Question

Consider the following Python code snippet.

def f(a, b):
    if (a == 0):
        return b
    if (a % 2 == 1):
        return 2 * f((a - 1) / 2, b)
    return b + f(a - 1, b)

print(f(15, 10))

The value printed by the code snippet is 160 (Answer in integer).

Hint:

Recursive functions often follow a divide-and-conquer approach. Breaking down the recursion tree step-by-step helps in understanding its behavior.

Answer 1

Step 1: Understanding the function behavior. 
The function f(a, b) follows a recursive pattern. 
If \( a = 0 \), it returns \( b \). 
If \( a \) is odd, it halves \( a - 1 \) and multiplies the result by 2.
Otherwise, it reduces \( a \) by 1 and adds \( b \).
Step 2: Evaluating f(15, 10).
1. \( f(15,10) = 2 \times f(7,10) \)
2. \( f(7,10) = 2 \times f(3,10) \)
3. \( f(3,10) = 2 \times f(1,10) \)
4. \( f(1,10) = 2 \times f(0,10) \)
5. \( f(0,10) = 10 \)
6. \( f(1,10) = 2 \times 10 = 20 \)
7. \( f(3,10) = 2 \times 20 = 40 \)
8. \( f(7,10) = 2 \times 40 = 80 \)
9. \( f(15,10) = 2 \times 80 = 160 \)
Thus, the output of the program is: 160.