perfect-numbers
This commit is contained in:
parent
58eac331ab
commit
00a1a882dd
|
@ -0,0 +1,26 @@
|
|||
{
|
||||
"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/"
|
||||
}
|
|
@ -0,0 +1 @@
|
|||
{"track":"elixir","exercise":"perfect-numbers","id":"a3a905652d3c4b7fbe13a8ea5819052b","url":"https://exercism.org/tracks/elixir/exercises/perfect-numbers","handle":"negrienko","is_requester":true,"auto_approve":false}
|
|
@ -0,0 +1,4 @@
|
|||
# Used by "mix format"
|
||||
[
|
||||
inputs: ["{mix,.formatter}.exs", "{config,lib,test}/**/*.{ex,exs}"]
|
||||
]
|
|
@ -0,0 +1,24 @@
|
|||
# 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
|
||||
|
|
@ -0,0 +1,75 @@
|
|||
# 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.
|
|
@ -0,0 +1,62 @@
|
|||
# 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/
|
|
@ -0,0 +1,41 @@
|
|||
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
|
|
@ -0,0 +1,28 @@
|
|||
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
|
|
@ -0,0 +1,65 @@
|
|||
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
|
|
@ -0,0 +1,2 @@
|
|||
ExUnit.start()
|
||||
ExUnit.configure(exclude: :pending, trace: true)
|
Loading…
Reference in New Issue