To solve the Longest Well-Performing Interval, convert the hours array into +1 and -1 values. Then, scan for the longest subarray with a positive sum. This approach leverages array scanning and hash lookups to efficiently solve the problem by tracking prefix sums.
Problem Statement
You are given a list of hours worked per day for an employee. A day is considered tiring if the number of hours worked exceeds 8 hours. Your task is to determine the length of the longest subarray where the number of tiring days outnumbers the non-tiring days. The list contains the hours worked each day, and you need to find the longest subarray with a positive sum of tiring days.
A well-performing interval is a subarray where the number of tiring days is strictly greater than the non-tiring days. The key to solving this problem is efficiently identifying and counting such intervals within the given array.
Examples
Example 1
Input: hours = [9,9,6,0,6,6,9]
Output: 3
The longest well-performing interval is [9,9,6].
Example 2
Input: hours = [6,6,6]
Output: 0
Example details omitted.
Constraints
- 1 <= hours.length <= 104
- 0 <= hours[i] <= 16
Solution Approach
Transform hours to +1/-1
Create a new array by converting the hours array into +1 for tiring days (hours > 8) and -1 for non-tiring days. This transformation simplifies the problem into finding the longest subarray with a positive sum.
Track prefix sums with a hash map
Use a hash map to store the first occurrence of each prefix sum while iterating through the array. The key insight is that if the prefix sum at two different indices is the same, the subarray between those indices has a sum of zero, and you can then check for the longest valid subarray.
Efficiently find the longest subarray
Iterate through the transformed array, update the prefix sum, and check if the current sum has been seen before. If it has, calculate the length of the subarray between the current and previous indices. Track the maximum length of these subarrays.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is O(n), where n is the length of the hours array. The space complexity is O(n) due to the storage of prefix sums in the hash map.
What Interviewers Usually Probe
- Can the candidate effectively convert the problem into an array of +1/-1 values?
- Does the candidate demonstrate understanding of prefix sum and hash map techniques?
- Is the candidate able to optimize the solution by tracking previous sums and finding the longest subarray?
Common Pitfalls or Variants
Common pitfalls
- Misunderstanding the conversion to +1/-1 for tiring and non-tiring days.
- Overcomplicating the solution without utilizing the prefix sum approach and hash map efficiently.
- Missing the fact that the problem requires finding a subarray with a positive sum rather than simply counting tiring days.
Follow-up variants
- Handling edge cases where there are no tiring days.
- Exploring variations where you are asked to find the shortest subarray with a positive sum.
- Solving the problem with a different data structure like a stack to manage sums.
How GhostInterview Helps
- GhostInterview helps by guiding you through the efficient approach of transforming the problem into an array of +1/-1 values.
- The solver assists in mapping prefix sums to track the longest subarray, ensuring an optimal solution.
- GhostInterview’s insights help avoid common mistakes by reinforcing the key patterns of prefix sums and hash lookups.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the key approach for solving Longest Well-Performing Interval?
The solution involves converting hours worked into +1/-1 values and finding the longest subarray with a positive sum using prefix sums and hash lookups.
How does the prefix sum technique apply to this problem?
The prefix sum technique helps efficiently track the cumulative sum as you iterate, allowing you to identify the longest well-performing subarray by comparing prefix sums at different indices.
What are common mistakes when solving the Longest Well-Performing Interval?
Common mistakes include not correctly converting the array into +1/-1 values or failing to utilize the prefix sum approach effectively.
How does hash map improve the performance of the solution?
Hash maps allow you to quickly check for previously seen prefix sums, enabling constant-time lookup and reducing the time complexity to O(n).
What other data structures can be used for this problem?
While hash maps are optimal, a stack-based approach can also be used to track prefix sums and manage subarrays, but it may be less efficient.
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