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.
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test "shouting" do
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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.
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
ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)
defmodule PerfectNumbers do
@spec classify(number :: integer) :: {:ok, atom} | {:error, String.t()}
def classify(number) when number > 0 do
case aliquot_sum(number) do
sum when sum === number -> {:ok, :perfect}
sum when sum > number -> {:ok, :abundant}
sum when sum < number -> {:ok, :deficient}
end
end
def classify(_),
do: {:error, "Classification is only possible for natural numbers."}
defp aliquot_sum(number),
do: aliquot_sum(number, div(number, 2), [])
defp aliquot_sum(_, 0, sum),
do: Enum.sum(sum)
defp aliquot_sum(number, index, sum) when rem(number, index) === 0,
do: aliquot_sum(number, index - 1, [index | sum])
defp aliquot_sum(number, index, sum),
do: aliquot_sum(number, index - 1, sum)
end
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