PEuler15.rb

def paths(row, col)
  return 1 if row == 3 && col == 3
  return 0 if row > 3 || col > 3
  return paths(row + 1, col) + paths(row, col + 1)
end
 
def new_path(tot_row, tot_col)
  curr_row = 0
  curr_col = 0
  known = {}
  
  #Get all values in each row
  until curr_col > tot_row do
    #Get all values in column
    until curr_row > tot_row do
      if curr_col == 0
        known[[curr_row,curr_col]] = 1
      elsif curr_row == curr_col
        val = known[[curr_row,curr_col - 1]] * 2
        known[[curr_row,curr_col]] = val
      else
        val = known[[curr_row,curr_col - 1]] + known[[curr_row - 1,curr_col]]
        known[[curr_row,curr_col]] =  val
      end
      curr_row += 1
    end
    curr_col += 1
    curr_row = curr_col
  end
  known[[tot_row, tot_col]]
end

st = Time.new
puts new_path(20,20).inspect
en = Time.new - st
puts en

def paths(row, col)
  return 1 if row == 19 && col == 19
  return 0 if row > 19 || col > 19
  return paths(row + 1, col) + paths(row, col + 1)
end