[perfect-numbers] Implementation

config.json

@@ -715,6 +715,15 @@
         "prerequisites": [],
         "difficulty": 1,
         "topics": []
+      },
+      {
+        "slug": "perfect-numbers",
+        "name": "Perfect Numbers",
+        "uuid": "0c3e15e2-cb3c-40d3-a9e6-c50f71d9c258",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 1,
+        "topics": []
       }
     ]
   },

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

@@ -0,0 +1,23 @@
+# 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**, **abundant**, or **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**: aliquot sum = number
+  - 6 is a perfect number because (1 + 2 + 3) = 6
+  - 28 is a perfect number because (1 + 2 + 4 + 7 + 14) = 28
+- **Abundant**: aliquot sum > number
+  - 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**: aliquot sum < number
+  - 8 is a deficient number because (1 + 2 + 4) = 7
+  - Prime numbers are deficient
+
+Implement a way to determine whether a given number is **perfect**.
+Depending on your language track, you may also need to implement a way to determine whether a given number is **abundant** or **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 +1,22 @@
+{
+  "authors": [
+    "habere-et-dispertire"
+  ],
+  "contributors": [
+    "m-dango"
+  ],
+  "files": {
+    "solution": [
+      "PerfectNumbers.rakumod"
+    ],
+    "test": [
+      "perfect-numbers.rakutest"
+    ],
+    "example": [
+      ".meta/solutions/PerfectNumbers.rakumod"
+    ]
+  },
+  "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/solutions/PerfectNumbers.rakumod

@@ -0,0 +1,20 @@
+unit module PerfectNumbers;
+
+enum AliquotSumType is export (
+  :Deficient(Less),
+  :Perfect(Same),
+  :Abundant(More),
+);
+
+sub prime-factors ( $n is copy ) {
+  gather for grep *.is-prime, flat 2 .. $n.sqrt, $n
+  -> $prime {
+    take $n     and last           if    $n.is-prime;
+    take $prime and $n div= $prime while $n %% $prime
+  }
+}
+
+sub aliquot-sum-type ( Int $n where 1..*, @pf = prime-factors( $n ) --> AliquotSumType ) is export {
+  return Deficient if @pf == ();
+  AliquotSumType( @pf.combinations( 1 .. @pf.end ).unique( with => &[eqv] ).map( { [*] $_ } ).sum.succ cmp $n )
+}

exercises/practice/perfect-numbers/.meta/solutions/perfect-numbers.rakutest

@@ -0,0 +1 @@
+../../perfect-numbers.rakutest

exercises/practice/perfect-numbers/.meta/template-data.yaml

@@ -0,0 +1,53 @@
+unit: module
+
+properties:
+  classify:
+    test: |-
+      if %case<expected><error>:exists {
+        sprintf(q:to/END/, %case<input><number>, %case<description>.raku);
+        dies-ok(
+            { aliquot-sum-type(%s) },
+            %s,
+        );
+        END
+      }
+      else {
+        sprintf(q:to/END/, %case<input><number>, %case<expected>.tc, %case<description>.raku);
+        cmp-ok(
+            aliquot-sum-type(%s),
+            "eqv",
+            %s,
+            %s,
+        );
+        END
+      }
+
+example: |-
+  enum AliquotSumType is export (
+    :Deficient(Less),
+    :Perfect(Same),
+    :Abundant(More),
+  );
+
+  sub prime-factors ( $n is copy ) {
+    gather for grep *.is-prime, flat 2 .. $n.sqrt, $n
+    -> $prime {
+      take $n     and last           if    $n.is-prime;
+      take $prime and $n div= $prime while $n %% $prime
+    }
+  }
+
+  sub aliquot-sum-type ( Int $n where 1..*, @pf = prime-factors( $n ) --> AliquotSumType ) is export {
+    return Deficient if @pf == ();
+    AliquotSumType( @pf.combinations( 1 .. @pf.end ).unique( with => &[eqv] ).map( { [*] $_ } ).sum.succ cmp $n )
+  }
+
+stub: |-
+  enum AliquotSumType is export (
+      :Deficient(Less),
+      :Perfect(Same),
+      :Abundant(More),
+  );
+
+  sub aliquot-sum-type ( $n --> AliquotSumType ) is export {
+  }

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/PerfectNumbers.rakumod

@@ -0,0 +1,10 @@
+unit module PerfectNumbers;
+
+enum AliquotSumType is export (
+    :Deficient(Less),
+    :Perfect(Same),
+    :Abundant(More),
+);
+
+sub aliquot-sum-type ( $n --> AliquotSumType ) is export {
+}

exercises/practice/perfect-numbers/perfect-numbers.rakutest

@@ -0,0 +1,93 @@
+#!/usr/bin/env raku
+use Test;
+use lib $?FILE.IO.dirname;
+use PerfectNumbers;
+
+cmp-ok( # begin: 163e8e86-7bfd-4ee2-bd68-d083dc3381a3
+    aliquot-sum-type(6),
+    "eqv",
+    Perfect,
+    "Perfect numbers: Smallest perfect number is classified correctly",
+); # end: 163e8e86-7bfd-4ee2-bd68-d083dc3381a3
+
+cmp-ok( # begin: 169a7854-0431-4ae0-9815-c3b6d967436d
+    aliquot-sum-type(28),
+    "eqv",
+    Perfect,
+    "Perfect numbers: Medium perfect number is classified correctly",
+); # end: 169a7854-0431-4ae0-9815-c3b6d967436d
+
+cmp-ok( # begin: ee3627c4-7b36-4245-ba7c-8727d585f402
+    aliquot-sum-type(33550336),
+    "eqv",
+    Perfect,
+    "Perfect numbers: Large perfect number is classified correctly",
+); # end: ee3627c4-7b36-4245-ba7c-8727d585f402
+
+cmp-ok( # begin: 80ef7cf8-9ea8-49b9-8b2d-d9cb3db3ed7e
+    aliquot-sum-type(12),
+    "eqv",
+    Abundant,
+    "Abundant numbers: Smallest abundant number is classified correctly",
+); # end: 80ef7cf8-9ea8-49b9-8b2d-d9cb3db3ed7e
+
+cmp-ok( # begin: 3e300e0d-1a12-4f11-8c48-d1027165ab60
+    aliquot-sum-type(30),
+    "eqv",
+    Abundant,
+    "Abundant numbers: Medium abundant number is classified correctly",
+); # end: 3e300e0d-1a12-4f11-8c48-d1027165ab60
+
+cmp-ok( # begin: ec7792e6-8786-449c-b005-ce6dd89a772b
+    aliquot-sum-type(33550335),
+    "eqv",
+    Abundant,
+    "Abundant numbers: Large abundant number is classified correctly",
+); # end: ec7792e6-8786-449c-b005-ce6dd89a772b
+
+cmp-ok( # begin: e610fdc7-2b6e-43c3-a51c-b70fb37413ba
+    aliquot-sum-type(2),
+    "eqv",
+    Deficient,
+    "Deficient numbers: Smallest prime deficient number is classified correctly",
+); # end: e610fdc7-2b6e-43c3-a51c-b70fb37413ba
+
+cmp-ok( # begin: 0beb7f66-753a-443f-8075-ad7fbd9018f3
+    aliquot-sum-type(4),
+    "eqv",
+    Deficient,
+    "Deficient numbers: Smallest non-prime deficient number is classified correctly",
+); # end: 0beb7f66-753a-443f-8075-ad7fbd9018f3
+
+cmp-ok( # begin: 1c802e45-b4c6-4962-93d7-1cad245821ef
+    aliquot-sum-type(32),
+    "eqv",
+    Deficient,
+    "Deficient numbers: Medium deficient number is classified correctly",
+); # end: 1c802e45-b4c6-4962-93d7-1cad245821ef
+
+cmp-ok( # begin: 47dd569f-9e5a-4a11-9a47-a4e91c8c28aa
+    aliquot-sum-type(33550337),
+    "eqv",
+    Deficient,
+    "Deficient numbers: Large deficient number is classified correctly",
+); # end: 47dd569f-9e5a-4a11-9a47-a4e91c8c28aa
+
+cmp-ok( # begin: a696dec8-6147-4d68-afad-d38de5476a56
+    aliquot-sum-type(1),
+    "eqv",
+    Deficient,
+    "Deficient numbers: Edge case (no factors other than itself) is classified correctly",
+); # end: a696dec8-6147-4d68-afad-d38de5476a56
+
+dies-ok( # begin: 72445cee-660c-4d75-8506-6c40089dc302
+    { aliquot-sum-type(0) },
+    "Invalid inputs: Zero is rejected (as it is not a positive integer)",
+); # end: 72445cee-660c-4d75-8506-6c40089dc302
+
+dies-ok( # begin: 2d72ce2c-6802-49ac-8ece-c790ba3dae13
+    { aliquot-sum-type(-1) },
+    "Invalid inputs: Negative integer is rejected (as it is not a positive integer)",
+); # end: 2d72ce2c-6802-49ac-8ece-c790ba3dae13
+
+done-testing;