Introduction

In this blog post, we will explore how to solve the LeetCode problem "810" 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 an array of integers nums represents the numbers written on a chalkboard. Alice and Bob take turns erasing exactly one number from the chalkboard, with Alice starting first. If erasing a number causes the bitwise XOR of all the elements of the chalkboard to become 0, then that player loses. The bitwise XOR of one element is that element itself, and the bitwise XOR of no elements is 0. Also, if any player starts their turn with the bitwise XOR of all the elements of the chalkboard equal to 0, then that player wins. Return true if and only if Alice wins the game, assuming both players play optimally. Example 1: Input: nums = [1,1,2] Output: false Explanation: Alice has two choices: erase 1 or erase 2. If she erases 1, the nums array becomes [1, 2]. The bitwise XOR of all the elements of the chalkboard is 1 XOR 2 = 3. Now Bob can remove any element he wants, because Alice will be the one to erase the last element and she will lose. If Alice erases 2 first, now nums become [1, 1]. The bitwise XOR of all the elements of the chalkboard is 1 XOR 1 = 0. Alice will lose. Example 2: Input: nums = [0,1] Output: true Example 3: Input: nums = [1,2,3] Output: true Constraints: 1 <= nums.length <= 1000 0 <= nums[i] < 216

Explanation

Here's the breakdown of the solution:

• XOR Sum: Calculate the XOR sum of all numbers in the array. This represents the initial state of the chalkboard.
• Winning Condition: Alice wins if the XOR sum is non-zero and the number of elements is even. If the XOR sum is 0, Alice loses immediately unless the initial state starts with 0 itself where alice wins.

• Optimal Play: If the XOR sum is non-zero, Alice must make a move that leaves a non-zero XOR sum for Bob. If there are an even number of elements, Alice will always have the last move, so she loses if she leaves XOR sum as 0. Therefore, she wins if the XOR sum isn't zero and there are an even number of elements initially.

• Runtime Complexity: O(n)

• Storage Complexity: O(1)

Code

    def xorGame(nums):
    """
    Determines if Alice wins the XOR game, assuming both players play optimally.

    Args:
        nums: A list of integers representing the numbers on the chalkboard.

    Returns:
        True if Alice wins, False otherwise.
    """

    xor_sum = 0
    for num in nums:
        xor_sum ^= num

    if xor_sum == 0:
        return True
    elif len(nums) % 2 == 0:
        return True
    else:
        return False