Add book-store exercise (exercism#106)

Author: keiravillekode

config.json

@@ -539,6 +539,14 @@
         "prerequisites": [],
         "difficulty": 6
       },
+      {
+        "slug": "book-store",
+        "name": "Book Store",
+        "uuid": "b98c9123-8c26-455f-9b1f-787fb61b5be0",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 7
+      },
       {
         "slug": "change",
         "name": "Change",

exercises/practice/book-store/.docs/instructions.append.md

@@ -0,0 +1,10 @@
+# Instructions append
+
+## Subtypes
+
+This exercise defines a Subtype called `Book`, for natural numbers 1 through 5.
+A Subtype can be thought of as a pair `⟨x, h⟩`, where x is the value and h is the proof of its validity.
+
+The value inside a Subtype (x, in this case) can be accessed by using .val, for example, `x.val`.
+Its proof can be accessed by using .property, for example, `x.property`.
+Both can also be accessed by pattern matching, as usual.

exercises/practice/book-store/.docs/instructions.md

@@ -0,0 +1,61 @@
+# Instructions
+
+To try and encourage more sales of different books from a popular 5 book series, a bookshop has decided to offer discounts on multiple book purchases.
+
+One copy of any of the five books costs $8.
+
+If, however, you buy two different books, you get a 5% discount on those two books.
+
+If you buy 3 different books, you get a 10% discount.
+
+If you buy 4 different books, you get a 20% discount.
+
+If you buy all 5, you get a 25% discount.
+
+Note that if you buy four books, of which 3 are different titles, you get a 10% discount on the 3 that form part of a set, but the fourth book still costs $8.
+
+Your mission is to write code to calculate the price of any conceivable shopping basket (containing only books of the same series), giving as big a discount as possible.
+
+For example, how much does this basket of books cost?
+
+- 2 copies of the first book
+- 2 copies of the second book
+- 2 copies of the third book
+- 1 copy of the fourth book
+- 1 copy of the fifth book
+
+One way of grouping these 8 books is:
+
+- 1 group of 5 (1st, 2nd,3rd, 4th, 5th)
+- 1 group of 3 (1st, 2nd, 3rd)
+
+This would give a total of:
+
+- 5 books at a 25% discount
+- 3 books at a 10% discount
+
+Resulting in:
+
+- 5 × (100% - 25%) × $8 = 5 × $6.00 = $30.00, plus
+- 3 × (100% - 10%) × $8 = 3 × $7.20 = $21.60
+
+Which equals $51.60.
+
+However, a different way to group these 8 books is:
+
+- 1 group of 4 books (1st, 2nd, 3rd, 4th)
+- 1 group of 4 books (1st, 2nd, 3rd, 5th)
+
+This would give a total of:
+
+- 4 books at a 20% discount
+- 4 books at a 20% discount
+
+Resulting in:
+
+- 4 × (100% - 20%) × $8 = 4 × $6.40 = $25.60, plus
+- 4 × (100% - 20%) × $8 = 4 × $6.40 = $25.60
+
+Which equals $51.20.
+
+And $51.20 is the price with the biggest discount.

exercises/practice/book-store/.meta/Example.lean

@@ -0,0 +1,45 @@
+namespace BookStore
+
+def Book := { x : Nat // x ≥ 1 ∧ x ≤ 5 }
+
+def tally (basket : List Book) : Array Nat := Id.run do
+  let mut result := Array.replicate 6 (0 : Nat)
+  for book in basket do
+    result := result.set! book.val (result[book.val]! + 1)
+  result
+
+def sort (array : Array Nat) : Array Nat :=
+  Array.qsort array (fun a b => a < b)
+
+def difference (array : Array Nat) : Array Nat := Id.run do
+  let mut result := Array.replicate 6 array[5]!
+  result := result.set! 0 0
+  for i in [1:6] do
+    result := result.set! (6 - i) (array[i]! - array[i - 1]!)
+  result
+
+def adjust (array : Array Nat) : Array Nat := Id.run do
+  let mut result := array.set! 0 0
+  let adjustment := min array[3]! array[5]!
+  result := result.set! 3 (array[3]! - adjustment)
+  result := result.set! 4 (array[4]! + 2 * adjustment)
+  result := result.set! 5 (array[5]! - adjustment)
+  result
+
+def price (array : Array Nat) : Nat :=
+  let one := array[1]!
+  let two := array[2]!
+  let three := array[3]!
+  let four := array[4]!
+  let five := array[5]!
+  800 * one + 1520 * two + 2160 * three + 2560 * four + 3000 * five
+
+def total (basket : List Book) : Nat :=
+  basket
+  |> tally
+  |> sort
+  |> difference
+  |> adjust
+  |> price
+
+end BookStore

exercises/practice/book-store/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "BookStore.lean"
+    ],
+    "test": [
+      "BookStoreTest.lean"
+    ],
+    "example": [
+      ".meta/Example.lean"
+    ]
+  },
+  "blurb": "To try and encourage more sales of different books from a popular 5 book series, a bookshop has decided to offer discounts of multiple-book purchases.",
+  "source": "Inspired by the harry potter kata from Cyber-Dojo.",
+  "source_url": "https://cyber-dojo.org/creator/home"
+}

exercises/practice/book-store/.meta/tests.toml

@@ -0,0 +1,64 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[17146bd5-2e80-4557-ab4c-05632b6b0d01]
+description = "Only a single book"
+
+[cc2de9ac-ff2a-4efd-b7c7-bfe0f43271ce]
+description = "Two of the same book"
+
+[5a86eac0-45d2-46aa-bbf0-266b94393a1a]
+description = "Empty basket"
+
+[158bd19a-3db4-4468-ae85-e0638a688990]
+description = "Two different books"
+
+[f3833f6b-9332-4a1f-ad98-6c3f8e30e163]
+description = "Three different books"
+
+[1951a1db-2fb6-4cd1-a69a-f691b6dd30a2]
+description = "Four different books"
+
+[d70f6682-3019-4c3f-aede-83c6a8c647a3]
+description = "Five different books"
+
+[78cacb57-911a-45f1-be52-2a5bd428c634]
+description = "Two groups of four is cheaper than group of five plus group of three"
+
+[f808b5a4-e01f-4c0d-881f-f7b90d9739da]
+description = "Two groups of four is cheaper than groups of five and three"
+
+[fe96401c-5268-4be2-9d9e-19b76478007c]
+description = "Group of four plus group of two is cheaper than two groups of three"
+
+[68ea9b78-10ad-420e-a766-836a501d3633]
+description = "Two each of first four books and one copy each of rest"
+
+[c0a779d5-a40c-47ae-9828-a340e936b866]
+description = "Two copies of each book"
+
+[18fd86fe-08f1-4b68-969b-392b8af20513]
+description = "Three copies of first book and two each of remaining"
+
+[0b19a24d-e4cf-4ec8-9db2-8899a41af0da]
+description = "Three each of first two books and two each of remaining books"
+
+[bb376344-4fb2-49ab-ab85-e38d8354a58d]
+description = "Four groups of four are cheaper than two groups each of five and three"
+
+[5260ddde-2703-4915-b45a-e54dbbac4303]
+description = "Check that groups of four are created properly even when there are more groups of three than groups of five"
+
+[b0478278-c551-4747-b0fc-7e0be3158b1f]
+description = "One group of one and four is cheaper than one group of two and three"
+
+[cf868453-6484-4ae1-9dfc-f8ee85bbde01]
+description = "One group of one and two plus three groups of four is cheaper than one group of each size"

exercises/practice/book-store/BookStore.lean

@@ -0,0 +1,8 @@
+namespace BookStore
+
+def Book := { x : Nat // x ≥ 1 ∧ x ≤ 5 }
+
+def total (basket : List Book) : Nat :=
+  sorry
+
+end BookStore