Exercise 1

Write a definition for a type named Circle with attributes center and radius, where center is a Point object and radius is a number.

Instantiate a Circle object that represents a circle with its center at (150, 100) and radius 75.

Write a function named point_in_circle that takes a Circle and a Point and returns true if the point lies in or on the boundary of the circle.

Write a function named rect_in_circle that takes a Circle and a Rectangle and returns true if the rectangle lies entirely in or on the boundary of the circle.

Write a function named rect_circle_overlap that takes a Circle and a Rectangle and returns true if any of the corners of the rectangle fall inside the circle. Or as a more challenging version, return true if any part of the rectangle falls inside the circle.

Exercise 2

Write a function called draw_rect that takes a Turtle object and a Rectangle and uses the turtle to draw the rectangle.

Write a function called draw_circle that takes a Turtle and a Circle and draws the circle.

Exercise 3

Write a function called mul_time that takes a MyTime object and a number and returns a new MyTime object that contains the product of the original MyTime and the number.

Then use mul_time to write a function that takes a MyTime object that represents the finishing time in a race, and a number that represents the distance, and returns a MyTime object that represents the average pace (time per mile).

Exercise* 4

The Base.Dates module provides Time objects that are similar to the MyTime objects in the lecture, but they provide a rich set of methods and operators. Read the documentation at https://docs.julialang.org/en/stable/stdlib/dates/.

Use this module to write a program that gets the current date and prints the day of the week.

Write a program that takes a birthday as input and prints the user’s age and the number of days, hours, minutes and seconds until their next birthday.

For two people born on different days, there is a day when one is twice as old as the other. That’s their Double Day. Write a program that takes two birthdays and computes their Double Day.

For a little more challenge, write the more general version that computes the day when one person is n times older than the other.

Exercise 5

Change the attributes of MyTime to be a single integer representing seconds since midnight. Then modify all the methods (and the function int_to_time) to work with the new implementation.

Exercise 6

Write a definition for a type named Kangaroo with an attribute named pouch_contents of type Array and the following methods:

  • An constructor that initializes pouch_contents to an empty array.

  • A method named put_in_pouch that takes a Kangaroo object and an object of any type and adds it to pouch_contents.

  • A show method that returns a string representation of the Kangaroo object and the contents of the pouch.

Test your code by creating two Kangaroo objects, assigning them to variables named kanga and roo, and then adding roo to the contents of kanga’s pouch.

Exercise 7

For the following program, draw a type diagram that shows these types and the relationships among them.

In [3]:
abstract type PingPongParent end

struct Ping <: PingPongParent

struct Pong <: PingPongParent
    pings :: Array{Ping, 1}
    function Pong(pings=Array{Ping, 1}())

function add_ping(pong::Pong, ping::Ping)
    push!(pong.pings, ping)

pong = Pong()
ping = Ping(pong)
add_ping(pong, ping)

Exercise 8

Write a method called deal_hands that takes three parameters, a deck, the number of hands and the number of cards per hand. It should create the appropriate number of Hand objects, deal the appropriate number of cards per hand, and return an array of Hands.

Exercise* 9

The following are the possible hands in poker, in increasing order of value and decreasing order of probability:

  • pair: two cards with the same rank

  • two pair: two pairs of cards with the same rank

  • three of a kind: three cards with the same rank

  • straight: five cards with ranks in sequence (aces can be high or low, so Ace-2-3-4-5 is a straight and so is 10-Jack-Queen-King-Ace, but Queen-King-Ace-2-3 is not.)

  • flush: five cards with the same suit

  • full house: three cards with one rank, two cards with another

  • four of a kind: four cards with the same rank

  • straight flush: five cards in sequence (as defined above) and with the same suit

The goal of this exercise is to estimate the probability of drawing these various hands.

  1. Add methods named has_pair, has_twopair, etc. that return true or false according to whether or not the hand meets the relevant criteria. Your code should work correctly for “hands” that contain any number of cards (although 5 and 7 are the most common sizes).

  2. Write a method named classify that figures out the highest-value classification for a hand and sets the label attribute accordingly. For example, a 7-card hand might contain a flush and a pair; it should be labeled “flush”.

  3. When you are convinced that your classification methods are working, the next step is to estimate the probabilities of the various hands. Write a function that shuffles a deck of cards, divides it into hands, classifies the hands, and counts the number of times various classifications appear.

  4. Print a table of the classifications and their probabilities. Run your program with larger and larger numbers of hands until the output values converge to a reasonable degree of accuracy. Compare your results to the values at http://en.wikipedia.org/wiki/Hand_rankings.

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