Question

Исполнитель Редактор получает на вход строку цифр и преобразовывает её. Редактор может выполнять две команды, в обеих командах v и w обозначают цепочки цифр. заменить (v, w) нашлось (v) Дана программа для исполнителя Редактор: НАЧАЛО ПОКА нашлось (25) ИЛИ нашлось (355) ИЛИ нашлось (4555) ЕСЛИ нашлось (25) ТО заменить (25, 4) КОНЕЦ ЕСЛИ ЕСЛИ нашлось (355) ТО заменить (355, 2) КОНЕЦ ЕСЛИ ЕСЛИ нашлось (4555) ТО заменить (4555, 3) КОНЕЦ ЕСЛИ КОНЕЦ ПОКА КОНЕЦ Какая строка получится в результате применения приведённой ниже программы к строке, в которой первая и последняя цифры – 3, а между ними стоит 100 цифр 5? В ответе запишите полученную строку.

Answer 1

Выполним несколько первых шагов алгоритма:
1 "3", 100 "5", 1 "3"
1 "2", 98 "5", 1 "3"
1 "4", 97 "5", 1 "3"
1 "3", 94 "5", 1 "3"
...
1 "3", 4 "5", 1 "3" - 355553
1 "2", 2 "5", 1 "3" - 2553
1 "4", 1 "5", 1 "3" - 453
Ответ: 453

Answer 2

Problem Analysis

The given program is a text editor that takes a string of digits as input and performs two commands. The commands involve replacing certain patterns of digits in the string. The program continues executing the commands until no more replacements can be made. The program stops when there are no more occurrences of the patterns "25", "355", or "4555" in the string.

The commands are as follows: - If the pattern "25" is found, it is replaced with "4". - If the pattern "355" is found, it is replaced with "2". - If the pattern "4555" is found, it is replaced with "3".

We need to determine the resulting string after applying the given program to a string that starts and ends with the digit "3" and has 100 occurrences of the digit "5" between them.

Solution

To solve this problem, we can simulate the execution of the program step by step. We start with the given string and apply the replacement rules until no more replacements can be made.

Here are the steps to solve the problem:

1. Initialize the string with the given conditions: "3" + "5" (repeated 100 times) + "3". 2. Apply the replacement rules iteratively until no more replacements can be made: - Replace "25" with "4". - Replace "355" with "2". - Replace "4555" with "3". 3. Repeat step 2 until no more replacements can be made. 4. The resulting string is the final string after all replacements have been made.

Let's apply these steps to solve the problem.

Solution Steps

1. Initialize the string: "3" + "5" (repeated 100 times) + "3". 2. Apply the replacement rules iteratively until no more replacements can be made: - Replace "25" with "4": "3" + "5" (repeated 100 times) + "3". - Replace "355" with "2": "3" + "5" (repeated 100 times) + "3". - Replace "4555" with "3": "3" + "5" (repeated 100 times) + "3". 3. No more replacements can be made, so the final string is "3" + "5" (repeated 100 times) + "3".

Answer

The resulting string after applying the given program to the string with the first and last digits as "3" and 100 occurrences of the digit "5" between them is "3" + "5" (repeated 100 times) + "3".