When preparing for coding interviews or sharpening your algorithmic problem-solving skills, sometimes the most straightforward problems can offer the most valuable lessons. The “Number of Steps to Reduce a Number to Zero” problem from Leetcode is one such exercise that appears simple at first glance but has several educational angles worth exploring.

In this comprehensive guide, we will break down the problem statement, dissect the constraints, explore multiple approaches for solving the problem, and analyze the time and space complexity of each solution.

## Problem Statement

The problem statement for “Number of Steps to Reduce a Number to Zero” reads:

Given a non-negative integer `num`

, return the number of steps to reduce it to zero.

If the current number is even, you have to divide it by 2; otherwise, you have to subtract 1 from it.

Examples:

```
Input: num = 14
Output: 6
Input: num = 8
Output: 4
Input: num = 123
Output: 12
```

## Approaches to Solve the Problem

### Iterative Approach

The most straightforward approach to solving this problem is by following the steps outlined in the problem statement. Starting from the number `num`

, we check if it is even or odd at each iteration and perform the corresponding operation (divide by 2 for even numbers, subtract 1 for odd numbers). We keep a counter to keep track of the number of steps taken.

Here’s a Python code snippet for this:

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

**Time Complexity**: O(log num)

**Space Complexity**: O(1)

### Recursive Approach

While the iterative approach is sufficient, you can also solve this problem using recursion for educational purposes.

Here’s a Python implementation:

```
def numberOfSteps(num):
if num == 0:
return 0
if num % 2 == 0:
return 1 + numberOfSteps(num // 2)
else:
return 1 + numberOfSteps(num - 1)
```

**Time Complexity**: O(log num)**Space Complexity**: O(log num)

## Why These Approaches Work

Both the iterative and recursive approaches essentially follow the same algorithm but in different forms. They continue the steps as defined in the problem statement until the number reduces to zero.

The reason for the logarithmic time and space complexity is that the number `num`

keeps getting halved when it’s even, which is a divide-and-conquer strategy, naturally resulting in a logarithmic complexity. The recursive approach has a logarithmic space complexity due to the stack frames it needs for each recursive call.

## Edge Cases

**Input Number is Zero**: According to the problem constraints, the input can be zero. Since zero is already reduced, no steps should be taken, and the function should return 0.

## Analyzing the Problem’s Simplicity and its Learning Points

Despite being a relatively straightforward problem, this question serves as an excellent introduction to:

**Basic Conditional Checks**: You need to determine whether the number is even or odd.**Looping Through Operations**: Whether using recursion or an iterative loop, you’re practicing how to navigate through a series of operations until a condition is met.**Understanding Time and Space Complexity**: It allows you to think about how efficient your solution is, even if the problem does not require an optimized solution due to its simplicity.

## Conclusion

The “Number of Steps to Reduce a Number to Zero” problem offers a delightful entry into the world of algorithmic problem-solving. Its seemingly straightforward nature makes it accessible, yet it offers avenues to explore more advanced topics like time and space complexity, recursion, and iterative vs. recursive approaches.