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

The optimal solution for Largest Combination With Bitwise AND Greater Than Zero runs in O(n) time and uses O(1) space. The time complexity is O(n) because we iterate through the candidates once and check each of the 24 bits, which is a constant factor.

What is the brute force solution for Largest Combination With Bitwise AND Greater Than Zero?

The brute force approach for Largest Combination With Bitwise AND Greater Than Zero is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible combinations of the array elements and calculating their bitwise AND. This is straightforward but inefficient, especially for larger arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Largest Combination With Bitwise AND Greater Than Zero?

Largest Combination With Bitwise AND Greater Than Zero uses the following concepts: Array, Hash Table, Bit Manipulation, Counting. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Largest Combination With Bitwise AND Greater Than Zero?

Always start with a brute force solution to understand the problem better. Look for patterns in the data, especially with bit manipulation problems. Discuss your thought process out loud during the interview to demonstrate your understanding.

What are common mistakes when solving Largest Combination With Bitwise AND Greater Than Zero?

Students often try to brute-force combinations without realizing the inefficiency. Failing to consider the properties of bitwise operations can lead to incorrect assumptions about the problem.

#2275

Largest Combination With Bitwise AND Greater Than Zero

Medium

ArrayHash TableBit ManipulationCountingHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution leverages the fact that for the bitwise AND to be greater than zero, we can focus on each bit position and count how many numbers have that bit set. The maximum count for any bit position gives us the size of the largest combination.

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Algorithm

3 steps

1Step 1: Initialize an array to count occurrences of each bit position (up to 24 bits).
2Step 2: For each number in the candidates, update the count for each bit position that is set (1).
3Step 3: The maximum value in the count array is the size of the largest combination with a bitwise AND greater than 0.

solution.py7 lines

1def largestCombination(candidates):
2    count = [0] * 24
3    for num in candidates:
4        for i in range(24):
5            if num & (1 << i):
6                count[i] += 1
7    return max(count)

ℹ

Complexity note: The time complexity is O(n) because we iterate through the candidates once and check each of the 24 bits, which is a constant factor.

1The bitwise AND operation requires at least one bit to be 1 in all numbers for the result to be greater than 0.
2Focusing on individual bit positions allows us to efficiently count potential combinations.

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