Add change exercise (#51)

Author: keiravillekode

config.json

@@ -335,17 +335,17 @@
         "difficulty": 5
       },
       {
-        "slug": "run-length-encoding",
-        "name": "Run-Length Encoding",
-        "uuid": "9b14d6e1-bd0e-4450-817f-e6e2c3958a3d",
+        "slug": "nth-prime",
+        "name": "Nth Prime",
+        "uuid": "fe8e3e7e-f239-40dc-8f3e-e07fa099da36",
         "practices": [],
         "prerequisites": [],
         "difficulty": 5
       },
       {
-        "slug": "nth-prime",
-        "name": "Nth Prime",
-        "uuid": "fe8e3e7e-f239-40dc-8f3e-e07fa099da36",
+        "slug": "run-length-encoding",
+        "name": "Run-Length Encoding",
+        "uuid": "9b14d6e1-bd0e-4450-817f-e6e2c3958a3d",
         "practices": [],
         "prerequisites": [],
         "difficulty": 5
@@ -365,6 +365,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 6
+      },
+      {
+        "slug": "change",
+        "name": "Change",
+        "uuid": "3aa8ad23-2691-478f-9a50-4c14ad6b753e",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 7
       }
     ]
   },

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": [
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "change.fut"
+    ],
+    "test": [
+      "test.fut"
+    ],
+    "example": [
+      ".meta/example.fut"
+    ]
+  },
+  "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.fut

@@ -0,0 +1,13 @@
+def find_fewest_coins (coins: []i32) (target: i32): []i32 =
+  let capacity = assert (target >= 0) (target + 1)
+  let (table_coins, table_counts) = loop (table_coins, table_counts) = (replicate (i64.i32 capacity) 0, replicate (i64.i32 capacity) 0) for i in 1..<capacity do
+    let (best_coin, best_count) = loop (best_coin, best_count) = (0, capacity) for coin in coins do
+      if coin > i || table_counts[i - coin] + 1 >= best_count then (best_coin, best_count) else
+      (coin, table_counts[i - coin] + 1)
+    in
+      (table_coins with [i] = best_coin, table_counts with [i] = best_count)
+  in
+    let (result, _, _) = loop (result, remaining, j) = assert (table_counts[target] < capacity) (replicate (i64.i32 table_counts[target]) 0, target, 0) while remaining > 0 do
+      (result with [j] = table_coins[remaining], remaining - table_coins[remaining], j + 1)
+    in
+      result 

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.fut

@@ -0,0 +1 @@
+def find_fewest_coins (coins: []i32) (target: i32): []i32 = ???

exercises/practice/change/test.fut

@@ -0,0 +1,69 @@
+import "change"
+
+-- change for 1 cent
+-- ==
+-- input { [1, 5, 10, 25] 1 }
+-- output { [1] }
+
+-- single coin change
+-- ==
+-- input { [1, 5, 10, 25, 100] 25 }
+-- output { [25] }
+
+-- multiple coin change
+-- ==
+-- input { [1, 5, 10, 25, 100] 15 }
+-- output { [5, 10] }
+
+-- change with Lilliputian Coins
+-- ==
+-- input { [1, 4, 15, 20, 50] 23 }
+-- output { [4, 4, 15] }
+
+-- change with Lower Elbonia Coins
+-- ==
+-- input { [1, 5, 10, 21, 25] 63 }
+-- output { [21, 21, 21] }
+
+-- large target values
+-- ==
+-- input { [1, 2, 5, 10, 20, 50, 100] 999 }
+-- output { [2, 2, 5, 20, 20, 50, 100, 100, 100, 100, 100, 100, 100, 100, 100] }
+
+-- possible change without unit coins available
+-- ==
+-- input { [2, 5, 10, 20, 50] 21 }
+-- output { [2, 2, 2, 5, 10] }
+
+-- another possible change without unit coins available
+-- ==
+-- input { [4, 5] 27 }
+-- output { [4, 4, 4, 5, 5, 5] }
+
+-- a greedy approach is not optimal
+-- ==
+-- input { [1, 10, 11] 20 }
+-- output { [10, 10] }
+
+-- no coins make 0 change
+-- ==
+-- input { [1, 5, 10, 21, 25] 0 }
+-- output { empty([0]i32) }
+
+-- error testing for change smaller than the smallest of coins
+-- ==
+-- input { [5, 10] 3 }
+-- error: Error*
+
+-- error if no combination can add up to target
+-- ==
+-- input { [5, 10] 94 }
+-- error: Error*
+
+-- cannot find negative change values
+-- ==
+-- input { [1, 2, 5] -5 }
+-- error: Error*
+
+def main (coins: []i32) (target: i32): []i32 =
+  find_fewest_coins coins target