How to represent "things" in the world inside a computer program

Fact:
There are things in the real world that are not numbers, e.g.: playing cards:

Review: how does the computer store information using just numbers ?

Information is stored inside a computer as numbers by using an encoding method
An encoding method is an agreement on how to represent certain facts by a code (= specific number)
Example: encoding the marital status information

How to represent a deck of playing cards inside a computer program

Let's examine a deck of playing cards:

4 suites: Spades, Heart, Clubs and Diamonds Each suite has: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King There are 52 number of cards in a deck

How to represent a deck of playing cards inside a computer program

We can represent the 52 cards in a deck with the numbers 0 - 51:

Ace 2 3 4 5 6 7 8 9 10 J Q K Spades: 0 1 2 3 4 5 6 7 8 9 10 11 12 Hearts: 13 14 15 16 17 18 19 20 21 22 23 24 25 Diamonds: 26 27 28 29 30 31 32 33 34 35 36 37 38 Clubs: 39 40 41 42 43 44 45 46 47 48 49 50 51

$64,000 question: how can we decode a number to its corresponding playing card ?

How to represent a deck of playing cards inside a computer program

The spades are represented with the numbers 0 - 12:

Ace 2 3 4 5 6 7 8 9 10 J Q K Spades: 0 1 2 3 4 5 6 7 8 9 10 11 12 Hearts: 13 14 15 16 17 18 19 20 21 22 23 24 25 Diamonds: 26 27 28 29 30 31 32 33 34 35 36 37 38 Clubs: 39 40 41 42 43 44 45 46 47 48 49 50 51

How to represent a deck of playing cards inside a computer program

The 4 of spades is represented by 3 = 0×13 + 3:

Ace 2 3 4 5 6 7 8 9 10 J Q K Spades: 0 1 2 3 4 5 6 7 8 9 10 11 12 Hearts: 13 14 15 16 17 18 19 20 21 22 23 24 25 Diamonds: 26 27 28 29 30 31 32 33 34 35 36 37 38 Clubs: 39 40 41 42 43 44 45 46 47 48 49 50 51

Note: 3 / 13 = 0 (the suit) and 3 % 13 = 3 (the rank)

How to represent a deck of playing cards inside a computer program

The hearts are represented with the numbers 13 - 25:

Ace 2 3 4 5 6 7 8 9 10 J Q K Spades: 0 1 2 3 4 5 6 7 8 9 10 11 12 Hearts: 13 14 15 16 17 18 19 20 21 22 23 24 25 Diamonds: 26 27 28 29 30 31 32 33 34 35 36 37 38 Clubs: 39 40 41 42 43 44 45 46 47 48 49 50 51

How to represent a deck of playing cards inside a computer program

The 4 of hearts is represented by 16 = 1×13 + 3:

Ace 2 3 4 5 6 7 8 9 10 J Q K Spades: 0 1 2 3 4 5 6 7 8 9 10 11 12 Hearts: 13 14 15 16 17 18 19 20 21 22 23 24 25 Diamonds: 26 27 28 29 30 31 32 33 34 35 36 37 38 Clubs: 39 40 41 42 43 44 45 46 47 48 49 50 51

Note: 16 / 13 = 1 (the suit) and 16 % 13 = 3 (the rank)

How to represent a deck of playing cards inside a computer program

The diamonds are represented with the numbers 26 - 38:

Ace 2 3 4 5 6 7 8 9 10 J Q K Spades: 0 1 2 3 4 5 6 7 8 9 10 11 12 Hearts: 13 14 15 16 17 18 19 20 21 22 23 24 25 Diamonds: 26 27 28 29 30 31 32 33 34 35 36 37 38 Clubs: 39 40 41 42 43 44 45 46 47 48 49 50 51

How to represent a deck of playing cards inside a computer program

The 4 of diamonds is represented by 29 = 2×13 + 3:

Ace 2 3 4 5 6 7 8 9 10 J Q K Spades: 0 1 2 3 4 5 6 7 8 9 10 11 12 Hearts: 13 14 15 16 17 18 19 20 21 22 23 24 25 Diamonds: 26 27 28 29 30 31 32 33 34 35 36 37 38 Clubs: 39 40 41 42 43 44 45 46 47 48 49 50 51

Note: 29 / 13 = 2 (the suit) and 29 % 13 = 3 (the rank)

How to represent a deck of playing cards inside a computer program

The clubs are represented with the numbers 39 - 51:

Ace 2 3 4 5 6 7 8 9 10 J Q K Spades: 0 1 2 3 4 5 6 7 8 9 10 11 12 Hearts: 13 14 15 16 17 18 19 20 21 22 23 24 25 Diamonds: 26 27 28 29 30 31 32 33 34 35 36 37 38 Clubs: 39 40 41 42 43 44 45 46 47 48 49 50 51

How to represent a deck of playing cards inside a computer program

The 4 of clubs is represented by 42 = 3×13 + 3:

Ace 2 3 4 5 6 7 8 9 10 J Q K Spades: 0 1 2 3 4 5 6 7 8 9 10 11 12 Hearts: 13 14 15 16 17 18 19 20 21 22 23 24 25 Diamonds: 26 27 28 29 30 31 32 33 34 35 36 37 38 Clubs: 39 40 41 42 43 44 45 46 47 48 49 50 51

Note: 42 / 13 = 3 (the suit) and 42 % 13 = 3 (the rank)

Quiz: which card is represented by the number 7 ?

Suppose you are dealt the card with the number 7 - what's the card ???

Ace 2 3 4 5 6 7 8 9 10 J Q K Spades: 0 1 2 3 4 5 6 7 8 9 10 11 12 Hearts: 13 14 15 16 17 18 19 20 21 22 23 24 25 Diamonds: 26 27 28 29 30 31 32 33 34 35 36 37 38 Clubs: 39 40 41 42 43 44 45 46 47 48 49 50 51

Quiz: which card is represented by the number 7 ?

7 / 13 = 0 ≡ spades and 7 % 13 = 7 ≡ rank 8 - Answer: 8 of spades

Ace 2 3 4 5 6 7 8 9 10 J Q K Spades: 0 1 2 3 4 5 6 7 8 9 10 11 12 Hearts: 13 14 15 16 17 18 19 20 21 22 23 24 25 Diamonds: 26 27 28 29 30 31 32 33 34 35 36 37 38 Clubs: 39 40 41 42 43 44 45 46 47 48 49 50 51

Quiz: which card is represented by the number 18 ?

Suppose you are dealt the card with the number 18 - what's the card ???

Ace 2 3 4 5 6 7 8 9 10 J Q K Spades: 0 1 2 3 4 5 6 7 8 9 10 11 12 Hearts: 13 14 15 16 17 18 19 20 21 22 23 24 25 Diamonds: 26 27 28 29 30 31 32 33 34 35 36 37 38 Clubs: 39 40 41 42 43 44 45 46 47 48 49 50 51

Quiz: which card is represented by the number 18 ?

18 / 13 = 1 ≡ hearts and 18 % 13 = 5 ≡ rank 6 - Answer: 6 of hearts

Ace 2 3 4 5 6 7 8 9 10 J Q K Spades: 0 1 2 3 4 5 6 7 8 9 10 11 12 Hearts: 13 14 15 16 17 18 19 20 21 22 23 24 25 Diamonds: 26 27 28 29 30 31 32 33 34 35 36 37 38 Clubs: 39 40 41 42 43 44 45 46 47 48 49 50 51

Method to interprete a card number in Java

The following method will translate a card number to English:

public static String num2Card( int n ) { /* -------------------------------------------------- Help arrays to translate the card code (0 - 51) to their English names -------------------------------------------------- */ String[] suits = {"Spades", "Hearts", "Diamonds", "Clubs"}; String[] ranks = {"Ace", "2", "3", "4", "5", "6", "7", "8", "9", "10", "Jack", "Queen", "King"}; int cardSuit = n / 13; // 0 => Spades, 1 => Hearts, etc int cardRank = n % 13; // 0 => Ace, 1 => 2, 2 => 3, etc return ranks[cardRank] + " of " + suits[cardSuit]; }

DEMO: demo/08-array/05-deck-of-card/Num2Card.java

How a computer program can simulate a card game

To represent a deck of cards, we use an array of 52 elements containing the number codes 0, 1, ..., 51 which represent all the cards in a deck:

public static void main(String[] args) { int[] deck = new int[52]; // Represents a deck of cards for ( int i = 0; i < deck.length; i++ ) deck[i] = i; // Card codes: 0, 1, 2, ...., 51 // Shuffle the deck of cards for (int i = 0; i < deck.length; i++) { // Generate an index randomly int j = (int)(Math.random() * deck.length); int temp = deck[i]; deck[i] = deck[j]; deck[j] = temp; } // Deal 4 cards for ( int i = 0; i < 4; i++ ) System.out.println( num2Card(deck[i]) ); }

How a computer program can simulate a card game

To simulate the shuffling of the deck we use the random shuffle code that we have studied before:

public static void main(String[] args) { int[] deck = new int[52]; // Represents a deck of cards for ( int i = 0; i < deck.length; i++ ) deck[i] = i; // Card codes: 0, 1, 2, ...., 51 // Randomly shuffle the deck of cards for (int i = 0; i < deck.length; i++) { // Generate an index randomly int j = (int)(Math.random() * deck.length); int temp = deck[i]; // Swap deck[i] = deck[j]; deck[j] = temp; } // Deal 4 cards for ( int i = 0; i < 4; i++ ) System.out.println( num2Card(deck[i]) ); }

How a computer program can simulate a card game

These are the first 4 cards of the shuffled deck:

public static void main(String[] args) { int[] deck = new int[52]; for ( int i = 0; i < deck.length; i++ ) deck[i] = i; // 0, 1, 2, ...., 51 // Randomly shuffle the deck of cards for (int i = 0; i < deck.length; i++) { // Generate an index randomly int j = (int)(Math.random() * deck.length); int temp = deck[i]; // Swap deck[i] = deck[j]; deck[j] = temp; } // "Deal" 4 cards for ( int i = 0; i < 4; i++ ) System.out.println( num2Card(deck[i]) ); }

DEMO: demo/08-array/05-deck-of-card/DealCard.java