How do you solve Maximum Bitwise AND After Increment Operations on LeetCode?

Maximum Bitwise AND After Increment Operations (LeetCode #3806) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Maximizing bits from highest to lowest is efficient.

What is the time complexity of Maximum Bitwise AND After Increment Operations?

The optimal solution for Maximum Bitwise AND After Increment Operations runs in O(n) time and uses O(1) space. The complexity is linear since we iterate through the bits (constant) and check each number once.

What is the brute force solution for Maximum Bitwise AND After Increment Operations?

The brute force approach for Maximum Bitwise AND After Increment Operations is Brute Force, with O(n²) time complexity and O(1) space complexity. Try every possible subset of size m, incrementing elements as needed to maximize the AND result. This method checks all combinations, which is inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Bitwise AND After Increment Operations?

Maximum Bitwise AND After Increment Operations uses the following concepts: Array, Greedy, Bit Manipulation, Sorting. The recommended patterns to study are: Greedy, Bit Manipulation.

What are the interview tips for Maximum Bitwise AND After Increment Operations?

Explain your thought process clearly. Discuss edge cases, like all elements being the same. Practice bit manipulation problems regularly.

What are common mistakes when solving Maximum Bitwise AND After Increment Operations?

Not considering all bits when checking increments. Failing to track the number of operations used correctly.

#3806

Maximum Bitwise AND After Increment Operations

Hard

ArrayGreedyBit ManipulationSortingGreedyBit Manipulation

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)

Use a greedy approach to maximize the AND bit by bit, starting from the highest bit. This ensures we use increments efficiently.

⚙️

Algorithm

3 steps

1Step 1: Iterate from the highest bit to the lowest (31 to 0).
2Step 2: For each bit, check if we can set it in the result by counting how many numbers can be incremented to have that bit set.
3Step 3: If we can set the bit with available increments, update the result.

solution.py9 lines

1def max_bitwise_and(nums, k, m):
2    res = 0
3    for bit in range(31, -1, -1):
4        count = sum((num | res) >> bit & 1 for num in nums)
5        needed = m - count
6        if needed <= k:
7            res |= (1 << bit)
8            k -= needed
9    return res

ℹ

Complexity note: The complexity is linear since we iterate through the bits (constant) and check each number once.

1Maximizing bits from highest to lowest is efficient.
2Increment operations should be used wisely to achieve the desired bitwise AND.

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