Introduction

In this blog post, we will explore how to solve the LeetCode problem "2317" 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

You are given a 0-indexed integer array nums. In one operation, select any non-negative integer x and an index i, then update nums[i] to be equal to nums[i] AND (nums[i] XOR x). Note that AND is the bitwise AND operation and XOR is the bitwise XOR operation. Return the maximum possible bitwise XOR of all elements of nums after applying the operation any number of times. Example 1: Input: nums = [3,2,4,6] Output: 7 Explanation: Apply the operation with x = 4 and i = 3, num[3] = 6 AND (6 XOR 4) = 6 AND 2 = 2. Now, nums = [3, 2, 4, 2] and the bitwise XOR of all the elements = 3 XOR 2 XOR 4 XOR 2 = 7. It can be shown that 7 is the maximum possible bitwise XOR. Note that other operations may be used to achieve a bitwise XOR of 7. Example 2: Input: nums = [1,2,3,9,2] Output: 11 Explanation: Apply the operation zero times. The bitwise XOR of all the elements = 1 XOR 2 XOR 3 XOR 9 XOR 2 = 11. It can be shown that 11 is the maximum possible bitwise XOR. Constraints: 1 <= nums.length <= 105 0 <= nums[i] <= 108

Explanation

Here's the solution:

• Key Idea: The operation nums[i] = nums[i] & (nums[i] ^ x) can only clear bits in nums[i]. The maximum XOR sum is achieved when we maximize the number of bits set to 1 in the result. We can determine which bits can be set to 1 independently. A bit can be set to 1 in the final XOR sum if there's a way to make the XOR sum of the nums[i]'s have that bit set. If any nums[i] has a 1 at a particular bit position, we can potentially set that bit to 0 via the given operation for that element and, hence control its contribution in the final XOR. Thus, we can find the bitwise OR of all elements in the array. This will give us the maximum possible value we can achieve through XOR operations.

• Bitwise OR: Calculate the bitwise OR of all elements in nums. This represents the maximum possible XOR sum.

• Complexity:

  • Runtime: O(n), where n is the length of the input array nums.
  • Storage: O(1)

Code

    def maximum_xor(nums):
    """
    Calculates the maximum possible bitwise XOR of all elements of nums after applying the operation any number of times.

    Args:
        nums: A list of non-negative integers.

    Returns:
        The maximum possible bitwise XOR of all elements.
    """

    result = 0
    for num in nums:
        result |= num
    return result