Longest Well-Performing Interval

Longest Well-Performing Interval - Problem

Array Hash Table Stack Monotonic Stack Prefix Sum Medium

We are given hours, a list of the number of hours worked per day for a given employee.

A day is considered to be a tiring day if and only if the number of hours worked is strictly greater than 8.

A well-performing interval is an interval of days for which the number of tiring days is strictly larger than the number of non-tiring days.

Return the length of the longest well-performing interval.

Input & Output

Example 1 — Basic Well-Performing Interval

$ Input: hours = [9,9,6,0,6,6,9]

› Output: 3

💡 Note: The longest well-performing interval is [9,9,6] from index 0 to 2. It has 2 tiring days (9>8, 9>8) and 1 non-tiring day (6≤8), so tiring > non-tiring.

Example 2 — No Well-Performing Interval

$ Input: hours = [6,6,6]

› Output: 0

💡 Note: All days have ≤8 hours, so no interval can have more tiring days than non-tiring days. The longest well-performing interval has length 0.

Example 3 — Entire Array is Well-Performing

$ Input: hours = [9,9,9]

› Output: 3

💡 Note: All days are tiring (>8 hours), so the entire array [9,9,9] is well-performing with 3 tiring days and 0 non-tiring days.

Constraints

1 ≤ hours.length ≤ 10⁴
0 ≤ hours[i] ≤ 16

Visualization

Tap to expand

Asked in

G Google 25 a Amazon 18 M Microsoft 15 f Facebook 12

The key insight is to transform this into a subarray sum problem: convert tiring days to +1 and non-tiring to -1, then find the longest subarray with positive sum. Best approach uses prefix sum with hash map in O(n) time and O(n) space.

Common Approaches

✓ Greedy

⏱️ Time: N/A Space: N/A

Brute Force - Check All Intervals

⏱️ Time: O(n³) Space: O(1)

For each starting position, extend the interval day by day and check if tiring days exceed non-tiring days. Track the maximum length found.

Monotonic Stack

⏱️ Time: O(n) Space: O(n)

Transform to +1/-1 array, then use a monotonic stack to find the longest subarray with positive sum. The stack maintains indices in decreasing order of their prefix sums.

Prefix Sum with Hash Map

⏱️ Time: O(n) Space: O(n)

Convert tiring days to +1 and non-tiring to -1. A well-performing interval has positive sum. Use prefix sums with hash map to efficiently find the longest subarray with positive sum.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

⚠ Quadratic Growth

Space Complexity

✓ Linear Space

32.0K Views

Medium Frequency

~25 min Avg. Time

892 Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen