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 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.

Largest Combination With Bitwise AND Greater Than Zero — LeetCode #2275 (Medium)

Tags: Array, Hash Table, Bit Manipulation, Counting

Related patterns: Hash Map, Array

Brute Force approach

Time complexity: O(n²). Space complexity: O(1).

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 time complexity is O(n²) because we are generating combinations and calculating the AND for each one, which can take up to n operations for each combination.

Step 1: Generate all possible combinations of the elements in the candidates array.
Step 2: For each combination, calculate the bitwise AND of its elements.
Step 3: Keep track of the size of the largest combination that has a bitwise AND greater than 0.

For candidates = [16, 17, 71, 62, 12, 24, 14]: 1. r = 1: combinations = [16], AND = 16 (size = 1) 2. r = 2: combinations = [16, 17], AND = 0 (size = 2) 3. r = 3: combinations = [16, 17, 71], AND = 0 (size = 3) 4. r = 4: combinations = [16, 17, 62, 24], AND = 16 (size = 4) 5. r = 5: combinations = [16, 17, 71, 62, 12], AND = 0 (size = 5) 6. r = 6: combinations = [16, 17, 71, 62, 12, 24], AND = 0 (size = 6) Final max size = 4.

Optimal Solution approach

Time complexity: O(n). Space complexity: 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.

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.

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

For candidates = [16, 17, 71, 62, 12, 24, 14]: 1. count = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 2. num = 16: count[4] = 1 3. num = 17: count[0] = 1, count[4] = 2 4. num = 71: count[0] = 2, count[1] = 1, count[2] = 1, count[4] = 3 5. num = 62: count[1] = 2, count[2] = 2, count[4] = 4 6. num = 12: count[2] = 3, count[3] = 1, count[4] = 5 Final max count = 5.

Key Insights

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

Common Mistakes

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.

Interview Tips

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.

#2275

Largest Combination With Bitwise AND Greater Than Zero

Medium

Array↗Hash Table↗Bit Manipulation↗Counting↗Hash Map↗Array↗

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(1)

⚙️

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.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.