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TheRealOwenReeskahgoh
TheRealOwenRees
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kahgoh
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Add perfect numbers exercise (#549)
Co-authored-by: Kah Goh <[email protected]>
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‎config.json

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

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

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

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

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

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

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

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

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# This is an auto-generated file.
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#
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# Regenerating this file via `configlet sync` will:
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# - Recreate every `description` key/value pair
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# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
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# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
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# - Preserve any other key/value pair
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#
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# As user-added comments (using the # character) will be removed when this file
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# is regenerated, comments can be added via a `comment` key.
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[163e8e86-7bfd-4ee2-bd68-d083dc3381a3]
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description = "Perfect numbers -> Smallest perfect number is classified correctly"
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[169a7854-0431-4ae0-9815-c3b6d967436d]
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description = "Perfect numbers -> Medium perfect number is classified correctly"
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[ee3627c4-7b36-4245-ba7c-8727d585f402]
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description = "Perfect numbers -> Large perfect number is classified correctly"
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[80ef7cf8-9ea8-49b9-8b2d-d9cb3db3ed7e]
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description = "Abundant numbers -> Smallest abundant number is classified correctly"
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[3e300e0d-1a12-4f11-8c48-d1027165ab60]
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description = "Abundant numbers -> Medium abundant number is classified correctly"
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[ec7792e6-8786-449c-b005-ce6dd89a772b]
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description = "Abundant numbers -> Large abundant number is classified correctly"
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[e610fdc7-2b6e-43c3-a51c-b70fb37413ba]
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description = "Deficient numbers -> Smallest prime deficient number is classified correctly"
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[0beb7f66-753a-443f-8075-ad7fbd9018f3]
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description = "Deficient numbers -> Smallest non-prime deficient number is classified correctly"
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[1c802e45-b4c6-4962-93d7-1cad245821ef]
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description = "Deficient numbers -> Medium deficient number is classified correctly"
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[47dd569f-9e5a-4a11-9a47-a4e91c8c28aa]
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description = "Deficient numbers -> Large deficient number is classified correctly"
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[a696dec8-6147-4d68-afad-d38de5476a56]
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description = "Deficient numbers -> Edge case (no factors other than itself) is classified correctly"
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[72445cee-660c-4d75-8506-6c40089dc302]
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description = "Invalid inputs -> Zero is rejected (as it is not a positive integer)"
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[2d72ce2c-6802-49ac-8ece-c790ba3dae13]
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description = "Invalid inputs -> Negative integer is rejected (as it is not a positive integer)"

‎exercises/practice/perfect-numbers/Makefile

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default: clean test
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test:
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dune runtest
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clean:
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dune clean
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.PHONY: clean

‎exercises/practice/perfect-numbers/dune

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

‎exercises/practice/perfect-numbers/dune-project

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(lang dune 1.1)

‎exercises/practice/perfect-numbers/perfect_numbers.ml

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let classify _ =
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failwith "'classify' is missing"

‎exercises/practice/perfect-numbers/perfect_numbers.mli

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val classify : int -> (string, string) result

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