Maximum Gap Between Consecutive Workers' Stations

# Maximum Gap Between Consecutive Workers' Stations You are given strings `skill` and `station`. Worker `i` requires the skill `skill[i]`, and station `j` supports `station[j]`. Assign every worker to a different station so that: - The station's supported skill matches the worker's required skill. - Assigned station indices strictly increase in worker order. If worker `i` is assigned index `j[i]`, the assignment's gap is the largest difference `j[i] - j[i - 1]` between consecutive workers. With only one worker, the gap is `0`. Return the maximum possible assignment gap. At least one valid assignment is guaranteed to exist. ### Function `int maximumGap(string skill, string station)` ### Example 1 **Input:** `skill = "aba", station = "aabxxbaa"` **Output:** `5` **Explanation:** Assign the workers to station indices `[0, 5, 7]`. Their skills are `a`, `b`, `a`, and their consecutive gaps are `5` and `2`. A gap larger than `5` is impossible: the `b` stations are at indices `2` and `5`, with matching `a` stations before and after them. ### Example 2 **Input:** `skill = "z", station = "azzzb"` **Output:** `0` **Explanation:** The single worker can use any matching `z` station. There is no pair of consecutive workers, so the assignment gap is `0`. ### Constraints - `1 <= skill.length <= station.length <= 100000` - Both strings contain only lowercase English letters. - A matching, strictly increasing assignment exists for all workers. ### Clarifications - Station indices are zero-based, and unused stations are allowed. - A gap is an index difference, not the number of unused stations strictly between two workers. - Maximize the largest consecutive-worker gap, not the smallest gap. - All workers must be assigned, including those before and after the pair producing the largest gap. ### What a Strong Answer Covers - Respecting skill matches, distinct stations and worker order simultaneously. - Widening a consecutive pair's gap without preventing a complete assignment. - Handling repeated skills, one worker and the full string-length limit.