Fibonacci and decode ways

Questions 1 to 5 of 8

1. 1. What does this program print? ``python def fib(n): a, b = 0, 1 for _ in range(n): a, b = b, a + b return b print(fib(5)) ``

   58313
2. 2. What does this program print? The second number is the count of calls. ``python calls = 0 def fib_naive(n): global calls calls += 1 if n < 2: return n return fib_naive(n - 1) + fib_naive(n - 2) f = fib_naive(6) print(f, calls) ``

   8 155 258 258 9
3. 3. In the matrix method, matrix_power(M, p) with M = [1 1; 1 0] and p = 8 calls multiply for each squaring of base and for each multiplication into result. How many calls to multiply are made in total?

   Type a number.

4. 4. Which statements about the matrix method for F(n) are true? Select all that apply.

   Pick every answer that is true.

   The loop runs about log2(n) times, with at most two matrix multiplications in each runThe time is O(n), because the loop runs n timesEach 2 by 2 matrix multiplication is a fixed set of 8 number multiplicationsWithout the modulo, the numbers in M^n grow with n, and Python keeps every digit, so big numbers slow the work down
5. 5. After the loop in fib(n) finishes, what do a and b hold?

   a is F(n) and b is F(n + 1)a is F(n - 1) and b is F(n)a is F(n + 1) and b is F(n)both hold F(n)