change (#60)

Author: glennj

config.json

@@ -462,6 +462,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 5
+      },
+      {
+        "slug": "change",
+        "name": "Change",
+        "uuid": "756a79f1-6149-4eef-a365-e3cfcaf9c999",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 6
       }
     ]
   },

exercises/practice/change/.busted

@@ -0,0 +1,5 @@
+return {
+  default = {
+    ROOT = { '.' }
+  }
+}

exercises/practice/change/.docs/instructions.md

@@ -0,0 +1,8 @@
+# Instructions
+
+Determine the fewest number of coins to give a customer so that the sum of their values equals the correct amount of change.
+
+## Examples
+
+- An amount of 15 with available coin values [1, 5, 10, 25, 100] should return one coin of value 5 and one coin of value 10, or [5, 10].
+- An amount of 40 with available coin values [1, 5, 10, 25, 100] should return one coin of value 5, one coin of value 10, and one coin of value 25, or [5, 10, 25].

exercises/practice/change/.docs/introduction.md

@@ -0,0 +1,26 @@
+# Introduction
+
+In the mystical village of Coinholt, you stand behind the counter of your bakery, arranging a fresh batch of pastries.
+The door creaks open, and in walks Denara, a skilled merchant with a keen eye for quality goods.
+After a quick meal, she slides a shimmering coin across the counter, representing a value of 100 units.
+
+You smile, taking the coin, and glance at the total cost of the meal: 88 units.
+That means you need to return 12 units in change.
+
+Denara holds out her hand expectantly.
+"Just give me the fewest coins," she says with a smile.
+"My pouch is already full, and I don't want to risk losing them on the road."
+
+You know you have a few options.
+"We have Lumis (worth 10 units), Viras (worth 5 units), and Zenth (worth 2 units) available for change."
+
+You quickly calculate the possibilities in your head:
+
+- one Lumis (1 × 10 units) + one Zenth (1 × 2 units) = 2 coins total
+- two Viras (2 × 5 units) + one Zenth (1 × 2 units) = 3 coins total
+- six Zenth (6 × 2 units) = 6 coins total
+
+"The best choice is two coins: one Lumis and one Zenth," you say, handing her the change.
+
+Denara smiles, clearly impressed.
+"As always, you've got it right."

exercises/practice/change/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "glennj"
+  ],
+  "files": {
+    "solution": [
+      "change.moon"
+    ],
+    "test": [
+      "change_spec.moon"
+    ],
+    "example": [
+      ".meta/example.moon"
+    ]
+  },
+  "blurb": "Correctly determine change to be given using the least number of coins.",
+  "source": "Software Craftsmanship - Coin Change Kata",
+  "source_url": "https://web.archive.org/web/20130115115225/http://craftsmanship.sv.cmu.edu:80/exercises/coin-change-kata"
+}

exercises/practice/change/.meta/example.moon

@@ -0,0 +1,51 @@
+-- Change making algorithm from
+-- http://www.ccs.neu.edu/home/jaa/CSG713.04F/Information/Handouts/dyn_prog.pdf
+
+-- This function generates two arrays:
+--
+-- C = maps the minimum number of coins required to make
+--     change for each n from 1 to amount.
+--     It is returned but only used internally in this
+--     application.
+--
+-- S = the _first_ coin used to make change for amount n
+--     (actually stores the coin _index_ into the
+--     denominations array)
+--
+change = (amount, denominations) ->
+  C = {[0]: 0}
+  S = {}
+
+  for p = 1, amount
+    min = math.maxinteger
+    coin_idx = nil
+
+    for i = 1, #denominations
+      if denominations[i] <= p
+        if C[p - denominations[i]] < min
+          min = 1 + C[p - denominations[i]]
+          coin_idx = i
+
+    C[p] = min
+    S[p] = coin_idx
+
+  C, S
+
+
+change_maker = (S, d, n) ->
+  result = {}
+  while n > 0
+    coin = d[S[n]]
+    assert coin, "can't make target with given coins"
+
+    table.insert result, 1, coin
+    n -= coin
+  result
+  
+
+{
+  make_change: (amount, coins) ->
+    assert amount >= 0, "target can't be negative"
+    _, first_coin = change amount, coins
+    change_maker first_coin, coins, amount
+}

exercises/practice/change/.meta/spec_generator.moon

@@ -0,0 +1,20 @@
+int_list = (list) -> "{#{table.concat list, ', '}}"
+
+{
+  module_imports: {'make_change'},
+
+  generate_test: (case, level) ->
+    local lines
+    if case.expected.error
+      lines = {
+        "f = -> make_change #{case.input.target}, #{int_list case.input.coins}",
+        "assert.has.error f, #{quote case.expected.error}"
+      }
+    else
+      lines = {
+        "result = make_change #{case.input.target}, #{int_list case.input.coins}",
+        "expected = #{int_list case.expected}",
+        "assert.are.same expected, result"
+      }
+    table.concat [indent line, level for line in *lines], '\n'
+}

exercises/practice/change/.meta/tests.toml

@@ -0,0 +1,49 @@
+# 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.
+
+[d0ebd0e1-9d27-4609-a654-df5c0ba1d83a]
+description = "change for 1 cent"
+
+[36887bea-7f92-4a9c-b0cc-c0e886b3ecc8]
+description = "single coin change"
+
+[cef21ccc-0811-4e6e-af44-f011e7eab6c6]
+description = "multiple coin change"
+
+[d60952bc-0c1a-4571-bf0c-41be72690cb3]
+description = "change with Lilliputian Coins"
+
+[408390b9-fafa-4bb9-b608-ffe6036edb6c]
+description = "change with Lower Elbonia Coins"
+
+[7421a4cb-1c48-4bf9-99c7-7f049689132f]
+description = "large target values"
+
+[f79d2e9b-0ae3-4d6a-bb58-dc978b0dba28]
+description = "possible change without unit coins available"
+
+[9a166411-d35d-4f7f-a007-6724ac266178]
+description = "another possible change without unit coins available"
+
+[ce0f80d5-51c3-469d-818c-3e69dbd25f75]
+description = "a greedy approach is not optimal"
+
+[bbbcc154-e9e9-4209-a4db-dd6d81ec26bb]
+description = "no coins make 0 change"
+
+[c8b81d5a-49bd-4b61-af73-8ee5383a2ce1]
+description = "error testing for change smaller than the smallest of coins"
+
+[3c43e3e4-63f9-46ac-9476-a67516e98f68]
+description = "error if no combination can add up to target"
+
+[8fe1f076-9b2d-4f44-89fe-8a6ccd63c8f3]
+description = "cannot find negative change values"

exercises/practice/change/change.moon

@@ -0,0 +1,4 @@
+{
+  make_change: (target_amount, denominations) ->
+    error 'Implement me'
+}

exercises/practice/change/change_spec.moon

@@ -0,0 +1,64 @@
+import make_change from require 'change'
+
+describe 'change', ->
+  it 'change for 1 cent', ->
+    result = make_change 1, {1, 5, 10, 25}
+    expected = {1}
+    assert.are.same expected, result
+
+  pending 'single coin change', ->
+    result = make_change 25, {1, 5, 10, 25, 100}
+    expected = {25}
+    assert.are.same expected, result
+
+  pending 'multiple coin change', ->
+    result = make_change 15, {1, 5, 10, 25, 100}
+    expected = {5, 10}
+    assert.are.same expected, result
+
+  pending 'change with Lilliputian Coins', ->
+    result = make_change 23, {1, 4, 15, 20, 50}
+    expected = {4, 4, 15}
+    assert.are.same expected, result
+
+  pending 'change with Lower Elbonia Coins', ->
+    result = make_change 63, {1, 5, 10, 21, 25}
+    expected = {21, 21, 21}
+    assert.are.same expected, result
+
+  pending 'large target values', ->
+    result = make_change 999, {1, 2, 5, 10, 20, 50, 100}
+    expected = {2, 2, 5, 20, 20, 50, 100, 100, 100, 100, 100, 100, 100, 100, 100}
+    assert.are.same expected, result
+
+  pending 'possible change without unit coins available', ->
+    result = make_change 21, {2, 5, 10, 20, 50}
+    expected = {2, 2, 2, 5, 10}
+    assert.are.same expected, result
+
+  pending 'another possible change without unit coins available', ->
+    result = make_change 27, {4, 5}
+    expected = {4, 4, 4, 5, 5, 5}
+    assert.are.same expected, result
+
+  pending 'a greedy approach is not optimal', ->
+    result = make_change 20, {1, 10, 11}
+    expected = {10, 10}
+    assert.are.same expected, result
+
+  pending 'no coins make 0 change', ->
+    result = make_change 0, {1, 5, 10, 21, 25}
+    expected = {}
+    assert.are.same expected, result
+
+  pending 'error testing for change smaller than the smallest of coins', ->
+    f = -> make_change 3, {5, 10}
+    assert.has.error f, "can't make target with given coins"
+
+  pending 'error if no combination can add up to target', ->
+    f = -> make_change 94, {5, 10}
+    assert.has.error f, "can't make target with given coins"
+
+  pending 'cannot find negative change values', ->
+    f = -> make_change -5, {1, 2, 5}
+    assert.has.error f, "target can't be negative"