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164. Maximum Gap

Difficulty Topics

Description

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

Solution

maximum-gap.py
class Solution:
    def maximumGap(self, nums: List[int]) -> int:
        n = len(nums)
        if n < 2: return 0

        mmax, mmin = float('-inf'), float('inf')

        for num in nums:
            mmax = max(mmax, num)
            mmin = min(mmin, num)

        gap = math.ceil((mmax - mmin) / (n - 1)) or 1
        bucket_max = [float('-inf') for _ in range(n)]
        bucket_min = [float('inf') for _ in range(n)]

        for num in nums:
            index = (num - mmin) // gap
            bucket_max[index] = max(bucket_max[index], num)
            bucket_min[index] = min(bucket_min[index], num)

        maxGap = float('-inf')
        prevMax = mmin

        for i in range(n):
            if bucket_max[i] == float('-inf') and bucket_min[i] == float('inf'): continue

            maxGap = max(maxGap, bucket_min[i] - prevMax)
            prevMax = bucket_max[i]

        return maxGap