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
For installation and learning resources, refer to the Ruby resources page.
For running the tests provided, you will need the Minitest gem. Open a terminal window and run the following command to install minitest:
gem install minitest
If you would like color output, you can
require 'minitest/pride' in
the test file, or note the alternative instruction, below, for running
the test file.
Run the tests from the exercise directory using the following command:
To include color from the command line:
ruby -r minitest/pride pascals_triangle_test.rb
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.
require 'minitest/autorun' require_relative 'pascals_triangle' class TriangleTest < Minitest::Test def test_one_row triangle = Triangle.new(1) assert_equal [], triangle.rows end def test_two_rows skip triangle = Triangle.new(2) assert_equal [, [1, 1]], triangle.rows end def test_three_rows skip triangle = Triangle.new(3) assert_equal [, [1, 1], [1, 2, 1]], triangle.rows end def test_fourth_row skip triangle = Triangle.new(4) assert_equal [1, 3, 3, 1], triangle.rows.last end def test_fifth_row skip triangle = Triangle.new(5) assert_equal [1, 4, 6, 4, 1], triangle.rows.last end def test_twentieth_row skip triangle = Triangle.new(20) 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_equal expected, triangle.rows.last end end
class Triangle # 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. def initialize(num_rows) @max_row = num_rows - 1 end def rows (0..max_row).map(&method(:generate_row)) end private attr_reader :max_row def generate_row(row_num) (0..row_num) .each .with_object(row_num) .map(&method(:binomial)) end # https://en.wikipedia.org/wiki/Binomial_theorem # "n (row_num) choose k (exponent)" => n!/(n - k)!k! def binomial(exponent, row_num) factorial(row_num) / (factorial(row_num - exponent) * factorial(exponent)) end # Provide starting accumulator for 0! == 1 def factorial(num) (1..num).reduce(1, :*) end end
A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.
Here are some questions to help you reflect on this solution and learn the most from it.