What algorithm or data structure is used to solve Longest Well-Performing Interval?

Longest Well-Performing Interval uses the following concepts: Array, Hash Table, Stack, Monotonic Stack, Prefix Sum. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Longest Well-Performing Interval?

Understand the problem requirements thoroughly Practice prefix sum problems to get comfortable Think about how to reduce the problem size using data structures like hashmaps

What are common mistakes when solving Longest Well-Performing Interval?

Not converting the problem to a prefix sum format Overlooking the need to track the first occurrence of prefix sums

Longest Well-Performing Interval — LeetCode #1124 (Medium)

Tags: Array, Hash Table, Stack, Monotonic Stack, Prefix Sum

Related patterns: Hash Map, Array

Brute Force approach

Time complexity: O(n²). Space complexity: O(1).

The brute force approach involves checking every possible subarray to determine if it is a well-performing interval. This means we will count the tiring and non-tiring days for each subarray and check if the tiring days are greater.

The time complexity is O(n²) because we are using two nested loops to check all subarrays. The space complexity is O(1) as we are using a constant amount of extra space.

Step 1: Initialize a variable to store the maximum length of well-performing intervals.
Step 2: Use two nested loops to generate all subarrays of the input array.
Step 3: For each subarray, count the number of tiring days (hours > 8) and non-tiring days (hours <= 8).
Step 4: If the number of tiring days is greater than non-tiring days, update the maximum length.
Step 5: Return the maximum length found.

For hours = [9,9,6,0,6,6,9]: 1. Start with i=0, j=0: tiringDays=1, nonTiringDays=0, maxLength=1 2. Now j=1: tiringDays=2, nonTiringDays=0, maxLength=2 3. Now j=2: tiringDays=2, nonTiringDays=1, maxLength=2 4. Now j=3: tiringDays=2, nonTiringDays=2, maxLength=2 5. Now j=4: tiringDays=2, nonTiringDays=2, maxLength=2 6. Now j=5: tiringDays=2, nonTiringDays=2, maxLength=2 7. Now j=6: tiringDays=3, nonTiringDays=2, maxLength=3 (found longest interval [9,9,6])

Common Mistakes

Not converting the problem to a prefix sum format
Overlooking the need to track the first occurrence of prefix sums

Interview Tips

Understand the problem requirements thoroughly
Practice prefix sum problems to get comfortable
Think about how to reduce the problem size using data structures like hashmaps

#1124

Longest Well-Performing Interval

Medium

Array↗Hash Table↗Stack↗Monotonic Stack↗Prefix Sum↗Hash Map↗Array↗

LeetCode ↗

Approaches

💡

Intuition

Time O(n²)Space O(1)

⚙️

Algorithm

5 steps

1Step 1: Initialize a variable to store the maximum length of well-performing intervals.
2Step 2: Use two nested loops to generate all subarrays of the input array.
3Step 3: For each subarray, count the number of tiring days (hours > 8) and non-tiring days (hours <= 8).
4Step 4: If the number of tiring days is greater than non-tiring days, update the maximum length.
5Step 5: Return the maximum length found.

solution.py14 lines

1def longestWPI(hours):
2    max_length = 0
3    n = len(hours)
4    for i in range(n):
5        tiring_days = 0
6        non_tiring_days = 0
7        for j in range(i, n):
8            if hours[j] > 8:
9                tiring_days += 1
10            else:
11                non_tiring_days += 1
12            if tiring_days > non_tiring_days:
13                max_length = max(max_length, j - i + 1)
14    return max_length

ℹ

Complexity note: The time complexity is O(n²) because we are using two nested loops to check all subarrays. The space complexity is O(1) as we are using a constant amount of extra space.

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