Perfect numbers exercise

config.json

@@ -614,6 +614,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 3
+      },
+      {
+        "slug": "perfect-numbers",
+        "name": "Perfect Numbers",
+        "uuid": "d7d076c6-8ed4-4dcd-ae15-199dc4b28cf7",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4
       }
     ]
   },

exercises/practice/perfect-numbers/.docs/instructions.md

@@ -0,0 +1,39 @@
+# Instructions
+
+Determine if a number is perfect, abundant, or deficient based on Nicomachus' (60 - 120 CE) classification scheme for positive integers.
+
+The Greek mathematician [Nicomachus][nicomachus] devised a classification scheme for positive integers, identifying each as belonging uniquely to the categories of [perfect](#perfect), [abundant](#abundant), or [deficient](#deficient) based on their [aliquot sum][aliquot-sum].
+The _aliquot sum_ is defined as the sum of the factors of a number not including the number itself.
+For example, the aliquot sum of `15` is `1 + 3 + 5 = 9`.
+
+## Perfect
+
+A number is perfect when it equals its aliquot sum.
+For example:
+
+- `6` is a perfect number because `1 + 2 + 3 = 6`
+- `28` is a perfect number because `1 + 2 + 4 + 7 + 14 = 28`
+
+## Abundant
+
+A number is abundant when it is less than its aliquot sum.
+For example:
+
+- `12` is an abundant number because `1 + 2 + 3 + 4 + 6 = 16`
+- `24` is an abundant number because `1 + 2 + 3 + 4 + 6 + 8 + 12 = 36`
+
+## Deficient
+
+A number is deficient when it is greater than its aliquot sum.
+For example:
+
+- `8` is a deficient number because `1 + 2 + 4 = 7`
+- Prime numbers are deficient
+
+## Task
+
+Implement a way to determine whether a given number is [perfect](#perfect).
+Depending on your language track, you may also need to implement a way to determine whether a given number is [abundant](#abundant) or [deficient](#deficient).
+
+[nicomachus]: https://en.wikipedia.org/wiki/Nicomachus
+[aliquot-sum]: https://en.wikipedia.org/wiki/Aliquot_sum

exercises/practice/perfect-numbers/.meta/config.json

@@ -0,0 +1,20 @@
+{
+  "authors": ["therealowenrees"],
+  "files": {
+    "solution": [
+      "perfect_numbers.ml"
+    ],
+    "test": [
+      "test.ml"
+    ],
+    "example": [
+      ".meta/example.ml"
+    ],
+    "editor": [
+      "perfect_numbers.mli"
+    ]
+  },
+  "blurb": "Determine if a number is perfect, abundant, or deficient based on Nicomachus' (60 - 120 CE) classification scheme for positive integers.",
+  "source": "Taken from Chapter 2 of Functional Thinking by Neal Ford.",
+  "source_url": "https://www.oreilly.com/library/view/functional-thinking/9781449365509/"
+}

exercises/practice/perfect-numbers/.meta/example.ml

@@ -0,0 +1,21 @@
+let classify n = 
+  let aliquot = function
+    | 1 -> 0
+    | n when n > 1 ->
+        let rec sum_factors acc factor =
+          if factor > n / 2 then acc
+          else if n mod factor = 0 then
+            sum_factors (acc + factor) (factor + 1)
+          else
+            sum_factors acc (factor + 1)
+        in
+        sum_factors 0 1
+    | _ -> 0 
+  in
+  match n with
+  | _ when n < 1 -> Error "Classification is only possible for positive integers."
+  | n -> 
+      let aliquot_sum = aliquot n in
+      if aliquot_sum = n then Ok "perfect"
+      else if aliquot_sum > n then Ok "abundant"
+      else Ok "deficient"

exercises/practice/perfect-numbers/.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.
+
+[163e8e86-7bfd-4ee2-bd68-d083dc3381a3]
+description = "Perfect numbers -> Smallest perfect number is classified correctly"
+
+[169a7854-0431-4ae0-9815-c3b6d967436d]
+description = "Perfect numbers -> Medium perfect number is classified correctly"
+
+[ee3627c4-7b36-4245-ba7c-8727d585f402]
+description = "Perfect numbers -> Large perfect number is classified correctly"
+
+[80ef7cf8-9ea8-49b9-8b2d-d9cb3db3ed7e]
+description = "Abundant numbers -> Smallest abundant number is classified correctly"
+
+[3e300e0d-1a12-4f11-8c48-d1027165ab60]
+description = "Abundant numbers -> Medium abundant number is classified correctly"
+
+[ec7792e6-8786-449c-b005-ce6dd89a772b]
+description = "Abundant numbers -> Large abundant number is classified correctly"
+
+[e610fdc7-2b6e-43c3-a51c-b70fb37413ba]
+description = "Deficient numbers -> Smallest prime deficient number is classified correctly"
+
+[0beb7f66-753a-443f-8075-ad7fbd9018f3]
+description = "Deficient numbers -> Smallest non-prime deficient number is classified correctly"
+
+[1c802e45-b4c6-4962-93d7-1cad245821ef]
+description = "Deficient numbers -> Medium deficient number is classified correctly"
+
+[47dd569f-9e5a-4a11-9a47-a4e91c8c28aa]
+description = "Deficient numbers -> Large deficient number is classified correctly"
+
+[a696dec8-6147-4d68-afad-d38de5476a56]
+description = "Deficient numbers -> Edge case (no factors other than itself) is classified correctly"
+
+[72445cee-660c-4d75-8506-6c40089dc302]
+description = "Invalid inputs -> Zero is rejected (as it is not a positive integer)"
+
+[2d72ce2c-6802-49ac-8ece-c790ba3dae13]
+description = "Invalid inputs -> Negative integer is rejected (as it is not a positive integer)"

exercises/practice/perfect-numbers/Makefile

@@ -0,0 +1,9 @@
+default: clean test
+
+test: 
+	dune runtest
+
+clean:
+	dune clean
+
+.PHONY: clean

exercises/practice/perfect-numbers/dune

@@ -0,0 +1,16 @@
+(executable
+ (name test)
+ (libraries base ounit2))
+
+(alias
+  (name    runtest)
+  (deps    (:x test.exe))
+  (action  (run %{x})))
+
+(alias
+  (name    buildtest)
+  (deps    (:x test.exe)))
+
+(env
+  (dev
+    (flags (:standard -warn-error -A))))

exercises/practice/perfect-numbers/dune-project

@@ -0,0 +1 @@
+(lang dune 1.1)

exercises/practice/perfect-numbers/perfect_numbers.ml

@@ -0,0 +1,2 @@
+let classify _ = 
+  failwith "'classify' is missing"

exercises/practice/perfect-numbers/perfect_numbers.mli

@@ -0,0 +1 @@
+val classify : int -> (string, string) result

exercises/practice/perfect-numbers/test.ml

@@ -0,0 +1,40 @@
+open OUnit2
+open Perfect_numbers
+
+let option_printer = function
+  | Error m  -> Printf.sprintf "Error \"%s\"" m
+  | Ok m -> Printf.sprintf "Ok \"%s\"" m
+
+let ae exp got _test_ctxt = assert_equal ~printer:option_printer exp got
+
+let tests = [
+  "Smallest perfect number is classified correctly" >::
+  ae (Ok "perfect") (classify (6));
+  "Medium perfect number is classified correctly" >::
+  ae (Ok "perfect") (classify (28));
+  "Large perfect number is classified correctly" >::
+  ae (Ok "perfect") (classify (33550336));
+  "Smallest abundant number is classified correctly" >::
+  ae (Ok "abundant") (classify (12));
+  "Medium abundant number is classified correctly" >::
+  ae (Ok "abundant") (classify (30));
+  "Large abundant number is classified correctly" >::
+  ae (Ok "abundant") (classify (33550335));
+  "Smallest prime deficient number is classified correctly" >::
+  ae (Ok "deficient") (classify (2));
+  "Smallest non-prime deficient number is classified correctly" >::
+  ae (Ok "deficient") (classify (4));
+  "Medium deficient number is classified correctly" >::
+  ae (Ok "deficient") (classify (32));
+  "Large deficient number is classified correctly" >::
+  ae (Ok "deficient") (classify (33550337));
+  "Edge case (no factors other than itself) is classified correctly" >::
+  ae (Ok "deficient") (classify (1));
+  "Zero is rejected (as it is not a positive integer)" >::
+  ae (Error "Classification is only possible for positive integers.") (classify (0));
+  "Negative integer is rejected (as it is not a positive integer)" >::
+  ae (Error "Classification is only possible for positive integers.") (classify (-1));
+]
+
+let () =
+  run_test_tt_main ("perfect-numbers tests" >::: tests)

templates/perfect-numbers/dune-project.tpl

@@ -0,0 +1 @@
+(lang dune 1.1)

templates/perfect-numbers/test.ml.tpl

@@ -0,0 +1,20 @@
+open OUnit2
+open Perfect_numbers
+
+let option_printer = function
+  | Error m  -> Printf.sprintf "Error \"%s\"" m
+  | Ok m -> Printf.sprintf "Ok \"%s\"" m
+
+let ae exp got _test_ctxt = assert_equal ~printer:option_printer exp got
+
+let tests = [
+  {{#cases}}
+    {{#cases}}
+      "{{description}}" >::
+        ae {{#input}}{{{expected}}} (classify ({{number}})){{/input}};
+    {{/cases}}
+  {{/cases}}
+]
+
+let () =
+  run_test_tt_main ("perfect-numbers tests" >::: tests)

test-generator/lib_generator/special_cases.ml

@@ -325,6 +325,13 @@ let edit_collatz_conjecture_expected = function
   | `Assoc [("error", `String m)] -> "(Error \"" ^ m ^ "\")"
   | x -> Yojson.Basic.to_string x
 
+let edit_perfect_numbers (ps: (string * json) list): (string * string) list =
+  let edit = function
+    | ("expected", `Assoc [("error", v)]) -> ("expected", "(Error " ^ json_to_string v ^ ")")
+    | ("expected", `String s) -> ("expected", "(Ok \"" ^ s ^ "\")")
+    | (k, v) -> (k, json_to_string v) in
+  List.map ps ~f:edit
+
 let unwrap_strings (ps: (string * json) list): (string * string) list option =
   let edit = function
     | (_, `String s) -> ("params", s)
@@ -348,6 +355,7 @@ let edit_parameters ~(slug: string) (parameters: (string * json) list) = match (
   | ("knapsack", ps) -> edit_knapsack ps |> Option.return
   | ("minesweeper", ps) -> edit_minesweeper ps |> Option.return
   | ("palindrome-products", ps) -> edit_palindrome_products ps |> Option.return
+  | ("perfect-numbers", ps) -> edit_perfect_numbers ps |> Option.return 
   | ("phone-number", ps) -> edit_expected ~f:edit_phone_number_expected ps |> Option.return
   | ("rectangles", ps) -> edit_rectangles ps |> Option.return
   | ("say", ps) -> edit_say ps |> Option.return