Determine if a number is perfect, abundant, or deficient based on Nicomachus' (60 - 120 CE) classification scheme for natural numbers.
The Greek mathematician Nicomachus devised a classification scheme for natural numbers, identifying each as belonging uniquely to the categories of perfect, abundant, or deficient based on their 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
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.
Execute the tests with:
$ elixir perfect_numbers_test.exs
In the test suites, all but the first test have been 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:
# @tag :pending
test "shouting" do
assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
end
Or, you can enable all the tests by commenting out the
ExUnit.configure
line in the test suite.
# ExUnit.configure exclude: :pending, trace: true
For more detailed information about the Elixir track, please see the help page.
Taken from Chapter 2 of Functional Thinking by Neal Ford. http://shop.oreilly.com/product/0636920029687.do
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
if !System.get_env("EXERCISM_TEST_EXAMPLES") do
Code.load_file("perfect_numbers.exs", __DIR__)
end
ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)
defmodule PerfectNumbersTest do
use ExUnit.Case
describe "Perfect numbers" do
# @tag :pending
test "Smallest perfect number is classified correctly" do
assert PerfectNumbers.classify(6) == {:ok, :perfect}
end
@tag :pending
test "Medium perfect number is classified correctly" do
assert PerfectNumbers.classify(28) == {:ok, :perfect}
end
@tag :pending
test "Large perfect number is classified correctly" do
assert PerfectNumbers.classify(33_550_336) == {:ok, :perfect}
end
end
describe "Abundant numbers" do
@tag :pending
test "Smallest abundant number is classified correctly" do
assert PerfectNumbers.classify(12) == {:ok, :abundant}
end
@tag :pending
test "Medium abundant number is classified correctly" do
assert PerfectNumbers.classify(30) == {:ok, :abundant}
end
@tag :pending
test "Large abundant number is classified correctly" do
assert PerfectNumbers.classify(33_550_335) == {:ok, :abundant}
end
end
describe "Deficient numbers" do
@tag :pending
test "Smallest prime deficient number is classified correctly" do
assert PerfectNumbers.classify(2) == {:ok, :deficient}
end
@tag :pending
test "Smallest non-prime deficient number is classified correctly" do
assert PerfectNumbers.classify(4) == {:ok, :deficient}
end
@tag :pending
test "Medium deficient number is classified correctly" do
assert PerfectNumbers.classify(32) == {:ok, :deficient}
end
@tag :pending
test "Large deficient number is classified correctly" do
assert PerfectNumbers.classify(33_550_337) == {:ok, :deficient}
end
@tag :pending
test "Edge case (no factors other than itself) is classified correctly" do
assert PerfectNumbers.classify(1) == {:ok, :deficient}
end
end
describe "Invalid inputs" do
@tag :pending
test "Zero is rejected (not a natural number)" do
assert PerfectNumbers.classify(0) ==
{:error, "Classification is only possible for natural numbers."}
end
@tag :pending
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
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`
"""
@types [:abundant, :perfect, :deficient]
@spec classify(number :: integer) :: ({ :ok, atom } | { :error, String.t() })
def classify(number) when number > 1 do
with sum <- aliquot_sum(number, :math.sqrt(number), 2, 1),
sgn <- sign(number - sum) do
{:ok, @types |> Enum.at(sgn + 1) }
else
err -> {:error, err}
end
end
def classify(n) when n < 1, do: { :error, "Classification is only possible for natural numbers." }
def classify(1), do: {:ok, :deficient} # special case
defp aliquot_sum(number, limit, candidate, acc) when candidate <= limit do
to_add = add_for(number, candidate)
aliquot_sum(number, limit, candidate + 1, acc + to_add)
end
defp aliquot_sum(_, _, _, acc), do: acc
defp add_for(number, candidate) when rem(number, candidate) != 0, do: 0
defp add_for(number, candidate) do
other = number/candidate
# if other == candidate that's the square root; only add ONCE
if other == candidate, do: candidate, else: candidate + other
end
defp sign(n) when n > 0, do: 1
defp sign(n) when n < 0, do: -1
defp sign(_) , do: 0
end
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