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How to Think Like a Computer Scientist

Chapter 15

Sets of objects

15.1 Composition

By now, you have seen several examples of composition. One of the first examples was using a method invocation as part of an expression. Another example is the nested structure of statements; you can put an if statement within a while loop, within another if statement, and so on.

Having seen this pattern, and having learned about lists and objects, you should not be surprised to learn that you can create lists of objects. You can also create objects that contain lists (as attributes); you can create lists that contain lists; you can create objects that contain objects; and so on.

In this chapter and the next, we will look at some examples of these combinations, using Card objects as an example.

15.2 `Card` objects

If you are not familiar with common playing cards, now would be a good time to get a deck, or else this chapter might not make much sense. There are fifty-two cards in a deck, each of which belongs to one of four suits and one of thirteen ranks. The suits are Spades, Hearts, Diamonds, and Clubs (in descending order in bridge). The ranks are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. Depending on the game that you are playing, the rank of Ace may be higher than King or lower than 2.

If we want to define a new object to represent a playing card, it is obvious what the attributes should be: rank and suit. It is not as obvious what type the attributes should be. One possibility is to use strings containing words like "Spade" for suits and "Queen" for ranks. One problem with this implementation is that it would not be easy to compare cards to see which had a higher rank or suit.

An alternative is to use integers to encode the ranks and suits. By "encode," we do not mean what some people think, which is to encrypt or translate into a secret code. What a computer scientist means by "encode" is "to define a mapping between a sequence of numbers and the items I want to represent." For example:

Spades -> 3
Hearts -> 2
Diamonds -> 1
Clubs -> 0

An obvious feature of this mapping is that the suits map to integers in order, so we can compare suits by comparing integers. The mapping for ranks is fairly obvious; each of the numerical ranks maps to the corresponding integer, and for face cards:

Jack -> 11
Queen -> 12
King -> 13

The reason we are using mathematical notation for these mappings is that they are not part of the Python program. They are part of the program design, but they never appear explicitly in the code. The class definition for the Card type looks like this:

class Card: def __init__(self, suit=0, rank=2): self.suit = suit self.rank = rank

As usual, we provide an initialization method that takes an optional parameter for each attribute. The default value of suit is 0, which represents Clubs.

To create a Card, we invoke the Card constructor with the suit and rank of the card we want.

threeOfClubs = Card(3, 1)

In the next section we'll figure out which card we just made.

15.3 Class attributes and the `str` method

In order to print Card objects in a way that people can easily read, we want to map the integer codes onto words. A natural way to do that is with lists of strings. We assign these lists to class attributes at the top of the class definition:

class Card: suitList = ["Clubs", "Diamonds", "Hearts", "Spades"] rankList = ["narf", "Ace", "2", "3", "4", "5", "6", "7", "8", "9", "10", "Jack", "Queen", "King"] #init method omitted def __str__(self): return (self.rankList[self.rank] + " of " + self.suitList[self.suit])

A class attribute is defined outside of any method, and it can be accessed from any of the methods in the class.

Inside __str__, we can use suitList and rankList to map the numerical values of suit and rank to strings. For example, the expression self.suitList[self.suit] means "use the attribute suit from the object self as an index into the class attribute named suitList, and select the appropriate string."

The reason for the "narf" in the first element in rankList is to act as a place keeper for the zero-eth element of the list, which should never be used. The only valid ranks are 1 to 13. This wasted item is not entirely necessary. We could have started at 0, as usual, but it is less confusing to encode 2 as 2, 3 as 3, and so on.

With the methods we have so far, we can create and print cards:

>>> card1 = Card(1, 11) >>> print card1 Jack of Diamonds

Class attributes like suitList are shared by all Card objects. The advantage of this is that we can use any Card object to access the class attributes:

>>> card2 = Card(1, 3) >>> print card2 3 of Diamonds >>> print card2.suitList[1] Diamonds

The disadvantage is that if we modify a class attribute, it affects every instance of the class. For example, if we decide that "Jack of Diamonds" should really be called "Jack of Swirly Whales," we could do this:

>>> card1.suitList[1] = "Swirly Whales" >>> print card1 Jack of Swirly Whales

The problem is that all of the Diamonds just became Swirly Whales:

>>> print card2 3 of Swirly Whales

It is usually not a good idea to modify class attributes.

15.4 Comparing cards

For primitive types, there are conditional operators (<, >, ==, etc.) that compare values and determine when one is greater than, less than, or equal to another. For user-defined types, we can override the behavior of the built-in operators by providing a method named __cmp__. By convention, __cmp__ has two parameters, self and other, and returns 1 if the first object is greater, -1 if the second object is greater, and 0 if they are equal to each other.

Some types are completely ordered, which means that you can compare any two elements and tell which is bigger. For example, the integers and the floating-point numbers are completely ordered. Some sets are unordered, which means that there is no meaningful way to say that one element is bigger than another. For example, the fruits are unordered, which is why you cannot compare apples and oranges.

The set of playing cards is partially ordered, which means that sometimes you can compare cards and sometimes not. For example, you know that the 3 of Clubs is higher than the 2 of Clubs, and the 3 of Diamonds is higher than the 3 of Clubs. But which is better, the 3 of Clubs or the 2 of Diamonds? One has a higher rank, but the other has a higher suit.

In order to make cards comparable, you have to decide which is more important, rank or suit. To be honest, the choice is arbitrary. For the sake of choosing, we will say that suit is more important, because a new deck of cards comes sorted with all the Clubs together, followed by all the Diamonds, and so on.

With that decided, we can write __cmp__:

def __cmp__(self, other): # check the suits if self.suit > other.suit: return 1 if self.suit < other.suit: return -1 # suits are the same... check ranks if self.rank > other.rank: return 1 if self.rank < other.rank: return -1 # ranks are the same... it's a tie return 0

In this ordering, Aces appear lower than Deuces (2s).

As an exercise, modify __cmp__ so that Aces are ranked higher than Kings.

15.5 Decks

Now that we have objects to represent Cards, the next logical step is to define a class to represent a Deck. Of course, a deck is made up of cards, so each Deck object will contain a list of cards as an attribute.

The following is a class definition for the Deck class. The initialization method creates the attribute cards and generates the standard set of fifty-two cards:

class Deck: def __init__(self): self.cards = [] for suit in range(4): for rank in range(1, 14): self.cards.append(Card(suit, rank))

The easiest way to populate the deck is with a nested loop. The outer loop enumerates the suits from 0 to 3. The inner loop enumerates the ranks from 1 to 13. Since the outer loop iterates four times, and the inner loop iterates thirteen times, the total number of times the body is executed is fifty-two (thirteen times four). Each iteration creates a new instance of Card with the current suit and rank, and appends that card to the cards list.

The append method works on lists but not, of course, tuples.

15.6 Printing the deck

As usual, when we define a new type of object we want a method that prints the contents of an object. To print a Deck, we traverse the list and print each Card:

class Deck: ... def printDeck(self): for card in self.cards: print card

Here, and from now on, the ellipsis (...) indicates that we have omitted the other methods in the class.

As an alternative to printDeck, we could write a __str__ method for the Deck class. The advantage of __str__ is that it is more flexible. Rather than just printing the contents of the object, it generates a string representation that other parts of the program can manipulate before printing, or store for later use.

Here is a version of __str__ that returns a string representation of a Deck. To add a bit of pizzazz, it arranges the cards in a cascade where each card is indented one space more than the previous card:

class Deck: ... def __str__(self): s = "" for i in range(len(self.cards)): s = s + " "*i + str(self.cards[i]) + "\n" return s

This example demonstrates several features. First, instead of traversing self.cards and assigning each card to a variable, we are using i as a loop variable and an index into the list of cards.

Second, we are using the string multiplication operator to indent each card by one more space than the last. The expression " "*i yields a number of spaces equal to the current value of i.

Third, instead of using the print command to print the cards, we use the str function. Passing an object as an argument to str is equivalent to invoking the __str__ method on the object.

Finally, we are using the variable s as an accumulator. Initially, s is the empty string. Each time through the loop, a new string is generated and concatenated with the old value of s to get the new value. When the loop ends, s contains the complete string representation of the Deck, which looks like this:

>>> deck = Deck() >>> print deck Ace of Clubs 2 of Clubs 3 of Clubs 4 of Clubs 5 of Clubs 6 of Clubs 7 of Clubs 8 of Clubs 9 of Clubs 10 of Clubs Jack of Clubs Queen of Clubs King of Clubs Ace of Diamonds

And so on. Even though the result appears on 52 lines, it is one long string that contains newlines.

15.7 Shuffling the deck

If a deck is perfectly shuffled, then any card is equally likely to appear anywhere in the deck, and any location in the deck is equally likely to contain any card.

To shuffle the deck, we will use the randrange function from the random module. With two integer arguments, a and b, randrange chooses a random integer in the range a <= x < b. Since the upper bound is strictly less than b, we can use the length of a list as the second argument, and we are guaranteed to get a legal index. For example, this expression chooses the index of a random card in a deck:

random.randrange(0, len(self.cards))

An easy way to shuffle the deck is by traversing the cards and swapping each card with a randomly chosen one. It is possible that the card will be swapped with itself, but that is fine. In fact, if we precluded that possibility, the order of the cards would be less than entirely random:

class Deck: ... def shuffle(self): import random nCards = len(self.cards) for i in range(nCards): j = random.randrange(i, nCards) self.cards[i], self.cards[j] = self.cards[j], self.cards[i]

Rather than assume that there are fifty-two cards in the deck, we get the actual length of the list and store it in nCards.

For each card in the deck, we choose a random card from among the cards that haven't been shuffled yet. Then we swap the current card (i) with the selected card (j). To swap the cards we use a tuple assignment, as in Section 9.2:

self.cards[i], self.cards[j] = self.cards[j], self.cards[i]

As an exercise, rewrite this line of code without using a sequence assignment.

15.8 Removing and dealing cards

Another method that would be useful for the Deck class is removeCard, which takes a card as an argument, removes it, and returns True if the card was in the deck and False otherwise:

class Deck: ... def removeCard(self, card): if card in self.cards: self.cards.remove(card) return True else: return False

The in operator returns true if the first operand is in the second, which must be a list or a tuple. If the first operand is an object, Python uses the object's __cmp__ method to determine equality with items in the list. Since the __cmp__ in the Card class checks for deep equality, the removeCard method checks for deep equality.

To deal cards, we want to remove and return the top card. The list method pop provides a convenient way to do that:

class Deck: ... def popCard(self): return self.cards.pop()

Actually, pop removes the last card in the list, so we are in effect dealing from the bottom of the deck.

One more operation that we are likely to want is the boolean function isEmpty, which returns true if the deck contains no cards:

class Deck: ... def isEmpty(self): return (len(self.cards) == 0)

15.9 Glossary

encode: To represent one set of values using another set of values by constructing a mapping between them.
class attribute: A variable that is defined inside a class definition but outside any method. Class attributes are accessible from any method in the class and are shared by all instances of the class.
accumulator: A variable used in a loop to accumulate a series of values, such as by concatenating them onto a string or adding them to a running sum.