Introduction

In this blog post, we will explore how to solve the LeetCode problem "2588" 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, you can: Choose two different indices i and j such that 0 <= i, j < nums.length. Choose a non-negative integer k such that the kth bit (0-indexed) in the binary representation of nums[i] and nums[j] is 1. Subtract 2k from nums[i] and nums[j]. A subarray is beautiful if it is possible to make all of its elements equal to 0 after applying the above operation any number of times. Return the number of beautiful subarrays in the array nums. A subarray is a contiguous non-empty sequence of elements within an array. Example 1: Input: nums = [4,3,1,2,4] Output: 2 Explanation: There are 2 beautiful subarrays in nums: [4,3,1,2,4] and [4,3,1,2,4]. - We can make all elements in the subarray [3,1,2] equal to 0 in the following way: - Choose [3, 1, 2] and k = 1. Subtract 21 from both numbers. The subarray becomes [1, 1, 0]. - Choose [1, 1, 0] and k = 0. Subtract 20 from both numbers. The subarray becomes [0, 0, 0]. - We can make all elements in the subarray [4,3,1,2,4] equal to 0 in the following way: - Choose [4, 3, 1, 2, 4] and k = 2. Subtract 22 from both numbers. The subarray becomes [0, 3, 1, 2, 0]. - Choose [0, 3, 1, 2, 0] and k = 0. Subtract 20 from both numbers. The subarray becomes [0, 2, 0, 2, 0]. - Choose [0, 2, 0, 2, 0] and k = 1. Subtract 21 from both numbers. The subarray becomes [0, 0, 0, 0, 0]. Example 2: Input: nums = [1,10,4] Output: 0 Explanation: There are no beautiful subarrays in nums. Constraints: 1 <= nums.length <= 105 0 <= nums[i] <= 106

Explanation

Here's the solution to the problem:

• Key Idea: A subarray is beautiful if the XOR sum of its elements is 0. This is because the given operation essentially allows us to cancel out bits in pairs. If the XOR sum is 0, it means all bits can be canceled out through a series of operations.
• Prefix XOR: Compute the prefix XOR array. This allows us to find the XOR sum of any subarray in O(1) time.

• Counting Beautiful Subarrays: Iterate through the prefix XOR array and use a hash map to count the number of times each prefix XOR value has occurred. The number of beautiful subarrays ending at the current index is equal to the number of times the current prefix XOR value has occurred previously.

• Complexity:

  • Runtime: O(n)
  • Storage: O(n)

Code

    def beautifulSubarrays(nums):
    """
    Calculates the number of beautiful subarrays in the given array.

    Args:
        nums: A list of integers.

    Returns:
        The number of beautiful subarrays.
    """

    n = len(nums)
    prefix_xor = [0] * (n + 1)
    for i in range(n):
        prefix_xor[i + 1] = prefix_xor[i] ^ nums[i]

    count = 0
    xor_counts = {}
    for xor_val in prefix_xor:
        if xor_val in xor_counts:
            count += xor_counts[xor_val]
            xor_counts[xor_val] += 1
        else:
            xor_counts[xor_val] = 1

    return count