Introduction

In this blog post, we will explore how to solve the LeetCode problem "1863" 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

The XOR total of an array is defined as the bitwise XOR of all its elements, or 0 if the array is empty. For example, the XOR total of the array [2,5,6] is 2 XOR 5 XOR 6 = 1. Given an array nums, return the sum of all XOR totals for every subset of nums. Note: Subsets with the same elements should be counted multiple times. 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. Example 1: Input: nums = [1,3] Output: 6 Explanation: The 4 subsets of [1,3] are: - The empty subset has an XOR total of 0. - [1] has an XOR total of 1. - [3] has an XOR total of 3. - [1,3] has an XOR total of 1 XOR 3 = 2. 0 + 1 + 3 + 2 = 6 Example 2: Input: nums = [5,1,6] Output: 28 Explanation: The 8 subsets of [5,1,6] are: - The empty subset has an XOR total of 0. - [5] has an XOR total of 5. - [1] has an XOR total of 1. - [6] has an XOR total of 6. - [5,1] has an XOR total of 5 XOR 1 = 4. - [5,6] has an XOR total of 5 XOR 6 = 3. - [1,6] has an XOR total of 1 XOR 6 = 7. - [5,1,6] has an XOR total of 5 XOR 1 XOR 6 = 2. 0 + 5 + 1 + 6 + 4 + 3 + 7 + 2 = 28 Example 3: Input: nums = [3,4,5,6,7,8] Output: 480 Explanation: The sum of all XOR totals for every subset is 480. Constraints: 1 <= nums.length <= 12 1 <= nums[i] <= 20

Explanation

Here's a breakdown of the solution:

• Subset Generation: The core idea is to iterate through all possible subsets of the input array nums. Since each element can either be present or absent in a subset, there are 2ⁿ subsets for an array of size n.
• XOR Calculation: For each subset, compute the XOR total by XORing all its elements. If the subset is empty, the XOR total is 0.

• Summation: Accumulate the XOR totals of all subsets to get the final result.

• Time and Space Complexity: The time complexity is O(n * 2ⁿ) because we iterate through all 2ⁿ subsets and, in the worst case, XOR up to n elements for each subset. The space complexity is O(1) as we use a constant amount of extra space.

Code

    def subsetXORSum(nums):
    """
    Calculates the sum of XOR totals for every subset of nums.

    Args:
        nums: A list of integers.

    Returns:
        The sum of all XOR totals for every subset of nums.
    """

    n = len(nums)
    total_xor_sum = 0

    for i in range(2**n):
        current_xor_sum = 0
        for j in range(n):
            if (i >> j) & 1:
                current_xor_sum ^= nums[j]
        total_xor_sum += current_xor_sum

    return total_xor_sum