Biggest box size, using dynamic programming

biggest_box_size.rb

#!/usr/bin/env ruby

input = [
  [1,0,0,0,1,0,0,0,0,1,0,0,0,0,0],
  [1,0,0,0,1,0,0,0,0,0,0,0,0,0,0],
  [1,0,0,0,1,0,0,0,0,1,0,0,0,0,0],
  [1,0,1,0,1,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,1,1,0,1,0,0,0,0,0],
  [0,0,0,0,0,0,0,1,0,0,0,0,1,0,0],
  [0,0,0,0,0,0,1,0,0,0,0,1,0,0,0],
  [0,0,0,0,0,0,1,0,0,1,0,0,1,0,0],
  [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],
  [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0]
]

def biggest_box_size(input)
  max_area = 0

  # make an empty array of arrays
  boxes = input.map { |row| [] }

  input.each_with_index do |row, i|
    row.each_with_index do |cell, j|
      left = j > 0 ? boxes[i][j - 1] : nil
      above = i > 0 ? boxes[i - 1][j] : nil

      boxes[i][j] =
        # [rows, columns]
        case
        when cell == 1
          # if the corner is filled, it doesn't complete a box
          [0, 0]
        when i.zero? && j.zero?
          # otherwise, if top-left corner, it has size 1x1
          [1, 1]
        when i.zero?
          # otherwise, if top row, it grows the left box by one column
          [1, left[1] + 1]
        when j.zero?
          # otherwise, if left column, it grows the above box by one row
          [above[0] + 1, 1]
        else
          # the general case
          # left box + column
          if left[0].zero?
            left_with_column_area = 0
          else
            left_with_column = [[left[0], above[0] + 1].min, left[1] + 1]
            left_with_column_area = left_with_column[0] * left_with_column[1]
          end
          # above box + row
          if above[1].zero?
            above_with_row_area = 0
          else
            above_with_row = [above[0] + 1, [above[1], left[1] + 1].min]
            above_with_row_area = above_with_row[0] * above_with_row[1]
          end
          # if both above and left is blocked
          if left_with_column_area.zero? && above_with_row_area.zero?
            # make a new box
            [1, 1]
          else
            # otherwise, take the larger one
            left_with_column_area > above_with_row_area ? left_with_column : above_with_row
          end
        end

      area = boxes[i][j][0] * boxes[i][j][1]
      max_area = area if area > max_area
    end
  end

  max_area
end

if __FILE__ == $0
  puts biggest_box_size(input)
end