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2044. Count Number of Maximum Bitwise-OR Subsets

Difficulty Topics

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.

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

Solution

count-number-of-maximum-bitwise-or-subsets.py
class Solution:
    def countMaxOrSubsets(self, nums: List[int]) -> int:
        n = len(nums)
        mp = collections.defaultdict(int)
        mmax = 0

        for x in nums: mmax |= x

        for mask in range(1, 1 << n):
            s = 0
            for j in range(n):
                if (mask >> j) & 1:
                    s |= nums[j]

            mp[s] += 1

        return mp[mmax]