What is the time complexity of Longest Subarray With Maximum Bitwise AND?

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

What data structures are used to solve Longest Subarray With Maximum Bitwise AND?

This problem uses Array, Bit Manipulation, Brainteaser. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Longest Subarray With Maximum Bitwise AND?

Insight 1: The maximum bitwise AND of any subarray of `nums` is the maximum element in `nums` itself. This is because a single element subarray's bitwise AND is the element itself. Insight 2: We don't need to compute bitwise ANDs of all possible subarrays. We just need to find the maximum number in the array and then find the longest contiguous subarray consisting only of that number.

Which companies ask LeetCode 2419. Longest Subarray With Maximum Bitwise AND in interviews?

This problem is frequently asked at fourkites.

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Longest Subarray With Maximum Bitwise AND - LeetCode 2419 Solution

Longest Subarray With Maximum Bitwise AND - Complete Solution Guide

Longest Subarray With Maximum Bitwise AND is LeetCode problem 2419, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given an integer array nums of size n . Consider a non-empty subarray from nums that has the maximum possible bitwise AND . In other words, let k be the maximum value of the bitwise AND of any subarray of nums . Then, only subarrays with a bitwise AND equal to k should be considered. Return the length of the longest such subarray . The bitwise AND of an array is the bitwise AND of all the numbers in it. A subarray is a contiguous sequence of elements within an array. Example 1: Input: nu

Detailed Explanation

The problem asks us to find the length of the longest subarray within a given integer array that has the maximum possible bitwise AND value. First, we need to determine what the maximum bitwise AND of any subarray could be. A crucial observation is that the maximum possible bitwise AND value of any subarray is simply the largest number in the array itself. Then we need to find the length of the longest subarray with elements that are equal to this maximum value.

Solution Approach

The solution involves a two-step process. First, we iterate through the array to find the maximum number. Second, we iterate through the array again, this time keeping track of the current length of a subarray consisting of only the maximum number. Whenever we encounter a number that is not equal to the maximum number, we reset the current length to 0. We continuously update the maximum length encountered so far.

Step-by-Step Algorithm

Step 1: Find the maximum number in the input array `nums`.
Step 2: Initialize `max_length` to 0 and `current_length` to 0.
Step 3: Iterate through the array `nums`.
Step 4: If the current number is equal to the maximum number, increment `current_length` by 1.
Step 5: If the current number is not equal to the maximum number, reset `current_length` to 0.
Step 6: Update `max_length` to the maximum of `max_length` and `current_length`.
Step 7: After iterating through the array, return `max_length`.

Key Insights

Insight 1: The maximum bitwise AND of any subarray of `nums` is the maximum element in `nums` itself. This is because a single element subarray's bitwise AND is the element itself.
Insight 2: We don't need to compute bitwise ANDs of all possible subarrays. We just need to find the maximum number in the array and then find the longest contiguous subarray consisting only of that number.
Insight 3: The problem can be solved using a single pass through the array after finding the maximum element.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Bit Manipulation, Brainteaser.

Companies

Asked at: fourkites.

Longest Subarray With Maximum Bitwise AND | LeetCode 2419

Medium

Array Bit Manipulation Brainteaser

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

Solution Code

Available in:

class Solution {
    public int longestSubarray(int[] nums) {
        int max_num = 0;
        for (int num : nums) {
            max_num = Math.max(max_num, num);
        }
        
        int max_length = 0;
        int current_length = 0;
        
        for (int num : nums) {
            if (num == max_num) {
                current_length += 1;
            } else {
                current_length = 0;
            }
            
            max_length = Math.max(max_length, current_length);
        }
        
        return max_length;
    }
}

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Problem Info

Description

Problem 2419: Longest Subarray With Maximum Bitwise AND - Detailed explanation and solution approaches.

Topics

Array Bit Manipulation Brainteaser

Companies

fourkites

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2419

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

7 steps

1
Step 1: Find the maximum number in the input array `nums`.
2
Step 2: Initialize `max_length` to 0 and `current_length` to 0.
3
Step 3: Iterate through the array `nums`.
4
Step 4: If the current number is equal to the maximum number, increment `current_length` by 1.
5
Step 5: If the current number is not equal to the maximum number, reset `current_length` to 0.
6
Step 6: Update `max_length` to the maximum of `max_length` and `current_length`.
7
Step 7: After iterating through the array, return `max_length`.

💡

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(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is determined by the number of iterations over the input array. Since we perform at most two iterations, the time complexity is O(n). The space complexity is constant because the amount of extra space used does not depend on the size of the input array.

📖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

Single Pass Approach

Combine finding the maximum and finding the longest subarray into a single loop. This avoids iterating over the array twice, but the core logic remains the same. During iteration, update the maximum element seen so far, if current element is greater than previously known maximum.

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

Trade-offs: This optimizes a small amount of overhead but doesn't change the fundamental complexity. In many languages, it would be considered to be slightly better style.

✨

Key Insights

1Insight 1: The maximum bitwise AND of any subarray of `nums` is the maximum element in `nums` itself. This is because a single element subarray's bitwise AND is the element itself.
2Insight 2: We don't need to compute bitwise ANDs of all possible subarrays. We just need to find the maximum number in the array and then find the longest contiguous subarray consisting only of that number.
3Insight 3: The problem can be solved using a single pass through the array after finding the maximum element.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Edge Cases

Edge case 1: An empty array. Although the constraints specify a minimum length of 1, handling an empty array gracefully is good practice. In this case, the code would likely throw an error in the max function. We would add a check at the beginning of the function to handle empty input arrays, returning 0 if nums is empty.
Edge case 2: An array with all the same numbers. In this case, the algorithm will correctly identify the maximum number (which will be the number itself), and the `max_length` will be equal to the length of the array.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly calculating the bitwise AND of subarrays. The problem statement can be misleading. It's easy to get bogged down in calculating the actual bitwise ANDs of various subarrays, but that's not necessary. The key insight is that the maximum possible bitwise AND is simply the largest element in the array.

✗Common mistake 2: Not resetting `current_length` when encountering a number that is not equal to the maximum number. This will lead to an incorrect `max_length`.

✅

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: Analyzing sensor data. Imagine a series of sensor readings, where a high reading indicates a critical event. You might want to find the longest continuous period where the sensor readings are at their maximum to determine the duration of the critical event.

🏦Real-world scenario 2: Stock market analysis. Identifying the longest period where a stock price remains at its peak value, indicating a period of sustained high performance.

💡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

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

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: August 19, 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

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 13

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

@DevExpert92Jul 6

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

@AlgoMasterJun 29

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Longest Subarray With Maximum Bitwise AND"?

For this medium-level Array 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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