How do you solve Number of Steps to Reduce a Number to Zero on LeetCode?

Number of Steps to Reduce a Number to Zero (LeetCode #1342) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(log n) time complexity and O(1) space complexity. Key insight: Understanding binary representation can simplify problems involving powers of two.

What is the brute force solution for Number of Steps to Reduce a Number to Zero?

The brute force approach for Number of Steps to Reduce a Number to Zero is Brute Force, with O(n) time complexity and O(1) space complexity. The brute-force approach simulates the process of reducing the number to zero by repeatedly applying the rules: divide by 2 if even, or subtract 1 if odd. This approach is straightforward and easy to understand, as it directly follows the problem's instructions. The optimal Optimal Solution approach improves this to O(log n).

What algorithm or data structure is used to solve Number of Steps to Reduce a Number to Zero?

Number of Steps to Reduce a Number to Zero uses the following concepts: Math, Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Binary Representation.

What are the interview tips for Number of Steps to Reduce a Number to Zero?

Always clarify the problem requirements before jumping into coding. Think about edge cases and test your solution against them. If time allows, try to optimize your solution after implementing the brute force.

What are common mistakes when solving Number of Steps to Reduce a Number to Zero?

Not considering edge cases like num = 0. Overcomplicating the problem instead of simulating the process.

#1342

Number of Steps to Reduce a Number to Zero

Easy

MathBit ManipulationBit ManipulationBinary Representation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n)	O(log n)
Space	O(1)	O(1)

💡

Intuition

Time O(log n)Space O(1)

The optimal solution leverages the properties of binary representation. Each time we divide by 2, we are effectively shifting the bits of the number to the right. This means that the number of steps can be calculated based on the number of bits in the binary representation of the number, along with the number of 1s (which represent the odd numbers).

⚙️

Algorithm

3 steps

1Step 1: Count the number of bits in the binary representation of num.
2Step 2: Count the number of 1s in the binary representation of num.
3Step 3: The total steps will be the number of bits (which represents the divisions by 2) plus the number of 1s (which represents the subtractions).

solution.py2 lines

1def numberOfSteps(num):
2    return bin(num).count('1') + num.bit_length() - 1

ℹ

Complexity note: The time complexity is O(log n) because we are dealing with the number of bits in the binary representation of num. The space complexity is O(1) as we are not using any additional data structures.

1Understanding binary representation can simplify problems involving powers of two.
2Counting bits can often lead to more efficient solutions.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.