Published at May 21 2019
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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
```

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:

```
ruby pascals_triangle_test.rb
```

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 [[1]], triangle.rows
end
def test_two_rows
skip
triangle = Triangle.new(2)
assert_equal [[1], [1, 1]], triangle.rows
end
def test_three_rows
skip
triangle = Triangle.new(3)
assert_equal [[1], [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.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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