Question

13.: Формальные исполнители Баллы: 3 Задан алгоритм обработки строки: Заменить в строке все символы 'A' на подстроку 'AB' и увеличить N на единицу. Если N=K, то завершить выполнение алгоритма, иначе перейти на шаг 2. Заменить в строке все символы 'B' на подстроку 'AB' и увеличить N на единицу. Если N=K, то завершить выполнение алгоритма, иначе перейти на шаг 3. Заменить в строке все подстроки 'AB' на символ 'A' и увеличить N на единицу. Если N=K, то завершить выполнение алгоритма, иначе перейти на шаг 1. Известно, что перед началом выполнения была строка 'AA', N=0 и K=43. Определите количество символов A в строке, получившейся после завершения алгоритма. В ответе укажите целое число.

Answer 1

Ответ:

32768

Объяснение:

Чисто символов "А" в строке вычисляется по формуле 2^([(K-2)/3]+2) , соответственно, 2^([(43-2)/3]+2) = 32768

Answer 2

Ответ:

Если я всё правильно понял, то на Python - примерно так:

st = 'AA'

N = 0

K = 43

while N != K:

   st = st.replace('A', 'AB')

   N += 1

   if N != K:

       st = st.replace('B', 'AB')

       N += 1

       if N != K:

           st = st.replace('AB', 'A')

           N += 1

print(st.count('A'))

Объяснение:

Выходит 32768 символов A

Answer 3

Problem Analysis

The given algorithm processes a string by replacing all occurrences of the character 'A' with the substring 'AB' and increasing the value of N by 1. If N becomes equal to K, the algorithm terminates. Otherwise, it proceeds to the next step, which involves replacing all occurrences of the character 'B' with the substring 'AB' and increasing N by 1. Again, if N becomes equal to K, the algorithm terminates. If not, it moves to the next step, which replaces all occurrences of the substring 'AB' with the character 'A' and increases N by 1. The algorithm then repeats the steps from the beginning.

We are given that the initial string is 'AA', N is 0, and K is 43. We need to determine the number of 'A' characters in the string after the algorithm terminates.

Solution

To solve this problem, we can simulate the steps of the algorithm until N becomes equal to K. We will keep track of the string after each step and count the number of 'A' characters.

Let's go through the steps of the algorithm:

1. Start with the string 'AA', N = 0, and K = 43. 2. Replace all occurrences of 'A' with 'AB' and increase N by 1. The string becomes 'ABAB', and N becomes 1. 3. Since N (1) is not equal to K (43), move to the next step. 4. Replace all occurrences of 'B' with 'AB' and increase N by 1. The string becomes 'ABABABAB', and N becomes 2. 5. Since N (2) is not equal to K (43), move to the next step. 6. Replace all occurrences of 'AB' with 'A' and increase N by 1. The string becomes 'AAAA', and N becomes 3. 7. Since N (3) is not equal to K (43), move to the next step. 8. Go back to step 2.

We can see that the string 'AAAA' is repeated in steps 2, 4, 6, and 8. Each repetition increases N by 1. Therefore, we can calculate the number of repetitions required to reach N = 43 by dividing 43 by 3 (the number of repetitions in each cycle). The remainder will give us the number of additional 'A' characters.

43 divided by 3 is 14 with a remainder of 1. This means that the string 'AAAA' is repeated 14 times, and there is an additional 'A' character.

Therefore, the final string after the algorithm terminates will have 14 * 4 + 1 = 57 'A' characters.

Answer

The number of 'A' characters in the string after the algorithm terminates is 57.