What is the time complexity of Reverse Bits?

The optimal solution has a time complexity of O(1).

What data structures are used to solve Reverse Bits?

This problem uses Divide and Conquer, Bit Manipulation. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Reverse Bits?

Insight 1: Understanding bitwise operators is crucial. We need to use bit shifting (` >`, `>>>`) and bitwise AND (`&`) to isolate and manipulate individual bits. Insight 2: Iterating through the bits of the integer is necessary to reverse them one by one. A loop is the natural choice for this task.

Which companies ask LeetCode 190. Reverse Bits in interviews?

This problem is frequently asked at Airbnb, Nvidia, Qualcomm.

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Reverse Bits - LeetCode 190 Solution

Reverse Bits - Complete Solution Guide

Reverse Bits is LeetCode problem 190, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Reverse bits of a given 32 bits unsigned integer. Note: Note that in some languages, such as Java, there is no unsigned integer type. In this case, both input and output will be given as a signed integer type. They should not affect your implementation, as the integer's internal binary representation is the same, whether it is signed or unsigned. In Java, the compiler represents the signed integers using 2's complement notation . Example 1: Input: n = 43261596 Output: 964176192 Explanation: Inte

Detailed Explanation

The problem asks you to reverse the bits of a 32-bit unsigned integer. The input is a single integer, `n`. The output is the integer formed by reversing the order of its bits. For example, if the input is represented in binary as `00000010100101000001111010011100`, the output should be `00111001011110000010100101000000`. The problem emphasizes that even though some languages (like Java) don't have unsigned integers, the underlying binary representation remains the same and should be treated as such.

Solution Approach

The provided solutions employ a loop that iterates 32 times (once for each bit). In each iteration, the least significant bit (LSB) of the input `n` is extracted using a bitwise AND operation (`n & 1`). This LSB is then shifted to its corresponding reversed position in the `result` variable using a left bit shift (`<<`). The input `n` is then right-shifted (`>>` in Python, C++, `>>>` in Java) to prepare for the next bit. This process continues until all 32 bits are processed.

Step-by-Step Algorithm

Step 1: Initialize a `result` variable to 0. This variable will store the reversed bits.
Step 2: Iterate 32 times using a `for` loop (representing the 32 bits).
Step 3: Extract the LSB of `n` using `n & 1`.
Step 4: Shift the extracted LSB to its reversed position in `result` using `bit << (31 - i)` (Python) or `result <<= 1; result |= (n & 1);` (C++, Java, C).
Step 5: Right-shift `n` by 1 bit (`n >>= 1` or `n >>>= 1`) to process the next bit.
Step 6: After the loop completes, `result` contains the reversed bits of `n`.

Key Insights

Insight 1: Understanding bitwise operators is crucial. We need to use bit shifting (`<<`, `>>`, `>>>`) and bitwise AND (`&`) to isolate and manipulate individual bits.
Insight 2: Iterating through the bits of the integer is necessary to reverse them one by one. A loop is the natural choice for this task.
Insight 3: The use of a bitmask (`& 1`) efficiently isolates the least significant bit (LSB) in each iteration.

Complexity Analysis

Time Complexity: O(1)

Space Complexity: O(1)

Topics

This problem involves: Divide and Conquer, Bit Manipulation.

Companies

Asked at: Airbnb, Nvidia, Qualcomm.

Reverse Bits | LeetCode 190

Easy

Divide and Conquer Bit Manipulation

Time: O(1)Space: O(1)

Solution Code

Available in:

class Solution {
    public int reverseBits(int n) {
        int result = 0;
        for (int i = 0; i < 32; i++) {
            result <<= 1;
            result |= (n & 1);
            n >>>= 1;
        }
        return result;
    }
}

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Problem Info

Description

Problem 190: Reverse Bits - Detailed explanation and solution approaches.

Topics

Divide and Conquer Bit Manipulation

Companies

AirbnbNvidiaQualcomm

Stats

Difficulty:Easy

Languages:4

Companies:3

Problem #:190

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

6 steps

1
Step 1: Initialize a `result` variable to 0. This variable will store the reversed bits.
2
Step 2: Iterate 32 times using a `for` loop (representing the 32 bits).
3
Step 3: Extract the LSB of `n` using `n & 1`.
4
Step 4: Shift the extracted LSB to its reversed position in `result` using `bit << (31 - i)` (Python) or `result <<= 1; result |= (n & 1);` (C++, Java, C).
5
Step 5: Right-shift `n` by 1 bit (`n >>= 1` or `n >>>= 1`) to process the next bit.
6
Step 6: After the loop completes, `result` contains the reversed bits of `n`.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(1)

⚡ Constant time - Super fast! Same speed regardless of input size.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The number of iterations is fixed at 32, regardless of the input value. The algorithm performs a constant number of operations for a 32-bit integer. Therefore, both time and space complexity are constant.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Lookup Table

Precompute a lookup table that maps each 32-bit integer to its reversed counterpart. This would involve a significant amount of preprocessing, but subsequent calls to the function would be O(1).

Time: O(1) for lookup (O(2^32) for table creation)Space: O(2^32)

Trade-offs: This approach is advantageous only if the function is called many times. The substantial space complexity makes it impractical for most scenarios.

Bit manipulation with multiple bit swaps

Instead of one bit at a time, swap groups of bits (e.g., nibbles or bytes) to improve speed slightly. This is more complex to implement but may have some performance benefit.

Time: O(1)Space: O(1)

Trade-offs: Slightly faster, but more complex code, so not always worth the trade-off.

✨

Key Insights

1Insight 1: Understanding bitwise operators is crucial. We need to use bit shifting (`<<`, `>>`, `>>>`) and bitwise AND (`&`) to isolate and manipulate individual bits.
2Insight 2: Iterating through the bits of the integer is necessary to reverse them one by one. A loop is the natural choice for this task.
3Insight 3: The use of a bitmask (`& 1`) efficiently isolates the least significant bit (LSB) in each iteration.

📚

Key Terms Explained

For Students

Edge Cases

Edge case 1: n = 0. The solution correctly handles this case by returning 0.
Edge case 2: n = maximum 32-bit integer (2^31 - 1 or 2^31 -2 depending on the constraints and signed/unsigned distinction). The algorithm still functions correctly, reversing all the bits.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrect use of bitwise operators. Confusing `>>` and `>>>` (Java) or using the wrong combination of AND and shift operators leads to incorrect results.

✗Common mistake 2: Off-by-one errors in the loop or bit shifting indices. Careful attention to the loop bounds and bit positions is essential for a correct solution.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Network programming. Reversing bits might be necessary for byte order conversion in network protocols.

🏦Real-world scenario 2: Cryptography. Bit manipulation is fundamental to many cryptographic algorithms, and bit reversal could be a part of a larger cryptographic function.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Use this problem to demonstrate clean code practices. Variable naming and code organization matter.

⚠️ Watch Out

Always test your solution with edge cases: empty input, single element, and boundary values.

👨‍💻 From Experience

This is one of the first problems I solved when learning Divide and Conquer. It's a great foundation for more complex problems.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: June 11, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 14

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 7

❓

Frequently Asked Questions

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Reverse Bits"?

For this easy-level Divide and Conquer problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether bit manipulation techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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