Leetcode #164: Maximum Gap
In this guide, we solve Leetcode #164 Maximum Gap in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Bucket Sort, Radix Sort, Sorting
Intuition
Sorting reveals structure that is hard to see in the original order.
Once sorted, a linear scan is usually enough to compute the answer.
Approach
Sort the data and sweep through it while maintaining a small state.
This keeps the logic straightforward and reliable.
Steps:
- Sort the data.
- Scan in order while maintaining state.
- Update the best answer.
Example
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.
Python Solution
class Solution:
def maximumGap(self, nums: List[int]) -> int:
n = len(nums)
if n < 2:
return 0
mi, mx = min(nums), max(nums)
bucket_size = max(1, (mx - mi) // (n - 1))
bucket_count = (mx - mi) // bucket_size + 1
buckets = [[inf, -inf] for _ in range(bucket_count)]
for v in nums:
i = (v - mi) // bucket_size
buckets[i][0] = min(buckets[i][0], v)
buckets[i][1] = max(buckets[i][1], v)
ans = 0
prev = inf
for curmin, curmax in buckets:
if curmin > curmax:
continue
ans = max(ans, curmin - prev)
prev = curmax
return ans
Complexity
The time complexity is , where is the length of string . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.