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davearonson's solution

to Pascal's Triangle in the Elixir Track

Published at Jul 13 2018 · 0 comments
Instructions
Test suite
Solution

Note:

This solution was written on an old version of Exercism. The tests below might not correspond to the solution code, and the exercise may have changed since this code was written.

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:

$ elixir pascals_triangle_test.exs

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

For more detailed information about the Elixir track, please see the help page.

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

if !System.get_env("EXERCISM_TEST_EXAMPLES") do
  Code.load_file("pascals_triangle.exs", __DIR__)
end

ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)

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
defmodule PascalsTriangle do
  @doc """
  Calculates the rows of a pascal triangle
  with the given height
  """
  @spec rows(integer) :: [[integer]]
  def rows(num) do
    do_rows(num, 1, [1], []) |> Enum.reverse
  end

  defp do_rows(max, max, prior, acc), do: [prior|acc]
  defp do_rows(max, cur, prior, acc) do
    do_rows(max, cur + 1, make_row(prior, [1]), [prior|acc])
  end
  
  defp make_row([_]         , acc), do: [1|acc]
  defp make_row([a|[b|more]], acc), do: make_row([b|more], [a+b|acc])

end

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