How do you solve Maximum OR on LeetCode?

Maximum OR (LeetCode #2680) 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 OR is best achieved by focusing operations on a single element.

What is the brute force solution for Maximum OR?

The brute force approach for Maximum OR is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves trying every possible combination of multiplying elements by 2 up to k times. This means we will calculate the OR for each possible configuration of the array after applying the operations. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum OR?

Maximum OR uses the following concepts: Array, Greedy, Bit Manipulation, Prefix Sum. The recommended patterns to study are: Bit Manipulation, Greedy Algorithms.

What are the interview tips for Maximum OR?

Explain your thought process clearly when discussing brute-force vs. optimal approaches. Be ready to justify why you chose to optimize in a certain way. Practice similar problems to recognize patterns in OR operations.

What are common mistakes when solving Maximum OR?

Not considering that all operations should be applied to one number. Forgetting to calculate the initial OR before modifications.

#2680

Maximum OR

Medium

ArrayGreedyBit ManipulationPrefix SumBit ManipulationGreedy Algorithms

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)

Instead of trying all combinations, we can focus on maximizing the OR by applying all k operations to a single element. This is because multiplying one number maximally increases its contribution to the overall OR.

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Algorithm

3 steps

1Step 1: Calculate the initial OR of the entire array.
2Step 2: For each element, calculate the OR after applying k multiplications to that element.
3Step 3: Keep track of the maximum OR obtained from all elements.

solution.py10 lines

1def maxOR(nums, k):
2    initial_or = 0
3    for num in nums:
4        initial_or |= num
5    max_or = initial_or
6    for num in nums:
7        modified_num = num * (2 ** k)
8        current_or = initial_or | modified_num
9        max_or = max(max_or, current_or)
10    return max_or

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Complexity note: This complexity is linear because we only traverse the array a couple of times, making it efficient for large inputs.

1Maximizing OR is best achieved by focusing operations on a single element.
2The bitwise OR operation accumulates bits, so larger numbers contribute more.

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