Maximum Gap

Given an unsorted array of numbers, the goal is to find the maximum difference between any two consecutive elements after the array has been sorted. This problem is fundamental in understanding sorting algorithms and efficient data manipulation, as it requires careful consideration of how to find the largest gap without necessarily performing a full sort if more optimal solutions exist.

Problem Description

You are given an array of integers nums. Your task is to find the maximum difference between two successive elements in its sorted form. If the array contains less than two elements, return 0.

Key Requirements:

• The difference must be between successive elements after sorting.
• If the input array has fewer than two elements, the maximum gap is considered 0.

Expected Behavior:

• The function should return a non-negative integer representing the maximum gap.

Edge Cases:

• An empty array.
• An array with a single element.
• An array with all identical elements.

Examples

Example 1:

Input: [3, 6, 9, 1]
Output: 3
Explanation: After sorting, the array becomes [1, 3, 6, 9]. The differences between successive elements are:
3 - 1 = 2
6 - 3 = 3
9 - 6 = 3
The maximum difference is 3.

Example 2:

Input: [10]
Output: 0
Explanation: The array has only one element, so the maximum gap is 0.

Example 3:

Input: [2, 4, 4, 4, 4, 1]
Output: 2
Explanation: After sorting, the array becomes [1, 2, 4, 4, 4, 4]. The differences between successive elements are:
2 - 1 = 1
4 - 2 = 2
4 - 4 = 0
4 - 4 = 0
4 - 4 = 0
The maximum difference is 2.

Constraints

• The number of elements in the array nums will be between 0 and 10^5.
• The values of the elements in nums will be between 0 and 10^9.
• You should aim for a solution with a time complexity better than O(N log N), where N is the number of elements in the array.

Notes

Consider the implications of the constraints, particularly the time complexity requirement. While a simple sort followed by iteration is a valid approach, it might not meet the optimal performance expectations. Think about algorithms that can find the maximum gap without fully sorting the entire array. You might also want to consider algorithms like bucket sort or radix sort, or explore approaches that don't involve explicit sorting at all.