exercises(perfect-numbers): implement (#184)

config.json

@@ -379,6 +379,24 @@
         ],
         "difficulty": 1
       },
+      {
+        "uuid": "2fbd5bd8-a839-42a3-9293-4ad577766a12",
+        "slug": "perfect-numbers",
+        "name": "Perfect Numbers",
+        "practices": [
+          "asserting",
+          "enums",
+          "integers",
+          "math"
+        ],
+        "prerequisites": [
+          "asserting",
+          "enums",
+          "integers",
+          "math"
+        ],
+        "difficulty": 1
+      },
       {
         "uuid": "866a09d8-6949-4363-b83f-7b9fefb53893",
         "slug": "two-fer",

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

@@ -0,0 +1,13 @@
+# Instructions append
+
+## Assert
+
+For this exercise, let's say that we want the caller to be responsible for calling `classify` only with a nonzero input.
+So please make the `classify` function assert that its input is nonzero.
+For more details, see the [Zig Language Reference][zig-reference] and the implementation of [`std.debug.assert`][assert].
+
+However, note that this exercise does not currently test an input of 0 (because `std.testing` does [not yet support expecting a panic][proposal]).
+
+[zig-reference]: https://ziglang.org/documentation/0.10.1/#unreachable
+[assert]: https://github.com/ziglang/zig/blob/0.10.1/lib/std/debug.zig#L267-L279
+[proposal]: https://github.com/ziglang/zig/issues/1356

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

@@ -0,0 +1,24 @@
+# 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 +1,19 @@
+{
+  "authors": [
+    "ee7"
+  ],
+  "files": {
+    "solution": [
+      "perfect_numbers.zig"
+    ],
+    "test": [
+      "test_perfect_numbers.zig"
+    ],
+    "example": [
+      ".meta/example.zig"
+    ]
+  },
+  "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.zig

@@ -0,0 +1,32 @@
+const std = @import("std");
+
+pub const Classification = enum {
+    deficient,
+    perfect,
+    abundant,
+};
+
+/// Returns the sum of the divisors of `n` (excluding `n` itself).
+/// For example, the aliquot sum of 15 is (1 + 3 + 5) = 9.
+fn aliquotSum(n: u64) u64 {
+    if (n == 1) return 0;
+    var result: u64 = 1;
+    var i: usize = 2;
+    const isqrt_n = std.math.sqrt(n);
+    while (i <= isqrt_n) : (i += 1) {
+        if (n % i == 0) result += i + (n / i);
+    }
+    // When `n` is a square number, we added the same divisor twice inside the loop.
+    if (isqrt_n * isqrt_n == n) result -= isqrt_n;
+    return result;
+}
+
+/// Returns whether `n` is less than, equal to, or greater than its aliquot sum.
+/// Asserts that `n` is nonzero.
+pub fn classify(comptime n: u64) Classification {
+    comptime std.debug.assert(n != 0);
+    const aliquot_sum = aliquotSum(n);
+    if (aliquot_sum < n) return Classification.deficient;
+    if (aliquot_sum > n) return Classification.abundant;
+    return Classification.perfect;
+}

exercises/practice/perfect-numbers/.meta/tests.toml

@@ -0,0 +1,51 @@
+# 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)"
+include = false
+
+[2d72ce2c-6802-49ac-8ece-c790ba3dae13]
+description = "Invalid inputs -> Negative integer is rejected (as it is not a positive integer)"
+include = false

exercises/practice/perfect-numbers/perfect_numbers.zig

@@ -0,0 +1,11 @@
+pub const Classification = enum {
+    deficient,
+    perfect,
+    abundant,
+};
+
+/// Asserts that `n` is nonzero.
+pub fn classify(n: u64) Classification {
+    _ = n;
+    @compileError("please implement the classify function");
+}

exercises/practice/perfect-numbers/test_perfect_numbers.zig

@@ -0,0 +1,72 @@
+const std = @import("std");
+const testing = std.testing;
+
+const perfect_numbers = @import("perfect_numbers.zig");
+const Classification = perfect_numbers.Classification;
+const classify = perfect_numbers.classify;
+
+test "smallest perfect number is classified correctly" {
+    const expected = Classification.perfect;
+    const actual = classify(6);
+    try testing.expectEqual(expected, actual);
+}
+
+test "medium perfect number is classified correctly" {
+    const expected = Classification.perfect;
+    const actual = classify(28);
+    try testing.expectEqual(expected, actual);
+}
+
+test "large perfect number is classified correctly" {
+    const expected = Classification.perfect;
+    const actual = classify(33_550_336);
+    try testing.expectEqual(expected, actual);
+}
+
+test "smallest abundant number is classified correctly" {
+    const expected = Classification.abundant;
+    const actual = classify(12);
+    try testing.expectEqual(expected, actual);
+}
+
+test "medium abundant number is classified correctly" {
+    const expected = Classification.abundant;
+    const actual = classify(30);
+    try testing.expectEqual(expected, actual);
+}
+
+test "large abundant number is classified correctly" {
+    const expected = Classification.abundant;
+    const actual = classify(33_550_335);
+    try testing.expectEqual(expected, actual);
+}
+
+test "smallest prime deficient number is classified correctly" {
+    const expected = Classification.deficient;
+    const actual = classify(2);
+    try testing.expectEqual(expected, actual);
+}
+
+test "smallest non-prime deficient number is classified correctly" {
+    const expected = Classification.deficient;
+    const actual = classify(4);
+    try testing.expectEqual(expected, actual);
+}
+
+test "medium deficient number is classified correctly" {
+    const expected = Classification.deficient;
+    const actual = classify(32);
+    try testing.expectEqual(expected, actual);
+}
+
+test "large deficient number is classified correctly" {
+    const expected = Classification.deficient;
+    const actual = classify(33_550_337);
+    try testing.expectEqual(expected, actual);
+}
+
+test "edge case (no factors other than itself) is classified correctly" {
+    const expected = Classification.deficient;
+    const actual = classify(1);
+    try testing.expectEqual(expected, actual);
+}