13. Objects of vectors¶
13.1. Enumerations¶
In Card objects we talked about mappings between real-world values like rank and suit, and internal representations like integers and strings. Although we created a mapping between ranks and integers, and between suits and integers, we pointed out that the mapping itself does not appear as part of the program.
Actually, C++ provides a feature called an enumeration that makes it possible to
(1) include a mapping as part of the program, and (2) define the set of values
that make up the mapping. For example, here is the definition of the enumerated
types Suit and Rank:
enum Suit {NONE, CLUBS, DIAMONDS, HEARTS, SPADES};
enum Rank {JOKER, TWO=2, THREE, FOUR, FIVE, SIX, SEVEN, EIGHT,
NINE, TEN, JACK, QUEEN, KING, ACE};
By default, the first value in the enumerated type maps to 0, the second to 1,
and so on. Within the Suit type, the value CLUBS is represented by the
integer 1, DIAMONDS is represented by 2, etc. By convention, the values in
enumerated types have names with all capital letters.
The definition of Rank overrides the default mapping and specifies that
TWO should be represented by the integer 2. The other values follow in the
usual way.
If you are splitting up your source code like we did in Header files,
you sould put these enum definitions in the .h file, so that they will
be available to each file that includes the header file.
With these types defined, we can use them anywhere. For example, the instance
variables rank and suit can be declared with type Rank and
Suit:
struct Card
{
Rank rank;
Suit suit;
Card(Suit s, Rank r);
};
Notice that the types of the parameters for the constructor have changed, too. Now, to create a card, we can use the values from the enumerated types as arguments:
Card card(DIAMONDS, JACK);
This code is much clearer than our previous alternative using integers.
Because we know that the values in the enumerated types are represented as
integers, we can use them as indices for a vector. Therefore the old
to_string function will work without modification. We have to make some
changes in build_deck though:
vector<Card> build_deck()
{
vector<Card> deck(52);
int i = 0;
for (Suit suit = CLUBS; suit <= SPADES; suit = Suit(suit+1)) {
for (Rank rank = TWO; rank <= ACE; rank = Rank(rank+1)) {
deck[i].suit = suit;
deck[i].rank = rank;
i++;
}
}
return deck;
}
In some ways, using enumerated types makes this code more readable, but there
is one complication. Strictly speaking, we are not allowed to do arithmetic
with enumerated types, so suit++ is not legal. On the other hand, in the
expression suit+1, C++ automatically converts the enumerated type to an
integer. Then we can take the result and typecast it back to the enumerated
type:
suit = Suit(suit+1);
rank = Rank(rank+1);
This could be improved by overloading the ++ operator for our enumerated
types, but we aren’t going to do that now.
13.2. switch statement revisted¶
It’s hard to mention enumerated types without mentioning
The switch statement we introduced back in the Conditionals and recursion,
chapter, because they often go hand in hand. switch statements work with
integers, characters, and enumerated types. For example, to convert a Suit
to the corresponding string, we could use something like:
switch(suit) {
case CLUBS: return "Clubs";
case DIAMONDS: return "Diamonds";
case HEARTS: return "Hearts";
case SPADES: return "Spades";
default: return "Not a valid suit";
}
In this case we don’t need break statements because the return
statements cause the flow of execution to return to the caller instead of
falling through to the next case.
In general, it is good style to include a default case in every switch
statement, to handle errors or unexpected values.
13.3. Decks¶
In Vectors of objects, we worked with a vector of objects, but
we also mentioned that it is possible to have an object that has a vector as
an instance variable. In this chapter we are going to create a new object,
called a Deck, that contains a vector of Cards.
The struct definition and constructor look like this:
struct Deck {
vector<Card> cards;
Deck(int n);
};
Deck::Deck(int size)
{
vector<Card> temp(size);
cards = temp;
}
The name of the instance variable is cards to help distinguish the Deck
object from the vector of Cards that it contains.
For now there is only one constructor. It creates a local variable named
temp, which it initializes by invoking the constructor for the vector
class, passing the size as a parameter. Then it copies the vector from
temp into the instance variable cards.
We can now create a deck of cards like this:
Deck deck(52);
Here is a state diagram showing what a Deck object looks like:
The object named deck has a single instance variable named cards, which
is a vector of Card objects. To access the cards in a deck we have to
compose the syntax for accessing an instance variable and the syntax for
selecting an element from a vector. For example, the expression
deck.cards[i].suite is its suit. The following loop
for (int i = 0; i < 52; i++) {
cout << deck.cards[i].to_string() << endl;
}
demonstrates how to traverse the deck and output each card. If we run this code, we’ll notice that we have created a deck containing 52 Jokers, which is probably not what we want.
13.4. Another constructor¶
Now that we have a Deck object, it would be useful to initialize the cards
in it. From Objects of vectors we have a function called
build_deck that we could use (with a few adaptations), but it might be
more natural to write a second Deck constructor.
Deck::Deck()
{
vector<Card> temp(52);
cards = temp;
int i = 0;
for (Suit suit = CLUBS; suit <= SPADES; suit = Suit(suit+1)) {
for (Rank rank = ACE; rank <= KING; rank = Rank(rank+1)) {
cards[i].suit = suit;
cards[i].rank = rank;
i++;
}
}
}
Notice how similar this function is to build_deck, except that we had to
change the syntax to make it a constructor. Now we can create a standard
52-card deck with the simple declaration Deck deck;
13.5. Deck member functions¶
Now that we have a Deck object, it makes sense to put all the functions
that pertain to Decks in the Deck structure definition. Looking at the
functions we have written so far, one obvious candidate is the one introduced
in the print_deck function section. Here’s how it looks, rewritten as a
Deck member function:
void Deck::print() const
{
for (int i = 0; i < cards.size(); i++) {
cout << cards[i].to_string() << endl;
}
}
As usual, we can refer to the instance variables of the current object without using dot notation.
For some functions, it is not obvious whether they should be member functions
of Card, member functions of Deck, or nonmember functions that take
Cards and Decks as arguments. The find_card we wrote in
Searching, for example, has a Card and a Deck as parameters,
but we could reasonably make it a member function of either type.
Here it is as a Deck member function:
int Deck::find(const Card& card) const
{
for (int i = 0; i < cards.size(); i++) {
if (cards[i] == card) return i;
}
return -1;
}
Writing it as a Card member function is a little tricky. Here it is:
int Card::find(const Deck& deck) const
{
for (int i = 0; i < deck.cards.size(); i++) {
if (deck.cards[i] == *this) return i;
}
return -1;
}
The first trick is that we have to use the keyword this to refer to the
Card the function is invoked on.
The second trick is getting around the fact that C++ does not make it easy to write two structure definitions that refer to each other. The problem is that when the compiler is reading the first structure definition, it doesn’t know about the second one yet.
One solution is to declare Deck is a structure, without defining it, by
adding:
// declare that Dec is a structure, without defining it
struct Deck;
before the declaration of the Card struct, so that we can refer to it
in the declaraton of find:
int find(const Deck& deck) const;
13.6. Shuffling¶
For most card games you need to be able to shuffle the deck; that is, put the cards in a random order. In Random numbers we saw how to generate random numbers, but it is not obvious how to use them to shuffle a deck.
One possibility is to model the way humans shuffle, which is usually by dividing the deck into two and then reassembling the deck by choosing alternately from each half deck. Since humans usually don’t shuffle perfectly, after about 7 iterations the order of the deck is pretty well randomized. But a computer program would have the annoying property of doing a perfect shuffle every time, which is not really very random. In fact, after 8 perfect shuffles, you would find the deck back in the same order you started in.
A better shuffling algorithm is to traverse the deck on card at a time, and at each iteration choose two cards and swap them.
Here is an outline of how this algorithm works. To sketch the program, we are using a combination of C++ statements and English words that is sometimes called pseudocode:
for (int i = 0; i < cards.size(); i++) {
// choose a random number between i and cards.size()
// swap the ith card and the randomly-chosen card
}
The nice thing about using pseudocode is that it often makes it clear what
functions you are going to need. In this case, we need something like
random_between, which chooses a random integer between the parameters l
and h, and swap_cards which takes two indices and switches the cards
at the indicated positions.
You can probably figure out how to write random_between by looking back at
Random numbers, although you will have to be careful about possibly
generating indices that are out of range. You can also figure out the
swap_cards function yourself, and we will leave the implementation of these
functions as exercises.
With random_between and swap_cards to help, we can add a shuffle
member function to Deck:
void Deck::shuffle()
{
for (int i = 0; i < cards.size(); i++) {
int rand_card = random_between(0, cards.size() - 1);
swap_cards(i, rand_card);
}
}
13.7. Sorting¶
Now that we have messed up the deck, we need a way to put it back in order. Ironically, there is an algorithm for sorting that is very similar to the algorithm for shuffling, called a selection sort.
As with shuffle, we are going to traverse the deck and at each location
choose another card and swap. The only difference is that this time instead of
choosing the other card at random, we are going to find the lowest card
remaining in the deck.
By “remaining in the deck”, we mean cards that are at or to the right of the
index i.
for (int i = 0; i < cards.size(); i++) {
// find the lowest card at or to the right of i
// swap the ith card and the lowest card
}
Again, the pseudocode helps with the design of helper functions. In this
case we can use the swap_cards that we have already written, so we only
need one new member function, which we’ll name find_lowest_between.
This process, using pseudocode to figure out what helper functions are needed is sometimes called top-down design, in contrast to the bottom-up design discussed in Counting.
With your growing skill in writting member functions, we will leave writting
find_lowest_between and sort as exercises.
13.8. Hands¶
How should we represent a hand or some other subset of a full deck? One easy
choice is to make a Deck object that has fewer than 52 cards.
We might want a function, subdeck, that takes a vector of cards and a
range of indices, and returns a new vector of cards that contains the specified
subset of the deck:
Deck Deck::subdeck(int l, int h) const
{
Deck sub(h-l+1);
for (int i = 0; i < sub.cards.size(); i++) {
sub.cards[i] = cards[l+i];
}
return sub;
}
To create the local variable named sub we are using the Deck
constructor that does not initialize the cards. The cards get initialized
when they are copied from the original deck.
The size of the subdeck is h-l+1 because both the low card and high card
are included. This sort of computation can be confusing, and lead to
off-by-one errors. Drawing a picture is usually the best way to avoid
them.
We will also want to be able to add and remove cards to our subdecks after they
are created. Let’s add Deck member functions, add_card, and
remove_card to take care of that.
C++ vectors have member functions push_back and pop_back that do just what we need.
push_back has the following prototype:
void push_back(const value_type& val);
It adds a new element, val, to the end of the vector, increasing its size
by 1. pop_back is a void function that removes the last element from
the vector and decreases its size by 1.
We can use these to write add_card and remove_card.
void Deck::add_card(const Card& c)
{
cards.push_back(c);
}
Card Deck::remove_card()
{
Card card = cards[cards.size()-1];
cards.pop_back();
return card;
}
13.9. Shuffling and dealing¶
In the Shuffling section, we wrote pseudocode for a shuffling algorithm.
Assuming that you completed the exercise and we have a Deck member function
called shuffle, we can use it to create hands:
Deck deck;
deck.shuffle();
Deck hand1 = deck.subdeck(0, 4);
Deck hand2 = deck.subdeck(5, 9);
Deck pack = deck.subdeck(10, 51);
This code puts the first 5 cards in one hand, the next 5 cards in the other, and the rest into the pack.
When you though about dealing, did you think we should give out one card at a time to each player in the round-robin sytle that is common in real card games? We could write code to do that, but it is unnecessary for our computer program. The round-robin convention is intended to mitigate imperfect shuffling and make it more difficult for the dealer to cheat. Neither of these is an issue for our program.
This example is a useful reminder of one of the dangers of engineering metaphors: sometimes we impose restrictions on computers that are unnecessary, or expect capabilities that are lacking, because we unthinkingly extend a metaphor past its breaking point. Beware of misleading analogies
13.10. Merge sort¶
In the Sorting section, we saw a simple sorting algorithm that turns out not to be very efficient. In order to sort \(n\) items, it has to traverse the vector \(n\) times, and each traversal takes an amount of time that is proportional to \(n\). The total time, therefore, is proportional to \(n^2\).
In this section, we will sketch a more efficient algorithm, called merge sort. To sort \(n\) items, merge sort takes time proportional to \(n log n\). That may not seem impressive, but as \(n\) gets bit, the difference between \(n^2\) and \(n log n\) can be enormous. Try out a few values of \(n\) and see.
The basic idea behind merge sort is this: if you have two subdecks, each of which has been sorted, it is easy (and fast) to merge them into a single, sorted deck. Try this out with a deck of cards:
For two subdecks with about 10 cards each and sort them so that when they are face up the lowest cards are on top. Place both decks face up in front of you.
Compare the top card from each deck and choose the lower one. Flip it over and add it to the merged deck.
Repeast step two until one of the decks is empty. Then take the remaining cards and add them to the merged deck.
The result should be a single sorted deck. Here’s what this looks like in pseudocode:
Deck merge(const Deck& d) const
{
// creates a new deck big enough for all the cards
Deck result(cards.size() + d.cards.size());
// use index i for place in first deck, j for place in second deck
int i = 0;
int j = 0;
// k traverses the result deck
for (int k = 0; k < result.cards.size(); k++) {
// if this is empty, d wins, if d is empty, this wins;
// otherwise, compare the two cards on top
// add winner to the new deck
}
return result;
}
The best way to test merge is to build and shuffle a deck, use subdeck to
form two (small) hands, then use the sort routine you wrote as an exercise to
sort the two halves. Then you can pass the two halves to merge to see if it
works.
Once you get that working, try a simple implementation of merge_sort:
Deck Deck::merge_sort() const
{
// find the midpoint of the deck
// divide the deck into two subdecks
// sort the subdecks using sort
// merge the two halves and return the result
}
Notice that the current object is declared const because merge_sort
does not modify it. Instead, it creates and returns a new Deck object.
If you can get that version working, the real fun begins! The magical thing
about merge sort is that it is recursive. At the point where you sort the
subdecks, why should you involve the old, slow selection sort? Why not invoke
the spiffy new merge_sort you are in the process of writing?
Not only is that a good idea, it is necessary in order to achieve the
promised performance advantage. In order to make it work, though, you have to
add a base case so that it doesn’t recurse forever. A simple base case is a
subdeck with 0 or 1 cards. If merge_sort receives such a small subdeck, it
can return it unmodified, since it is already sorted.
The recursive version of merge_sort should look something like this:
Deck Deck::merge_sort() const
{
// if the deck is 0 or 1 cards, return it
// find the midpoint of the deck
// divide the deck into two subdecks
// sort the subdecks using merge_sort
// merge the two halves and return the result
}
As usual, there are two ways to think about recursive programs: you can think through the entire flow of execution, or you can make the “leap of faith.” We have deliberately contructed this example to encourage you to make the leap of faith.
When you were using sort to sort the subdecks, you didn’t feel compelled
to follow the flow of execution, right? You just assumed that the sort
function would work because you already debugged it. All you did to make
merge_sort recursive was replace one sort algorithm with another. There is
no reason to read the program differently.
Well, actually you have to give some thought to getting the base case right and making sure that you reach it eventually, but other than that, writing the recursive version should be no problem. Good luck!
13.11. Making a game¶
Now that we have objects that represent cards and decks, let’s use them to make a game. One of the simplest card games that children play is called War.
Initally, the deck is divided evenly into two piles, one for each player. During each round (refered to as a “battle”), each player takes the top card from their pile and places it, face up, in the center. Whoever has the highest-ranking card, with Aces high and ignoring suit, takes the two cards and adds them to the bottom of their pile.
When the two cards are of the same rank a “war” ensues, with each player then placing three cards from the top of their pile into the center face down, followed by a fourth card face up. The winner is again the player with the highest card face up, who takes all of the cards now in the center.
The game continues until one player has won the entire deck, which can happen either by loosing a battle with the loosing player’s last card, or by the loosing player being unable to provide the required cards in a war.
While we have Cards and Decks for making our war game, there are
two problems with our current implementations of these that need to be fixed
to make them suitable for our game:
Comparing cards in war ignores suites and uses ace-high when comparing ranks. This means our current implementation of the
==and>member functions will need to be changed.Cards in the two player’s “piles” need to be removed from one end of the pile and added to the other end. Our
Deckobject uses a vector to store cards, and vectors do not provide an efficient way to implement this behavior.
13.12. Inheritance¶
We can use inheritance
to create a new WarCard object that behaves just like a Card object in
every way except in it’s comparison behavior. When we compare WarCards,
only rank matters, not suit.
The definition of WarCard in the header file looks like this:
struct WarCard : Card
{
using Card::Card;
bool operator==(const WarCard& c2) const;
bool operator>(const WarCard& c2) const;
};
The : Card following WarCard tells the compiler that the WarCard
object is a derived object that inherits from its parent Card
object. The using Card::Card line is a
using-declaration that tells
the compiler that WarCards inherit the constructors of its parent.
Finally, we use
function overriding to
tell the compiler that we will be creating new implementations of
== and >. We can then implement these member functions
in the .cpp file with:
bool WarCard::operator==(const WarCard& c2) const
{
return (rank == c2.rank);
}
bool WarCard::operator>(const WarCard& c2) const
{
// Handle Jokers high
if (rank == JOKER && c2.rank != JOKER) return true;
if (c2.rank == JOKER && rank != JOKER) return false;
// Handle rest of ranks
if (rank > c2.rank) return true;
return false;
}
Since we defined <, >=, <=, and !== for cards using their
logical equivalence to these two functions, we do not need to overide them
for War cards.
13.13. Piles of WarCards¶
We have another problem to solve before we can implement our War game.
Decks use a vector
to store a collection of card objects. Vectors are an example a data structure, which is an organization,
management, and storage format for data chosen for efficient access.
Vectors served well as a data structure for decks, since they permitted the efficient access and swapping of cards throughout the deck needed for shuffling. Vectors will not server well for what we need for our War game, however, since for that we need a collection of cards which:
can grow and shrink in size efficiently.
supports the efficient adding of cards to one end of the collection, and removal from the other end.
C++ has another data structure, called a queue, that provides just what we are looking for.
With a queue to store WarCards, we can create a Pile object whose
header looks like this:
struct Pile
{
queue<WarCard> cards;
// constructors
Pile();
Pile(const Deck& d);
// function
int size();
// modifiers
void add_card(const WarCard& c);
WarCard remove_card();
void move_cards(Pile& p);
};
Piles have two constructors, one which creates an empty pile of war cards
and another which will populate a pile from a shuffled subdeck. We will add war cards to one end of the pile and remove them from the other by using the
push and pop member functions of queues that do just what we want.
Finally, we want a move_cards member function that will remove war cards
from one pile and add them to another. The implementation of these functions
looks like this:
Pile::Pile() {}
Pile::Pile(const Deck& d) {
for (int i = 0; i < d.cards.size(); i++) {
cards.push(WarCard(d.cards[i].suit, d.cards[i].rank));
}
}
int Pile::size()
{
return cards.size();
}
void Pile::add_card(const WarCard& c)
{
cards.push(c);
}
WarCard Pile::remove_card()
{
WarCard c = cards.front();
cards.pop();
return c;
}
void Pile::move_cards(Pile& p)
{
while (p.size() > 0) {
add_card(p.remove_card());
}
}
13.14. Glossary¶
- pseudocode¶
A way of designing programs by writing rough drafts in a combination of English and C++.
- helper function¶
A small function that does not do anything enormously useful by itself, but which helps another, more useful, function.
- inheritance¶
A mechanism for basing an object on another object to avoid duplication of code following the DRY principle.
- merge sort¶
An algorithm for sorting a collection of values. Mergesort is faster than…