Introduction

In this blog post, we will explore how to solve the LeetCode problem "2044" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

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. 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

Explanation

Here's the approach and Python code to solve this problem:

• Find the Maximum OR: First, calculate the maximum possible bitwise OR value that can be achieved from any subset of the input array nums.

• Count Subsets with Maximum OR: Iterate through all possible non-empty subsets of nums and count the number of subsets whose bitwise OR equals the maximum OR value found in the previous step.

• Runtime Complexity: O(n * 2ⁿ), where n is the length of nums.

• Storage Complexity: O(1)

Code

    def count_max_or_subsets(nums):
    """
    Finds the maximum possible bitwise OR of a subset of nums and returns the
    number of different non-empty subsets with the maximum bitwise OR.
    """
    max_or = 0
    for num in nums:
        max_or |= num

    count = 0
    n = len(nums)

    for i in range(1, 1 << n):  # Iterate through all non-empty subsets
        current_or = 0
        for j in range(n):
            if (i >> j) & 1:
                current_or |= nums[j]

        if current_or == max_or:
            count += 1

    return count