Introduction

In this blog post, we will explore how to solve the LeetCode problem "2527" 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. The effective value of three indices i, j, and k is defined as ((nums[i] | nums[j]) & nums[k]). The xor-beauty of the array is the XORing of the effective values of all the possible triplets of indices (i, j, k) where 0 <= i, j, k < n. Return the xor-beauty of nums. Note that: val1 | val2 is bitwise OR of val1 and val2. val1 & val2 is bitwise AND of val1 and val2. Example 1: Input: nums = [1,4] Output: 5 Explanation: The triplets and their corresponding effective values are listed below: - (0,0,0) with effective value ((1 | 1) & 1) = 1 - (0,0,1) with effective value ((1 | 1) & 4) = 0 - (0,1,0) with effective value ((1 | 4) & 1) = 1 - (0,1,1) with effective value ((1 | 4) & 4) = 4 - (1,0,0) with effective value ((4 | 1) & 1) = 1 - (1,0,1) with effective value ((4 | 1) & 4) = 4 - (1,1,0) with effective value ((4 | 4) & 1) = 0 - (1,1,1) with effective value ((4 | 4) & 4) = 4 Xor-beauty of array will be bitwise XOR of all beauties = 1 ^ 0 ^ 1 ^ 4 ^ 1 ^ 4 ^ 0 ^ 4 = 5. Example 2: Input: nums = [15,45,20,2,34,35,5,44,32,30] Output: 34 Explanation: The xor-beauty of the given array is 34. Constraints: 1 <= nums.length <= 105 1 <= nums[i] <= 109

Explanation

Here's the solution with explanation, complexity analysis, and the code:

• Key Idea: The problem can be simplified significantly by recognizing a pattern in the bitwise operations. The xor-beauty is actually the XOR of all the numbers in the input array. This is derived from properties of bitwise operations and how they distribute when considering all possible triplets.
• Simplification: Instead of iterating through all possible triplets, we simply XOR all elements of the array.

• Optimization: No extra space is needed, and the operation is linear.

• Complexity:

  • Runtime: O(n) - single pass through the array.
  • Storage: O(1) - constant extra space.

Code

    def xor_beauty(nums):
    """
    Calculates the xor-beauty of an array.

    Args:
        nums: A list of integers.

    Returns:
        The xor-beauty of the array.
    """
    result = 0
    for num in nums:
        result ^= num
    return result