Question

Синформатикой у исполнителя калькулятор две команды, которым присвоены номера: 1. прибавь 1 2. умножь на 3 сколько есть программ, которые число 5 преобразуют в число 49? интересует само решение

Answer 1

Поиск пути по принципу дерева

Код на Руби
def f0(number, log) #
  v = 1
  n = number + v
  # log = "#{log} + #{v}"
  log = "#{log} + 1"
  return [n, log]
end

def f1(number, log) #
  v = 3
  n = number * v
  # log = "#{log} + #{v}"
  log = "(#{log}) * 3"
  return [n, log]
end

def countWays(start_num, end_num, op_number, max_steps = 0)
  ways = {}
  ways.store(start_num.to_s, start_num)

  max_steps = max_steps == 0 ? (start_num - end_num).abs : max_steps
  count = 0

  for steps in 1..max_steps
      # puts "steps = #{steps}"
      new_ways = {}
      ways.each_pair{|log, num|

          for k in 0..op_number-1
              num1, log1 = f0(num, log) if k == 0
              num1, log1 = f1(num, log) if k == 1

              if num1 == end_num then
                  log1 += " = " + end_num.to_s
                  count += 1
                  puts log1
              elsif num1.between?(start_num, end_num)
                  new_ways.store(log1, num1)
              else
                  # log1 = log1 + " = " + num1.to_s + " BAD "
                  # puts log1
              end
          end
      }
      # p [steps, ways.size, new_ways.size]
      ways = new_ways
  end
  return count
end

p countWays(5, 49, 2, 49)

Вывод
((5) * 3 + 1) * 3 + 1 = 49
((5) * 3) * 3 + 1 + 1 + 1 + 1 = 49
(5 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) * 3 + 1 = 49
(5 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) * 3 + 1 + 1 + 1 + 1 = 49
(5 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) * 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 49
(5 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) * 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 49
(5 + 1 + 1 + 1 + 1 + 1 + 1 + 1) * 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 49
(5 + 1 + 1 + 1 + 1 + 1 + 1) * 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 49
(5 + 1 + 1 + 1 + 1 + 1) * 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 49
(5 + 1 + 1 + 1 + 1) * 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 49
(5 + 1 + 1 + 1) * 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 49
(5 + 1 + 1) * 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 49
(5 + 1) * 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 49
(5) * 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 49
5 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 49
15

ответ 15 вариантов программ

Как это решается аналитически я не знаю, но программно явно быстрее