How do you solve Maximum Gap on LeetCode?

Maximum Gap (LeetCode #164) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding the relationship between the range of numbers and the number of buckets is crucial.

What is the brute force solution for Maximum Gap?

The brute force approach for Maximum Gap is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves sorting the array and then finding the maximum difference between successive elements. This is straightforward but inefficient for large arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Gap?

Maximum Gap uses the following concepts: Array, Sorting, Bucket Sort, Radix Sort. The recommended patterns to study are: Bucket Sort, Array.

What are the interview tips for Maximum Gap?

Always clarify edge cases with the interviewer before diving into the solution. Explain your thought process clearly while coding; it helps the interviewer follow along. If you get stuck, try to break the problem down into smaller parts or consider a brute force solution first.

What are common mistakes when solving Maximum Gap?

Forgetting to handle edge cases like arrays with less than two elements. Not considering the case where all elements are the same, leading to incorrect outputs.

#164

Maximum Gap

Medium

ArraySortingBucket SortRadix SortBucket SortArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal approach uses the concept of bucket sort to find the maximum gap without sorting the entire array. This method is efficient and runs in linear time.

⚙️

Algorithm

4 steps

1Step 1: Find the minimum and maximum values in the array.
2Step 2: Calculate the bucket size and the number of buckets needed.
3Step 3: Place each number in the appropriate bucket.
4Step 4: Calculate the maximum gap by checking the maximum difference between the minimum of the next bucket and the maximum of the current bucket.

solution.py23 lines

1# Full working Python code
2
3def maximum_gap(nums):
4    if len(nums) < 2:
5        return 0
6    min_val, max_val = min(nums), max(nums)
7    if min_val == max_val:
8        return 0
9    bucket_size = max(1, (max_val - min_val) // (len(nums) - 1))
10    bucket_count = (max_val - min_val) // bucket_size + 1
11    buckets = [[float('inf'), float('-inf')] for _ in range(bucket_count)]
12    for num in nums:
13        idx = (num - min_val) // bucket_size
14        buckets[idx][0] = min(buckets[idx][0], num)
15        buckets[idx][1] = max(buckets[idx][1], num)
16    max_gap = 0
17    previous_max = min_val
18    for bucket in buckets:
19        if bucket[0] == float('inf'):
20            continue
21        max_gap = max(max_gap, bucket[0] - previous_max)
22        previous_max = bucket[1]
23    return max_gap

ℹ

Complexity note: The time complexity is O(n) because we only traverse the array a constant number of times. The space complexity is O(n) due to the additional space used for the buckets.

1Understanding the relationship between the range of numbers and the number of buckets is crucial.
2The maximum gap can only occur between the maximum of one bucket and the minimum of the next non-empty bucket.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.