Introduction

In this blog post, we will explore how to solve the LeetCode problem "164" 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

Given an integer array nums, return the maximum difference between two successive elements in its sorted form. If the array contains less than two elements, return 0. You must write an algorithm that runs in linear time and uses linear extra space. Example 1: Input: nums = [3,6,9,1] Output: 3 Explanation: The sorted form of the array is [1,3,6,9], either (3,6) or (6,9) has the maximum difference 3. Example 2: Input: nums = [10] Output: 0 Explanation: The array contains less than 2 elements, therefore return 0. Constraints: 1 <= nums.length <= 105 0 <= nums[i] <= 109

Explanation

Here's a breakdown of the approach, followed by the Python code:

• Bucket Sort Idea: Divide the range of numbers into equal-sized buckets. The maximum difference will not occur within a bucket (because if there was a bigger difference within a bucket, the bucket size could have been smaller, contradicting its initial definition based on min/max of the whole array). Therefore, the maximum difference will occur between the maximum value of one bucket and the minimum value of the next non-empty bucket.
• Bucket Creation: Determine the maximum and minimum values in the input array. Calculate the ideal bucket size based on the number of elements and the range. Create buckets to hold the minimum and maximum values encountered within each bucket.

• Iterate and Find Max Gap: Iterate through the buckets, tracking the previous bucket's maximum and calculating the difference with the current bucket's minimum.

• Time & Space Complexity: O(n) time, O(n) space.

Code

    def maximumGap(nums):
    """
    Finds the maximum difference between two successive elements in its sorted form.

    Args:
        nums: A list of integers.

    Returns:
        The maximum difference between two successive elements in its sorted form.
    """
    n = len(nums)
    if n < 2:
        return 0

    min_val = min(nums)
    max_val = max(nums)

    if min_val == max_val:
        return 0

    bucket_size = max(1, (max_val - min_val) // (n - 1))
    bucket_count = (max_val - min_val) // bucket_size + 1

    min_buckets = [float('inf')] * bucket_count
    max_buckets = [float('-inf')] * bucket_count

    for num in nums:
        bucket_index = (num - min_val) // bucket_size
        min_buckets[bucket_index] = min(min_buckets[bucket_index], num)
        max_buckets[bucket_index] = max(max_buckets[bucket_index], num)

    max_gap = 0
    previous_max = max_buckets[0]
    for i in range(1, bucket_count):
        if min_buckets[i] == float('inf'):
            continue
        max_gap = max(max_gap, min_buckets[i] - previous_max)
        previous_max = max_buckets[i]

    return max_gap