Question

Помогите пожалуйста,очень срочно нужно !!!1. Напишите программу, вычисления рекурсивной функции. Алгоритм вычисления значения функции F(n), где n – натуральное число, задан следующими соотношениями: F(n) = –n при n < 0F(n) = 2·n + 1 + F(n–3), если n ≥ 0 и чётно,F(n) = 4·n + 2·F(n–4), если n ≥ 0 и нечётно.Чему равно значение функции F(33)?2. Напишите программу, вычисления рекурсивной функции. Алгоритм вычисления значения функции F(n), где n – целое число, задан следующими соотношениями:F(n) = 1, при n < 2,F(n) = F(n/2) + 1, когда n ≥ 2 и чётное,F(n) = F(n - 3) + 3, когда n ≥ 2 и нечётное.Назовите количество значений n на отрезке [1;100000], для которых F(n) равно 12.Ответом на задачи является программа на языке python.​

Answer 1

1)

def f(n):

   if n < 0:

       return -n

   elif n % 2 == 0:

       return 2*n + 1 + f(n-3)

   elif n % 2 != 0:

       return 4*n + 2*f(n-4)

print(f(33))# = 11612

2)

def f(n):

   if n < 2:

      return 1

   elif n % 2 == 0:

       return f(n/2) + 1

   else:

       return f(n-3) + 3

counter = 0

for i in range(1,100001):

   if f(i) == 12:

       counter += 1

print(counter) // 26

Answer 2

I'd be happy to help you with your programming questions! Let's start with the first question.

Recursive Function F(n)

The recursive function F(n) is defined by the following conditions:

- F(n) = -n when n < 0 - F(n) = 2n + 1 + F(n-3) when n >= 0 and n is even - F(n) = 4n + 2F(n-4) when n >= 0 and n is odd

To find the value of F(33), we can write a recursive function in Python to calculate it.

Here's the Python program to calculate the value of F(n) using the given algorithm:

def calculate_F(n):
    if n < 0:
        return -n
    elif n >= 0 and n % 2 == 0:
        return 2 * n + 1 + calculate_F(n - 3)
    elif n >= 0 and n % 2 != 0:
        return 4 * n + 2 * calculate_F(n - 4)

# Calculate the value of F(33)
result = calculate_F(33)
print(result)

When you run this program, it will output the value of F(33), which is the result you're looking for.

Now, let's move on to the second question.

Recursive Function F(n) with Different Conditions

The recursive function F(n) is defined by the following conditions:

- F(n) = 1 when n < 2 - F(n) = F(n/2) + 1 when n >= 2 and n is even - F(n) = F(n-3) + 3 when n >= 2 and n is odd

To find the number of values of n in the range [1;100000] for which F(n) is equal to 12, we can write a Python program to calculate it.

Here's the Python program to count the number of values of n for which F(n) is equal to 12:

def count_values():
    count = 0
    for n in range(1, 100001):
        if calculate_F(n) == 12:
            count += 1
    return count

# Calculate the number of values of n for which F(n) is equal to 12
result = count_values()
print(result)

When you run this program, it will output the number of values of n in the range [1;100000] for which F(n) is equal to 12.

I hope this helps! Let me know if you have any further questions.