What is the time complexity of Largest Combination With Bitwise AND Greater Than Zero?

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

What data structures are used to solve Largest Combination With Bitwise AND Greater Than Zero?

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

What are the key insights for solving Largest Combination With Bitwise AND Greater Than Zero?

Insight 1: We don't need to generate all combinations explicitly. Instead, we can iterate through each bit position (0 to 23, since 2^24 > 10^7) and count how many numbers have that bit set to 1. This avoids generating all possible combinations, which would be computationally expensive. Insight 2: If a particular bit position has 'k' numbers with that bit set to 1, any combination of these 'k' numbers will have a bitwise AND greater than 0 (specifically, the value of that bit).

Which companies ask LeetCode 2275. Largest Combination With Bitwise AND Greater Than Zero in interviews?

This problem is frequently asked at Jump Trading.

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Largest Combination With Bitwise AND Greater Than Zero - LeetCode 2275 Solution

Largest Combination With Bitwise AND Greater Than Zero - Complete Solution Guide

Largest Combination With Bitwise AND Greater Than Zero is LeetCode problem 2275, 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

The bitwise AND of an array nums is the bitwise AND of all integers in nums . For example, for nums = [1, 5, 3] , the bitwise AND is equal to 1 & 5 & 3 = 1 . Also, for nums = [7] , the bitwise AND is 7 . You are given an array of positive integers candidates . Compute the bitwise AND for all possible combinations of elements in the candidates array. Return the size of the largest combination of candidates with a bitwise AND greater than 0 . Example 1: Input: candidates = [16,17,71,62,12,24,14] O

Detailed Explanation

The problem asks us to find the largest possible combination of numbers from a given array `candidates` such that the bitwise AND of all the numbers in the combination is greater than 0. We need to iterate through all possible combinations and find the one with the maximum size that satisfies the AND condition. The constraints are that the array length is up to 10^5, and each number is between 1 and 10^7.

Solution Approach

The solution iterates through each bit position from 0 to 23 (since the largest number is less than 2^24). For each bit position, it counts the number of elements in the `candidates` array that have that bit set to 1. The maximum count across all bit positions is the answer. This is because the bitwise AND of any combination of the numbers having that particular bit set will result in a value greater than 0.

Step-by-Step Algorithm

Step 1: Initialize `max_len` to 0. This variable will store the maximum size of a valid combination found so far.
Step 2: Iterate through the bit positions from 0 to 23 (inclusive). This is because the largest number in candidates is less than 2^24, so we only need to check up to the 23rd bit.
Step 3: For each bit position `i`, initialize `current_len` to 0. This variable will store the number of elements in the `candidates` array that have the i-th bit set to 1.
Step 4: Iterate through the `candidates` array. For each number `num`, check if the i-th bit is set to 1 using the bitwise AND operator `(num >> i) & 1`. If it is set, increment `current_len`.
Step 5: After iterating through all the numbers in `candidates` for the current bit position `i`, update `max_len` with the maximum of `max_len` and `current_len`. This ensures that `max_len` always stores the maximum size of a valid combination found so far.
Step 6: After iterating through all the bit positions, return `max_len`.

Key Insights

Insight 1: We don't need to generate all combinations explicitly. Instead, we can iterate through each bit position (0 to 23, since 2^24 > 10^7) and count how many numbers have that bit set to 1. This avoids generating all possible combinations, which would be computationally expensive.
Insight 2: If a particular bit position has 'k' numbers with that bit set to 1, any combination of these 'k' numbers will have a bitwise AND greater than 0 (specifically, the value of that bit).
Insight 3: We are looking for the *largest* combination, so for each bit position, we are interested in the *count* of numbers with that bit set, as it indicates the size of a potential combination.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Hash Table, Bit Manipulation, Counting.

Companies

Asked at: Jump Trading.

Largest Combination With Bitwise AND Greater Than Zero | LeetCode 2275

Medium

Array Hash Table Bit Manipulation Counting

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

Solution Code

Available in:

class Solution {
    public int largestCombination(int[] candidates) {
        int max_len = 0;
        for (int i = 0; i < 24; i++) {
            int current_len = 0;
            for (int num : candidates) {
                if (((num >> i) & 1) > 0) {
                    current_len++;
                }
            }
            max_len = Math.max(max_len, current_len);
        }
        return max_len;
    }
}

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Problem Info

Description

Problem 2275: Largest Combination With Bitwise AND Greater Than Zero - Detailed explanation and solution approaches.

Topics

Array Hash Table Bit Manipulation Counting

Companies

Jump Trading

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2275

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 `max_len` to 0. This variable will store the maximum size of a valid combination found so far.
2
Step 2: Iterate through the bit positions from 0 to 23 (inclusive). This is because the largest number in candidates is less than 2^24, so we only need to check up to the 23rd bit.
3
Step 3: For each bit position `i`, initialize `current_len` to 0. This variable will store the number of elements in the `candidates` array that have the i-th bit set to 1.
4
Step 4: Iterate through the `candidates` array. For each number `num`, check if the i-th bit is set to 1 using the bitwise AND operator `(num >> i) & 1`. If it is set, increment `current_len`.
5
Step 5: After iterating through all the numbers in `candidates` for the current bit position `i`, update `max_len` with the maximum of `max_len` and `current_len`. This ensures that `max_len` always stores the maximum size of a valid combination found so far.
6
Step 6: After iterating through all the bit positions, return `max_len`.

💡

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 nested loops. The outer loop iterates a fixed number of times (24), making it a constant factor. The inner loop iterates through the `candidates` array. The space complexity is constant because it only uses a few integer variables, regardless of 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

Bitset Approach

We can use a bitset to represent each number. Then, for each bit position, iterate through the candidates and check if the corresponding bit is set in the bitset. The number of set bits would then be counted.

Time: O(n)Space: O(1). The size of bitset will be constant as the constraint on the size of numbers is limited.

Trade-offs: Bitset approach can be faster depending on the hardware and compiler optimizations, but its essentially similar to the provided solution in time complexity. It might be slightly more readable.

✨

Key Insights

1Insight 1: We don't need to generate all combinations explicitly. Instead, we can iterate through each bit position (0 to 23, since 2^24 > 10^7) and count how many numbers have that bit set to 1. This avoids generating all possible combinations, which would be computationally expensive.
2Insight 2: If a particular bit position has 'k' numbers with that bit set to 1, any combination of these 'k' numbers will have a bitwise AND greater than 0 (specifically, the value of that bit).
3Insight 3: We are looking for the *largest* combination, so for each bit position, we are interested in the *count* of numbers with that bit set, as it indicates the size of a potential combination.

📚

Key Terms Explained

For Students

Array

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

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

Edge Cases

Edge case 1: An empty `candidates` array. The algorithm correctly returns 0 in this case, because the `current_len` will always be 0, and `max_len` is initialized to 0.
Edge case 2: A `candidates` array where all numbers are 0. The algorithm correctly returns 0 in this case, since no bit is ever set.
Edge case 3: A `candidates` array containing only one number. The algorithm will check each bit of that number and return 1 if any bit is set, otherwise 0, both of which are correct.
Edge case 4: A `candidates` array where all numbers are the same. This doesn't change the algorithm's execution and the answer will be the length of the array if the numbers are non-zero.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Trying to generate all combinations of numbers explicitly. This approach has an exponential time complexity (O(2^n)) and will likely result in a Time Limit Exceeded (TLE) error.

✗Common mistake 2: Incorrectly calculating the bitwise AND. Understanding how the bitwise AND operator works is crucial to solve this problem.

✗Common mistake 3: Not considering all the bit positions. For numbers up to 10^7, you need to check up to the 23rd bit (0-indexed), not fewer bits.

✅

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: Database indexing. Finding sets of data records that have certain bits in common can improve query performance in databases.

🏦Real-world scenario 2: Network routing. Determining which network nodes share certain characteristics (represented as bits) can help optimize routing protocols.

🎮Real-world scenario 3: Data analysis. Identifying common attributes (represented as bits) among data points can reveal patterns and insights.

💡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.

👨‍💻 From Experience

This problem pattern appears frequently in real codebases. I've used similar logic when building production systems.

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: September 24, 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 13

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

@AlgoMasterJul 6

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJun 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 do I choose between a hash map and a hash set?

Use a hash set when you only need to track presence/absence of elements (like detecting duplicates). Use a hash map when you need to associate values with keys (like counting frequencies or storing indices). Hash sets use less memory since they only store keys.

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 "Largest Combination With Bitwise AND Greater Than Zero"?

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 hash table techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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