Leetcode #2044: Count Number of Maximum Bitwise-OR Subsets
In this guide, we solve Leetcode #2044 Count Number of Maximum Bitwise-OR Subsets in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Bit Manipulation, Array, Backtracking, Enumeration
Intuition
We must explore combinations of choices, but many branches can be pruned early.
Backtracking enumerates valid candidates while keeping the search space under control.
Approach
Use DFS to build candidates step by step, and backtrack when constraints are violated.
Pruning keeps the exploration practical for typical constraints.
Steps:
- Define the decision tree.
- DFS through choices and backtrack.
- Prune invalid paths early.
Example
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]
Python Solution
class Solution:
def countMaxOrSubsets(self, nums: List[int]) -> int:
def dfs(i, t):
nonlocal ans, mx
if i == len(nums):
if t == mx:
ans += 1
return
dfs(i + 1, t)
dfs(i + 1, t | nums[i])
ans = 0
mx = reduce(lambda x, y: x | y, nums)
dfs(0, 0)
return ans
Complexity
The time complexity is , and the space complexity is , where is the length of the array . The space complexity is , where is the length of the array .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.