 size: 2
Is deck1 empty?: false

Testing deck2
deck2 size: 1
deck2 deal: ten of diamonds (point value = 10)
deck2 size: 0
Is deck2 empty?: true

Testing deck3
deck3 size: 2
deck3 deal: queen of clubs (point value = 12)
deck3 size: 1
Is deck3 empty?: false
*/

Picture Lab: Activity 6

Picture Lab – Activity 6
Mirroring pictures

balloons

Exercises:
1. Write the method mirrorVerticalRightToLeft that mirrors a picture around a mirror placed vertically from right to left. Hint: you can copy the body of mirrorVertical and only change one line in the body of the method to accomplish this. Write a class (static) test method called testMirrorVerticalRightToLeft in PictureTester to test this new method and call it in the main method.

  1. Write the method mirrorHorizontal that mirrors a picture around a mirror placed horizontally at the middle of the height of the picture. Mirror from top to bottom as shown in the pictures below (Figure 8). Write a class (static) test method in PictureTester to test this new method and call it in the main method.

  2. Write the method mirrorHorizontalBotToTop that mirrors the picture around a mirror placed horizontally from bottom to top. Hint: you can copy the body of mirrorHorizontal and only change one line to accomplish this. Write a class (static) test method in PictureTester to test this new method and call it in the main method.

  3. Challenge — Work in groups to figure out the algorithm for the method mirrorDiagonal that mirrors just a square part of the picture from bottom left to top right around a mirror placed on the diagonal line (the diagonal line is the one where the row index equals the column index). This will copy the triangular area to the left and below the diagonal line as shown below. This is like folding a square piece of paper from the bottom left to the top right, painting just the bottom left triangle and then (while the paint is still wet) folding the paper up to the top right again. The paint would be copied from the bottom left to the top right as shown in the pictures below (Figure 9). Write a class (static) test method in PictureTester to test this new method and call it in the main method.
    figure9