## Description

Given an unsorted array, find the maximum difference between the successive elements in its sorted form.

Return 0 if the array contains less than 2 elements.

Example 1:

Input: [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: 
Output: 0
Explanation: The array contains less than 2 elements, therefore return 0.


Note:

• You may assume all elements in the array are non-negative integers and fit in the 32-bit signed integer range.
• Try to solve it in linear time/space.

## Solutions

### 1. Bucket Sort

# Time: O(n)
# Space: O(n)
class Solution:
def maximumGap(self, nums: List[int]) -> int:
if len(nums) < 2 or min(nums) == max(nums):
return 0
min_v, max_v = min(nums), max(nums)
size = math.ceil((max_v - min_v) / (len(nums) - 1))
# bucket store min_v and max_v
bucket = [[None, None] for _ in range((max_v - min_v) // size + 1)]
for num in nums:
bckt = bucket[(num - min_v) // size]
bckt = num if bckt is None else min(bckt, num)
bckt = num if bckt is None else max(bckt, num)
bucket = [bckt for bckt in bucket if bckt is not None]

res = 0
for i in range(1, len(bucket)):
res = max(res, bucket[i] - bucket[i - 1])
return res
# 18/18 cases passed (68 ms)
# Your runtime beats 53.43 % of python3 submissions
# Your memory usage beats 66.67 % of python3 submissions (13.7 MB)