164. Maximum Gap

📋 Đề Bài

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

💻 Lời Giải

Python 0164-maximum-gap.py

class Solution:
    def maximumGap(self, nums: List[int]) -> int:
        n = len(nums)
        
        if n < 2:
            return 0
        
        minVal, maxVal = min(nums), max(nums)
        
        if minVal == maxVal:
            return 0
        
        sizeBucket = ceil((maxVal - minVal) / (n - 1))
        buckets = [[math.inf, -math.inf] for _ in range(n)]
        
        for i in range(n):
            j = (nums[i] - minVal) // sizeBucket
            buckets[j][0] = min(buckets[j][0], nums[i])
            buckets[j][1] = max(buckets[j][1], nums[i])
                
        prev = buckets[0][1]
        answ = sizeBucket
                
        for i in range(1, n):
            if buckets[i][0] == math.inf:
                continue
            answ = max(answ, buckets[i][0] - prev)
            prev = buckets[i][1]
        
        return answ