#1342

Easy

LeetCode Problem Workspace

Number of Steps to Reduce a Number to Zero

Reduce a number to zero using bit manipulation and math. Simulate the process step-by-step based on whether the number is odd or even.

math bit manipulation

Problem Statement

Given an integer num, you need to determine how many steps it takes to reduce it to zero. In each step, if the number is even, divide it by 2. If the number is odd, subtract 1 from it. The process repeats until the number reaches zero.

For example, starting with num = 14, you would first divide by 2, resulting in 7. Then subtract 1 to get 6, divide by 2 to get 3, subtract 1 to get 2, divide by 2 to get 1, and finally subtract 1 to reach 0. The total number of steps is 6.

Examples

Example 1

Input: num = 14

Output: 6

Step 1) 14 is even; divide by 2 and obtain 7. Step 2) 7 is odd; subtract 1 and obtain 6. Step 3) 6 is even; divide by 2 and obtain 3. Step 4) 3 is odd; subtract 1 and obtain 2. Step 5) 2 is even; divide by 2 and obtain 1. Step 6) 1 is odd; subtract 1 and obtain 0.

Example 2

Input: num = 8

Output: 4

Step 1) 8 is even; divide by 2 and obtain 4. Step 2) 4 is even; divide by 2 and obtain 2. Step 3) 2 is even; divide by 2 and obtain 1. Step 4) 1 is odd; subtract 1 and obtain 0.

Example 3

Input: num = 123

Output: 12

Example details omitted.

Constraints

0 <= num <= 106

Solution Approach

Simulate the Steps

Simulate the process by repeatedly checking if the number is even or odd. If even, divide by 2, and if odd, subtract 1. Count the total number of steps taken.

Optimize with Bit Manipulation

For a faster solution, use bit manipulation to check if the number is even or odd. Use bitwise operators to quickly perform the division by 2 (right shift) or subtraction (subtract 1).

Edge Case Consideration

Make sure to handle the edge case where num = 0, as no steps are required to reduce zero to zero. Also, account for the maximum constraint where num can be as large as 1,000,000.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity depends on the number of steps required to reduce num to zero. Since each operation (either dividing by 2 or subtracting 1) reduces the problem size logarithmically, the time complexity is approximately O(log n). Space complexity is O(1) since only a few variables are used for computation.

What Interviewers Usually Probe

Can the candidate demonstrate the ability to break down a simple problem into smaller, manageable steps?
Does the candidate understand the use of bit manipulation for optimization?
Can the candidate explain edge cases and handle them efficiently?

Common Pitfalls or Variants

Common pitfalls

Failing to handle the edge case when num is 0.
Not leveraging bit manipulation for efficient computation, leading to slower solutions.
Forgetting to properly count the number of steps and incorrectly returning the result.

Follow-up variants

Optimize the solution by using bitwise operations to reduce time complexity.
Change the problem to require tracking the operations performed, such as adding an operation history.
Instead of counting steps, return the series of numbers obtained during the process.

FAQ

What is the main concept behind the 'Number of Steps to Reduce a Number to Zero' problem?

The problem involves reducing a number to zero by simulating the process of dividing by 2 if the number is even, or subtracting 1 if it's odd. The goal is to count how many steps it takes.

How can bit manipulation optimize solving the 'Number of Steps to Reduce a Number to Zero' problem?

Bit manipulation can optimize the solution by using bitwise operators to check if a number is even (right shift) or odd (subtract 1), which can speed up the process of dividing and subtracting.

What are the edge cases to consider when solving this problem?

The edge cases include when the input is 0 (no steps required) and when the number is large, ensuring that the solution remains efficient even for the maximum input value.

How is the time complexity determined for this problem?

The time complexity is determined by the number of steps needed to reduce num to zero, which is approximately O(log n) because each operation reduces the number by a factor of 2 or 1.

Can this problem be solved using recursion?

Yes, the problem can be solved using recursion by repeatedly calling the function for each step (dividing by 2 or subtracting 1) until the base case (0) is reached. However, iterative solutions are often preferred for efficiency.

terminal

Solution

Solution 1

#### Python3

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class Solution:
    def numberOfSteps(self, num: int) -> int:
        ans = 0
        while num:
            if num & 1:
                num -= 1
            else:
                num >>= 1
            ans += 1
        return ans

Solution 2

#### Python3

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class Solution:
    def numberOfSteps(self, num: int) -> int:
        ans = 0
        while num:
            if num & 1:
                num -= 1
            else:
                num >>= 1
            ans += 1
        return ans

Continue Practicing

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