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Gotta Snatch'Em All
Gotta Snatch'Em All

Gotta Snatch'Em All

Learning Exercise

Introduction

Set

A Set a is a sequence of unique values of type a. The values have to be of the comparable type (Int, Float, Time, Char, String, and tuples or lists of comparable types).

You can transform lists and sets into each other with Set.toList and Set.fromList. Because of the internal structure of Set, it is guaranteed that a list obtained from Set.fromList will be sorted.

Set.fromList [2, 3, 3, 3, 1, 1, 2]
    --> Set.fromList [1, 2, 3]

Set.toList (Set.fromList [2, 3, 3, 3, 1, 1, 2])
    --> [1, 2, 3]

You can create and populate sets with Set.empty, Set.singleton, Set.insert and Set.remove.

Set.empty
    --> Set.fromList []

Set.singleton "hi"
    --> Set.fromList ["hi"]

eightyEight = Set.singleton 88

Set.insert 88 eightyEight
    --> Set.fromList [88]

Set.insert 89 eightyEight
    --> Set.fromList [88, 89]

Set.remove 88 eightyEight
    --> Set.fromList []

Set.remove 89 eightyEight
    --> Set.fromList [88]

You can query the contents of a set with the functions Set.member, Set.isEmpty and Set.size.

Set.member 88 eightyEight
    --> True

Set.isEmpty eightyEight
    --> False

Set.size eightyEight
    --> 1

Set can be combined with Set.union, Set.intersect and Set.diff.

a = Set.fromList [1, 10, 100]
b = Set.fromList [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

Set.union a b
    --> Set.fromList [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100]

Set.intersect a b
    --> Set.fromList [1, 10]

Set.diff a b
    --> Set.fromList [100]

Set.diff b a
    --> Set.fromList [2, 3, 4, 5, 6, 7, 8, 9]

You can filter and partition sets.

even n = modBy 2 n == 0

Set.filter even b
    --> Set.fromList [2, 4, 6, 8, 10]

Set.partition even b
    --> (Set.fromList [2, 4, 6, 8, 10], Set.fromList [1, 3, 5, 7, 9])

Instructions

Your nostalgia for Blorkemon™️ cards is showing no sign of slowing down, you even started collecting them again, and you are getting your friends to join you.

In this exercise, a Card collection is represented by Set Card, since duplicate cards are not important when your goal is to get all existing cards.

1. Start a collection

You really want your friends to join your Blorkemon™️ madness, and the best way is to kickstart their collection by giving them one card.

Implement newCollection, which transforms a card into a collection.

newCollection "Newthree"
    --> Set.fromList ["Newthree"]

2. Grow the collection

Once you have a collection, it takes a life of its owm and must grow.

Implement addCard, which takes a Card and a collection, and returns a Tuple with two values: a Bool that indicates if the Card was already in the collection, and the collection with the card added.

addCard "Scientuna" (Set.fromList ["Newthree"])
    --> (False, Set.fromList ["Newthree", "Scientuna"])

3. Start trading

Now that your friends are Blorkemon™️ crazy again, you can use this to grow your own collection by trading cards.

Not every trade is worth doing, or can be done at all. You cannot trade a card you don't have, and you shouldn't trade a card for one that you already have.

Implement tradeCard, that takes two cards to trade (yours and theirs) and your current collection. The return value is a Tuple of two values: a Bool stating if the trade is possible and worth doing, and the collection you would end up with if you did the trade (even if it's not actually possible).

tradeCard "Scientuna" "Newthree" (Set.fromList ["Scientuna"])
    --> (True, Set.fromList ["Newthree"])

4. There can be only one of each

You find an old stash of cards in a flea market. You must sort the cards and remove the duplicates to compare the list to your collection.

Implement removeDuplicates which will sort a list of cards and return a list of sorted, unique cards.

removeDuplicates ["Newthree", "Newthree", "Newthree", "Scientuna"]
    --> ["Newthree", "Scientuna"]

5. Cards they don't have

Time to feel good about your collection.

Implement extraCards, which takes your collection and some other collection, and returns the number of cards that the other collection doesn't have.

extraCards (Set.fromList ["Scientuna"]) (Set.fromList ["Newthree", "Scientuna"])
    --> 0

6. Cards they all have

You and your Blorkemon™️ enthusiast friends gather and wonder which cards are the most common.

Implement boringCards, which takes a list of collections and returns a list of sorted cards that all collections have.

boringCards [Set.fromList ["Scientuna"], Set.fromList ["Newthree", "Scientuna"]]
    --> ["Scientuna"]

7. All of the cards

Do you and your friends collectively own all of the Blorkemon™️ cards?

Implement totalCards, which takes a list of collections and returns the total number of different cards in the all of the collections.

totalCards [Set.fromList ["Scientuna"], Set.fromList ["Newthree", "Scientuna"]]
    --> 2

8. Shiny for the win

You nephew is coming to visit you soon, and you feel like impressing him. Kids like shiny things right? Blorkemon™️ cards can be shiny!

Implement splitShinyCards, which takes a collection and returns a Tuple with two lists of sorted cards: one with all the cards that start with "Shiny" and one with the other cards.

splitShinyCards (Set.fromList ["Newthree", "Scientuna", "Shiny Scientuna"])
    --> (["Shiny Scientuna"], ["Newthree", "Scientuna"])
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