Python Coding challenge - Day 514| What is the output of the following Python Code?

 

Code Explanation:

Function: reduce_to_one(n)

This function implements a process related to the Collatz conjecture — it reduces a number n down to 1 by following these rules recursively, and it counts the number of steps taken.

1. Base Case: Check if n is already 1

if n == 1:

    return 0

What it does:

If the input number n is already 1, the function returns 0 because no more steps are needed to reduce it further.

This is the stopping condition for the recursion.

2. If n is Even

if n % 2 == 0:

    return 1 + reduce_to_one(n // 2)

What it does:

If n is even (i.e., divisible by 2), it divides n by 2 and makes a recursive call on this smaller number.

It adds 1 to count this step (the division by 2).

The function keeps going until it reaches 1.

3. If n is Odd

else:

    return 1 + reduce_to_one(3 * n + 1)

What it does:

If n is odd, it applies the formula 3 * n + 1 and recursively calls itself with this new value.

Again, adds 1 to count this step.

4. Example Call and Output

print(reduce_to_one(3))

How it works step-by-step for n = 3:

Step Current n Action Next n Steps so far

1 3 (odd) 3 * 3 + 1 = 10 10 1

2 10 (even) 10 // 2 = 5 5 2

3 5 (odd) 3 * 5 + 1 = 16 16 3

4 16 (even) 16 // 2 = 8 8 4

5 8 (even) 8 // 2 = 4 4 5

6 4 (even) 4 // 2 = 2 2 6

7 2 (even) 2 // 2 = 1 1 7

8 1 Stop - 0 (base case)

Total steps taken: 7

The function returns 7.

Output:

7