algoadvance

1. Input: What is the range and type of input values?
2. Output: What is expected as output?
3. Constraints: Any specific constraints, edge cases to consider, e.g., negative numbers?

Strategy

To solve this problem, we need to reduce a given number to zero following these rules:

• If the number is even, divide it by 2.
• If the number is odd, subtract 1 from it. We count the number of steps required to achieve zero.

Given the problem, a clear strategy involves a simple iterative approach:

1. Initialize a step counter.
2. Loop until the number becomes zero.
3. Depending on whether the current number is even or odd, either divide by 2 or subtract 1.
4. Increment the step counter accordingly.
5. Return the step counter once the number is zero.

Time Complexity

• The time complexity is O(log n) since for each even number, we are performing a division by 2, which reduces the number’s bit length logarithmically.
• The auxiliary space complexity is O(1) as we are using a constant amount of extra space.

Python Code

Here is the implementation of the described strategy:

def numberOfSteps(num: int) -> int:
    steps = 0
    
    while num > 0:
        if num % 2 == 0:
            num //= 2
        else:
            num -= 1
        steps += 1
    
    return steps

# Example Test
print(numberOfSteps(14))  # Output: 6
print(numberOfSteps(8))  # Output: 4
print(numberOfSteps(123))  # Output: 12

In this code:

• We start with the given number num.
• We use a loop that continues until num is reduced to zero.
• Inside the loop, we check if num is even or odd and perform the necessary operation.
• We count each operation by incrementing steps.

This simple iterative approach ensures we handle different cases and reduce the number to zero efficiently.

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