Count Number of Maximum Bitwise-OR Subsets

Problem Description

Given an integer array nums, find the maximum possible bitwise OR of a subset of nums and return the number of different non-empty subsets with the maximum bitwise OR.

Key Insights

• The maximum bitwise OR of a subset can be obtained by performing a bitwise OR on all elements in the subset.
• To find the number of subsets that achieve this maximum, we need to consider the unique elements that contribute to the maximum OR.
• The total number of non-empty subsets of a collection of elements is given by 2^n - 1, where n is the number of elements.

Space and Time Complexity

Time Complexity: O(n), where n is the length of the input array, as we only need to iterate through the array a few times. Space Complexity: O(1), as we are using a constant amount of space for variables.

Solution

To solve the problem, we can use the following approach:

1. First, iterate through the nums array to compute the maximum possible bitwise OR by ORing all elements together.
2. Then, identify all elements in nums that contribute to this maximum bitwise OR.
3. Count how many times each of these elements appears in the original array.
4. The number of different non-empty subsets that can be formed using these elements is calculated as 2^(count of unique elements) - 1, where we include all possible combinations of these elements.

Code Solutions