a.rb

class Mino
  # I L O S T
  attr_reader :type
  def initialize(type)
    @type = type
  end

  def bottoms
    case type
    when "I"
      [0]
    when "L", "O"
      [0, 0]
    when "S"
      [0, 0, 1]
    when "T"
      [1, 0, 1]
    end
  end

  def tops
    case type
    when "I"
      [4]
    when "L"
      [3, 1]
    when "O"
      [2, 2]
    when "S"
      [1, 2, 2]
    when "T"
      [1, 1, 1]
      # [2, 2, 2]
    end
  end

  def width
    bottoms.size
  end
end

class Field
  attr_reader :heights
  def initialize
    @heights = []
  end

  def put(mino, idx)
    bs = mino.bottoms
    bs.each.with_index(idx) { |_, i| heights[i] ||= 0 }
    hs = heights[idx, mino.width].map { |e| e || 0 }
    tmp = hs.map.with_index do |h, i|
      bs.map { |b| b + h - bs[i] }
    end
    tmp = tmp.select do |es|
      es.map.with_index(idx) { |e, i| heights[i] <= e }.all?
    end
    h = tmp.first.first
    mino.tops.each.with_index(idx) { |e, i| heights[i] = h + e }
    # puts heights.map { |e| e || 0 }.join(' ')
  end

  def max_height
    heights.map { |e| e || 0 }.max
  end
end

class Solver
  attr_reader :field
  def run(input)
    @field = Field.new
    input.scan(/\d+\D/).each do |str|
      i = str[0..-1].to_i
      type = str[-1]
      mino = Mino.new(type)
      field.put(mino, i)
    end
    field.max_height.to_s
  end
end

test.rb

require_relative './a.rb'

module Foo
  def self.no
    @no ||= 0
  end

  def self.test(input, expected)
    no
    solver = Solver.new
    actual = solver.run(input)
    if actual == expected
      puts "No.#{no} OK"
    else
      puts "No.#{no} NG"
      puts "actual:   " + actual
      puts "expected: " + expected
    end
    @no += 1
  end
  test("1O3L0I0T", "5")
  test("0I", "4")
  test("0I0I", "8")
  test("0I1I2I3I4I", "4")
  test("0S0I", "5")
  test("0I0S", "6")
  test("2S0T2O3I", "8")
  test("4O4T1T0S4L1L3L", "10")
  test("0S2S4S6S8S10S12S14S", "16")
  test("14S12S10S8S6S4S2S0S", "2")
  test("5I2O10I0O4L10T9T11L8I2I10I12O7L12T12T12S11T9O10O13I12O10O7I9I7O0S1O2S0L1L", "23")
  test("9T14L10L8T4I1T3S5I8T12O3S7L9O7L14T2I7O3S6S2L0L13T10O4I9T7L8S0I12O9S11L11T14T", "27")
  test("9S9S7O11O16I2T9O12L10T9O0O13I9O1I2T14S7O9S11T5L7I14T13O0T12I3S10L10O7I15I6S2L12S8I16I3L", "23")
  test("11T13I16S15T7O10L12S1I5I8S5I13I15O8S9I1T12I1S5S0L14I12L16T2S2S8L2S14L16O4I13L15L13S11S9T13S9S3L6O", "22")
  test("12L10S7I5L14T12S9L1T14I0I5L1T2O18T9L0I15I16L10S1O15I0L17O5L18T4I18L7L7I13I3I12I2S3T5T3S16L14S14O11O15T14S", "17")
  test("0S18S2S19I14T7L14L2L6I9I0L4I5L13L15I8S8T2I5I7O18T3S1T7I2L8O0S20T9I14T5L5I1T4L9O8T19T5S12O16T19L4O10O10T14L", "24")
  test("7T5L6S4S8T6S10I19O20L14I18L21S7I11S11O1L13T20O9I7L2T8L2S20L3O14L9T17I8L8S14I6T2O11T21O18O6T15T1S3L6O19S18O20S19O16T6S14T", "26")
  test("18S2I4S16L13S17I21O8I17T8I14O12T20I20S19S16S13T12T20I22I15O2I2I8I2S18I9I9T6O13O13L17I2L20L2L4I9I19O11T3S10O2S18T12I5O11S19O21S6I17T17S", "26")
  test("11L5S0T22S18O13T2O22S15I12I21T16I3I1I22L11L11L22O13S24S15L13T15S19L10O15T7S24T19L0T13O11I12T13S4I24L15O3S19O10L19O0S20L7O11L21I22S18T19T23O8I22S24L0S", "21")
  test("7L7I11T7S18O17L8S15L9I3O24S3O1O5O14L9T13S2O25S22T10T8L24S18S13T1O1L6I10I4S13O3S7L10T1T4L17S20I18O15S25S23S21I19T6O24S9L2O2O15L12L8L8O18I18L0T5O", "31")
  test("999I999I999I999I999I999I999I999I999I999I999I", "44")
end