Smallest Subarrays With Maximum Bitwise OR

Problem Description

You are given a 0-indexed array nums of length n, consisting of non-negative integers. For each index i from 0 to n - 1, you must determine the size of the minimum sized non-empty subarray of nums starting at i (inclusive) that has the maximum possible bitwise OR.

Key Insights

• The bitwise OR operation combines bits from multiple numbers, resulting in a value that retains 1s in any position where at least one number has a 1.
• The maximum possible bitwise OR for a given starting index can be computed by considering all subsequent elements.
• The goal is to find the shortest contiguous subarray starting from each index that achieves this maximum bitwise OR.
• A naive solution would examine all possible subarrays, leading to a time complexity of O(n^2), which is inefficient for larger arrays.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

To solve this problem efficiently, we can use a sliding window approach combined with a greedy strategy. We maintain the maximum bitwise OR value encountered as we iterate through the array. For each starting index i, we progressively expand the subarray until we reach the maximum OR value. We also keep track of the size of this subarray to ensure we find the minimum length needed.

1. Initialize an array answer to store the result.
2. Iterate through each index i from 0 to n - 1.
3. For each index i, initialize a variable current_or to track the bitwise OR value and another variable length to count the size of the subarray.
4. Expand the subarray by adding elements until the current_or is equal to the maximum OR value found from index i.
5. Store the length of the subarray in the answer array.

This approach ensures that we efficiently compute the answer in linear time.

Code Solutions