Published at Jul 13 2018
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Instructions

Test suite

Solution

A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which,

```
a**2 + b**2 = c**2
```

For example,

```
3**2 + 4**2 = 9 + 16 = 25 = 5**2.
```

There exists exactly one Pythagorean triplet for which a + b + c = 1000.

Find the product a * b * c.

Execute the tests with:

```
$ elixir pythagorean_triplet_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.

Problem 9 at Project Euler http://projecteuler.net/problem=9

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("pythagorean_triplet.exs", __DIR__)
end
ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)
defmodule PythagoreanTripletTest do
use ExUnit.Case
# @tag :pending
test "sum" do
triplet = [3, 4, 5]
assert Triplet.sum(triplet) == 12
end
@tag :pending
test "product" do
triplet = [3, 4, 5]
assert Triplet.product(triplet) == 60
end
@tag :pending
test "pythagorean" do
triplet = [3, 4, 5]
assert Triplet.pythagorean?(triplet)
end
@tag :pending
test "not pythagorean" do
triplet = [5, 6, 7]
refute Triplet.pythagorean?(triplet)
end
@tag :pending
test "triplets up to 10" do
triplets = Triplet.generate(1, 10)
assert Enum.map(triplets, &Triplet.product/1) == [60, 480]
end
@tag :pending
test "triplets from 11 up to 20" do
triplets = Triplet.generate(11, 20)
assert Enum.map(triplets, &Triplet.product/1) == [3840]
end
@tag :pending
test "triplets where sum is 180 and max factor is 100" do
triplets = Triplet.generate(1, 100, 180)
assert Enum.map(triplets, &Triplet.product/1) == [118_080, 168_480, 202_500]
end
end
```

```
defmodule Triplet do
@doc """
Calculates sum of a given triplet of integers.
"""
@spec sum([non_neg_integer]) :: non_neg_integer
def sum(triplet) do
triplet |> Enum.reduce(&+/2)
end
@doc """
Calculates product of a given triplet of integers.
"""
@spec product([non_neg_integer]) :: non_neg_integer
def product(triplet) do
triplet |> Enum.reduce(&*/2)
end
@doc """
Determines if a given triplet is pythagorean. That is, do the squares of a and b add up to the square of c?
"""
@spec pythagorean?([non_neg_integer]) :: boolean
def pythagorean?([a, b, c]) do
a * a + b * b == c * c
end
@doc """
Generates a list of pythagorean triplets from a given min (or 1 if no min) to a given max.
"""
@spec generate(non_neg_integer, non_neg_integer) :: [list(non_neg_integer)]
def generate(min, max) do
low = trunc(:math.sqrt(min * 2)) # inverse of min*min/2
# not sure if this is high enough really; the math makes my head hurt
high = max * :math.sqrt(2)
# feed it only even current-numbers
do_generate(min, low + rem(low, 2), max, high, [])
end
defp do_generate(_ , cur, _ , high, acc) when cur > high, do: acc
defp do_generate(min, cur, max, high, acc) do
# yeah, ++ is kinda slow... but to avoid this
# we'd have to pass the acc all the way down,
# and tack on each dicksonized factoring, yuck!
do_generate(min, cur+2, max, high, acc ++ dicksons_triples(min, cur, max))
end
# triples generated with dickson's method; see
# https://en.wikipedia.org/wiki/Formulas_for_generating_Pythagorean_triples#Dickson.27s_method
# method chosen because "All Pythagorean triples may be found by this method."
# whereas other methods only find certain families.
defp dicksons_triples(min, cur, max) do
factorings(trunc(cur * cur / 2))
|> Enum.map(&(dicksonize(cur, &1)))
|> Enum.filter(&(all_within?(&1, min, max)))
end
defp factorings(num) do
# this gives us no dups, and in sorted order
(1..trunc(:math.sqrt(num)))
|> Enum.filter(&(rem(num, &1)) == 0)
|> Enum.map(&([&1, trunc(num/&1)]))
end
defp dicksonize(r, [s,t]) do
[r+s, r+t, r+s+t]
end
defp all_within?([n|rest], min, max) do
n <= max && n >= min && all_within?(rest, min, max)
end
defp all_within?([], _, _), do: true
@doc """
Generates a list of pythagorean triplets from a given min to a given max, whose values add up to a given sum.
"""
@spec generate(non_neg_integer, non_neg_integer, non_neg_integer) :: [list(non_neg_integer)]
def generate(min, max, sum) do
generate(min, max) |> Enum.filter(&(Enum.sum(&1) == sum))
end
end
```

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