<div> 🟡 2024-10-18 #array #backtracking #bit_manipulation #enumeration </div>Given an integer array <code>nums</code>, find the maximum possible bitwise OR of a subset of <code>nums</code> and return the number of different non-empty subsets with the maximum bitwise OR.

An array <code>a</code> is a subset of an array <code>b</code> if <code>a</code> can be obtained from <code>b</code> by deleting some (possibly zero) elements of <code>b</code>. Two subsets are considered different if the indices of the elements chosen are different.

The bitwise OR of an array <code>a</code> is equal to <code>a[0] OR a[1] OR ... OR a[a.length - 1]</code> (0-indexed).

&nbsp;
Example 1:

<pre>Input: nums = [3,1]
Output: 2
Explanation: The maximum possible bitwise OR of a subset is 3. There are 2 subsets with a bitwise OR of 3:
- [3]
- [3,1]
</pre>

Example 2:

<pre>Input: nums = [2,2,2]
Output: 7
Explanation: All non-empty subsets of [2,2,2] have a bitwise OR of 2. There are 23 - 1 = 7 total subsets.
</pre>

Example 3:

<pre>Input: nums = [3,2,1,5]
Output: 6
Explanation: The maximum possible bitwise OR of a subset is 7. There are 6 subsets with a bitwise OR of 7:
- [3,5]
- [3,1,5]
- [3,2,5]
- [3,2,1,5]
- [2,5]
- [2,1,5]</pre>

&nbsp;
Constraints:

<ul>
<li><code>1 &lt;= nums.length &lt;= 16</code></li>
<li><code>1 &lt;= nums[i] &lt;= 105</code></li>
</ul>

🟡 2024-10-18 
 #array #backtracking #bit_manipulation #enumeration 

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.
An array a is a subset of an array b if a can be obtained from b by deleting some (possibly zero) elements of b. Two subsets are considered different if the indices of the elements chosen are different.
The bitwise OR of an array a is equal to a[0] OR a[1] OR ... OR a[a.length - 1] (0-indexed).
 
Example 1:
Input: nums = [3,1]
Output: 2
Explanation: The maximum possible bitwise OR of a subset is 3. There are 2 subsets with a bitwise OR of 3:
- [3]
- [3,1]


Example 2:
Input: nums = [2,2,2]
Output: 7
Explanation: All non-empty subsets of [2,2,2] have a bitwise OR of 2. There are 23 - 1 = 7 total subsets.


Example 3:
Input: nums = [3,2,1,5]
Output: 6
Explanation: The maximum possible bitwise OR of a subset is 7. There are 6 subsets with a bitwise OR of 7:
- [3,5]
- [3,1,5]
- [3,2,5]
- [3,2,1,5]
- [2,5]
- [2,1,5]
 
Constraints:
1 <= nums.length <= 16
1 <= nums[i] <= 105

2044.count-number-of-maximum-bitwise-or-subsets