perfect-numbers

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Danil Negrienko 2024-07-07 20:55:46 -04:00
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{
"authors": [
"DoggettCK"
],
"contributors": [
"angelikatyborska",
"Cohen-Carlisle",
"devonestes",
"neenjaw",
"sotojuan"
],
"files": {
"solution": [
"lib/perfect_numbers.ex"
],
"test": [
"test/perfect_numbers_test.exs"
],
"example": [
".meta/example.ex"
]
},
"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/"
}

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{"track":"elixir","exercise":"perfect-numbers","id":"a3a905652d3c4b7fbe13a8ea5819052b","url":"https://exercism.org/tracks/elixir/exercises/perfect-numbers","handle":"negrienko","is_requester":true,"auto_approve":false}

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# Used by "mix format"
[
inputs: ["{mix,.formatter}.exs", "{config,lib,test}/**/*.{ex,exs}"]
]

24
elixir/perfect-numbers/.gitignore vendored Normal file
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# The directory Mix will write compiled artifacts to.
/_build/
# If you run "mix test --cover", coverage assets end up here.
/cover/
# The directory Mix downloads your dependencies sources to.
/deps/
# Where third-party dependencies like ExDoc output generated docs.
/doc/
# Ignore .fetch files in case you like to edit your project deps locally.
/.fetch
# If the VM crashes, it generates a dump, let's ignore it too.
erl_crash.dump
# Also ignore archive artifacts (built via "mix archive.build").
*.ez
# Ignore package tarball (built via "mix hex.build").
perfect_numbers-*.tar

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# Help
## Running the tests
From the terminal, change to the base directory of the exercise then execute the tests with:
```bash
$ mix test
```
This will execute the test file found in the `test` subfolder -- a file ending in `_test.exs`
Documentation:
* [`mix test` - Elixir's test execution tool](https://hexdocs.pm/mix/Mix.Tasks.Test.html)
* [`ExUnit` - Elixir's unit test library](https://hexdocs.pm/ex_unit/ExUnit.html)
## Pending tests
In test suites of practice exercises, all but the first test have been tagged to be skipped.
Once you get a test passing, you can unskip the next one by commenting out the relevant `@tag :pending` with a `#` symbol.
For example:
```elixir
# @tag :pending
test "shouting" do
assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
end
```
If you wish to run all tests at once, you can include all skipped test by using the `--include` flag on the `mix test` command:
```bash
$ mix test --include pending
```
Or, you can enable all the tests by commenting out the `ExUnit.configure` line in the file `test/test_helper.exs`.
```elixir
# ExUnit.configure(exclude: :pending, trace: true)
```
## Useful `mix test` options
* `test/<FILE>.exs:LINENUM` - runs only a single test, the test from `<FILE>.exs` whose definition is on line `LINENUM`
* `--failed` - runs only tests that failed the last time they ran
* `--max-failures` - the suite stops evaluating tests when this number of test failures
is reached
* `--seed 0` - disables randomization so the tests in a single file will always be ran
in the same order they were defined in
## Submitting your solution
You can submit your solution using the `exercism submit lib/perfect_numbers.ex` command.
This command will upload your solution to the Exercism website and print the solution page's URL.
It's possible to submit an incomplete solution which allows you to:
- See how others have completed the exercise
- Request help from a mentor
## Need to get help?
If you'd like help solving the exercise, check the following pages:
- The [Elixir track's documentation](https://exercism.org/docs/tracks/elixir)
- The [Elixir track's programming category on the forum](https://forum.exercism.org/c/programming/elixir)
- [Exercism's programming category on the forum](https://forum.exercism.org/c/programming/5)
- The [Frequently Asked Questions](https://exercism.org/docs/using/faqs)
Should those resources not suffice, you could submit your (incomplete) solution to request mentoring.
If you're stuck on something, it may help to look at some of the [available resources](https://exercism.org/docs/tracks/elixir/resources) out there where answers might be found.

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# Perfect Numbers
Welcome to Perfect Numbers on Exercism's Elixir Track.
If you need help running the tests or submitting your code, check out `HELP.md`.
## 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
## Source
### Created by
- @DoggettCK
### Contributed to by
- @angelikatyborska
- @Cohen-Carlisle
- @devonestes
- @neenjaw
- @sotojuan
### Based on
Taken from Chapter 2 of Functional Thinking by Neal Ford. - https://www.oreilly.com/library/view/functional-thinking/9781449365509/

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defmodule PerfectNumbers do
@doc """
Determine the aliquot sum of the given `number`, by summing all the factors
of `number`, aside from `number` itself.
Based on this sum, classify the number as:
:perfect if the aliquot sum is equal to `number`
:abundant if the aliquot sum is greater than `number`
:deficient if the aliquot sum is less than `number`
"""
@spec classify(number :: integer) :: {:ok, atom} | {:error, String.t()}
def classify(number) when number <= 0, do: {:error, "Classification is only possible for natural numbers."}
def classify(1), do: {:ok, :deficient}
def classify(number) do
sum =
number
|> divisors()
|> Enum.sum()
cond do
sum == number ->
{:ok, :perfect}
sum > number ->
{:ok, :abundant}
sum < number ->
{:ok, :deficient}
end
end
defp divisors(number) do
for i <- 1..round(number ** 0.5), reduce: [] do
acc -> if rem(number, i) == 0, do: [i, div(number, i) | acc], else: acc
end
|> Enum.uniq()
|> Enum.sort()
|> Enum.drop(-1)
end
end

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defmodule PerfectNumbers.MixProject do
use Mix.Project
def project do
[
app: :perfect_numbers,
version: "0.1.0",
# elixir: "~> 1.8",
start_permanent: Mix.env() == :prod,
deps: deps()
]
end
# Run "mix help compile.app" to learn about applications.
def application do
[
extra_applications: [:logger]
]
end
# Run "mix help deps" to learn about dependencies.
defp deps do
[
# {:dep_from_hexpm, "~> 0.3.0"},
# {:dep_from_git, git: "https://github.com/elixir-lang/my_dep.git", tag: "0.1.0"}
]
end
end

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defmodule PerfectNumbersTest do
use ExUnit.Case
describe "Perfect numbers" do
test "Smallest perfect number is classified correctly" do
assert PerfectNumbers.classify(6) == {:ok, :perfect}
end
test "Medium perfect number is classified correctly" do
assert PerfectNumbers.classify(28) == {:ok, :perfect}
end
test "Large perfect number is classified correctly" do
assert PerfectNumbers.classify(33_550_336) == {:ok, :perfect}
end
end
describe "Abundant numbers" do
test "Smallest abundant number is classified correctly" do
assert PerfectNumbers.classify(12) == {:ok, :abundant}
end
test "Medium abundant number is classified correctly" do
assert PerfectNumbers.classify(30) == {:ok, :abundant}
end
test "Large abundant number is classified correctly" do
assert PerfectNumbers.classify(33_550_335) == {:ok, :abundant}
end
end
describe "Deficient numbers" do
test "Smallest prime deficient number is classified correctly" do
assert PerfectNumbers.classify(2) == {:ok, :deficient}
end
test "Smallest non-prime deficient number is classified correctly" do
assert PerfectNumbers.classify(4) == {:ok, :deficient}
end
test "Medium deficient number is classified correctly" do
assert PerfectNumbers.classify(32) == {:ok, :deficient}
end
test "Large deficient number is classified correctly" do
assert PerfectNumbers.classify(33_550_337) == {:ok, :deficient}
end
test "Edge case (no factors other than itself) is classified correctly" do
assert PerfectNumbers.classify(1) == {:ok, :deficient}
end
end
describe "Invalid inputs" do
test "Zero is rejected (not a natural number)" do
assert PerfectNumbers.classify(0) ==
{:error, "Classification is only possible for natural numbers."}
end
test "Negative integer is rejected (not a natural number)" do
assert PerfectNumbers.classify(-1) ==
{:error, "Classification is only possible for natural numbers."}
end
end
end

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ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)