Introduction

In this blog post, we will explore how to solve the LeetCode problem "3011" 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 array of positive integers nums. In one operation, you can swap any two adjacent elements if they have the same number of set bits. You are allowed to do this operation any number of times (including zero). Return true if you can sort the array in ascending order, else return false. Example 1: Input: nums = [8,4,2,30,15] Output: true Explanation: Let's look at the binary representation of every element. The numbers 2, 4, and 8 have one set bit each with binary representation "10", "100", and "1000" respectively. The numbers 15 and 30 have four set bits each with binary representation "1111" and "11110". We can sort the array using 4 operations: - Swap nums[0] with nums[1]. This operation is valid because 8 and 4 have one set bit each. The array becomes [4,8,2,30,15]. - Swap nums[1] with nums[2]. This operation is valid because 8 and 2 have one set bit each. The array becomes [4,2,8,30,15]. - Swap nums[0] with nums[1]. This operation is valid because 4 and 2 have one set bit each. The array becomes [2,4,8,30,15]. - Swap nums[3] with nums[4]. This operation is valid because 30 and 15 have four set bits each. The array becomes [2,4,8,15,30]. The array has become sorted, hence we return true. Note that there may be other sequences of operations which also sort the array. Example 2: Input: nums = [1,2,3,4,5] Output: true Explanation: The array is already sorted, hence we return true. Example 3: Input: nums = [3,16,8,4,2] Output: false Explanation: It can be shown that it is not possible to sort the input array using any number of operations. Constraints: 1 <= nums.length <= 100 1 <= nums[i] <= 28

Explanation

Here's the breakdown of the solution:

• Calculate Set Bits: Compute the number of set bits for each element in the input array.
• Simulate Bubble Sort: Simulate bubble sort, but only allow swaps between adjacent elements if they have the same number of set bits.

• Check Sorted Array: After the simulated bubble sort, check if the array is sorted in ascending order.

• Runtime Complexity: O(n^2), where n is the length of the input array, due to the bubble sort simulation.

• Storage Complexity: O(n), where n is the length of the input array, to store the initial nums and bits array.

Code

    def canSortArray(nums):
    """
    Determines if an array can be sorted by swapping adjacent elements with the same number of set bits.

    Args:
      nums: A list of positive integers.

    Returns:
      True if the array can be sorted, False otherwise.
    """

    n = len(nums)
    bits = [bin(num).count('1') for num in nums]

    swapped = True
    while swapped:
        swapped = False
        for i in range(n - 1):
            if nums[i] > nums[i + 1] and bits[i] == bits[i + 1]:
                nums[i], nums[i + 1] = nums[i + 1], nums[i]
                swapped = True

    for i in range(n - 1):
        if nums[i] > nums[i + 1]:
            return False

    return True