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paulfioravanti's solution

to Pascal's Triangle in the Elixir Track

Published at Aug 10 2019 · 0 comments
Instructions
Test suite
Solution

Compute Pascal's triangle up to a given number of rows.

In Pascal's Triangle each number is computed by adding the numbers to the right and left of the current position in the previous row.

    1
   1 1
  1 2 1
 1 3 3 1
1 4 6 4 1
# ... etc

Running tests

Execute the tests with:

$ mix test

Pending tests

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

If you're stuck on something, it may help to look at some of the available resources out there where answers might be found.

Source

Pascal's Triangle at Wolfram Math World http://mathworld.wolfram.com/PascalsTriangle.html

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

pascals_triangle_test.exs

defmodule PascalsTriangleTest do
  use ExUnit.Case

  # @tag pending
  test "one row" do
    assert PascalsTriangle.rows(1) == [[1]]
  end

  @tag :pending
  test "two rows" do
    assert PascalsTriangle.rows(2) == [[1], [1, 1]]
  end

  @tag :pending
  test "three rows" do
    assert PascalsTriangle.rows(3) == [[1], [1, 1], [1, 2, 1]]
  end

  @tag :pending
  test "fourth row" do
    assert List.last(PascalsTriangle.rows(4)) == [1, 3, 3, 1]
  end

  @tag :pending
  test "fifth row" do
    assert List.last(PascalsTriangle.rows(5)) == [1, 4, 6, 4, 1]
  end

  @tag :pending
  test "twentieth row" do
    expected = [
      1,
      19,
      171,
      969,
      3876,
      11_628,
      27_132,
      50_388,
      75_582,
      92_378,
      92_378,
      75_582,
      50_388,
      27_132,
      11_628,
      3876,
      969,
      171,
      19,
      1
    ]

    assert List.last(PascalsTriangle.rows(20)) == expected
  end
end

test_helper.exs

ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)
defmodule PascalsTriangle do
  @doc """
  Calculates the rows of a pascal triangle
  with the given height
  """
  @spec rows(integer) :: [[integer]]
  def rows(num) do
    # https://en.wikipedia.org/wiki/Pascal%27s_triangle
    # "The rows of Pascal's triangle are conventionally enumerated
    # starting with row n = 0 at the top (the 0th row)", so instantly decrement
    # the number of rows by 1.
    0..(num - 1)
    |> Enum.map(&generate_row/1)
  end

  defp generate_row(row_num) do
    0..row_num
    |> Enum.map(&binomial(&1, row_num))
  end

  # https://en.wikipedia.org/wiki/Binomial_theorem
  # "n (row_num) choose k (exponent)" => n!/(n - k)!k!
  defp binomial(exponent, row_num) do
    factorial(row_num) / (factorial(row_num - exponent) * factorial(exponent))
  end

  defp factorial(0), do: 1

  defp factorial(num) do
    1..num
    |> Enum.reduce(1, &*/2)
  end
end

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