After watching a couple Numberphile videos on YouTube about Catalan Numbers and Pascal's Triangle, I wrote a Pascal's Triangle implementation in Ruby as a fun little exercise. https://youtu.be/fczN0BCx0xs https://youtu.be/0iMtlus-afo

pascals_triangle.rb

def pascals_triangle total_rows=3, start_value=1
  rows = []

  (total_rows + 1).times do |current_row|
    if current_row == 1
      rows << [nil, start_value]
      next
    end

    row = [nil]
    current_row.times do |item|
      previous_row = rows[current_row - 1]

      left_parent  = previous_row[item].to_i
      right_parent = previous_row[item + 1].to_i

      row << left_parent + right_parent
    end

    rows << row
  end

  rows.shift           # delete the implied 0, 0 row
  rows.each &:compact! # delete the placeholder leading nil
end

def format_triangle triangle
  triangle_width = triangle.last.length * 2 - 1

  # for centering numbers as the get wider than one digit
  widest_number = triangle.last.max.to_s.length
  padding       = ' ' * widest_number

  triangle.map.with_index do |row, index|
    inner_width   = row.length * 2 - 1
    outer_width   = (triangle_width - inner_width) / 2
    outer_padding = Array.new outer_width, padding

    padded_row = row.flat_map { |item| [item.to_s.center(widest_number), padding] }
    padded_row.pop

    [outer_padding, padded_row, outer_padding].flatten.join
  end
end

def formatted_pascals_triangle total_rows=3, start_value=1
  format_triangle(pascals_triangle total_rows, start_value)
end

##########################################

# to show 2D array structure
pascals_triangle(1).each { pp it }
puts
pascals_triangle(2).each { pp it }
puts
pascals_triangle(3).each { pp it }
puts
pascals_triangle(10).each { pp it }
puts

# to show printing visually formatted as a triangle too
puts formatted_pascals_triangle 10

pascals_triangle_output.txt

[1]

[1]
[1, 1]

[1]
[1, 1]
[1, 2, 1]

[1]
[1, 1]
[1, 2, 1]
[1, 3, 3, 1]
[1, 4, 6, 4, 1]
[1, 5, 10, 10, 5, 1]
[1, 6, 15, 20, 15, 6, 1]
[1, 7, 21, 35, 35, 21, 7, 1]
[1, 8, 28, 56, 70, 56, 28, 8, 1]
[1, 9, 36, 84, 126, 126, 84, 36, 9, 1]

                            1                            
                         1     1                         
                      1     2     1                      
                   1     3     3     1                   
                1     4     6     4     1                
             1     5    10    10     5     1             
          1     6    15    20    15     6     1          
       1     7    21    35    35    21     7     1       
    1     8    28    56    70    56    28     8     1    
 1     9    36    84    126   126   84    36     9     1