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
Execute the tests with:
$ mix test
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.
Pascal's Triangle at Wolfram Math World http://mathworld.wolfram.com/PascalsTriangle.html
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
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
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(n) do
Enum.map(1..n, &row/1)
end
defp row(1), do: [1]
defp row(n) do
[0 | row(n - 1)]
|> Enum.chunk_every(2, 1, [0])
|> Enum.map(&Enum.sum/1)
end
end
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