The problem can be solved efficiently using a sliding window approach. Maintain the minimum and maximum values within the window to track the validity of the subarray. By adjusting the window as needed, we can ensure the absolute difference condition holds true while maximizing the subarray length.
Problem Statement
You are given an array of integers, nums, and an integer, limit. Your task is to return the size of the longest non-empty subarray where the absolute difference between any two elements in this subarray is less than or equal to limit.
A sliding window approach is required to efficiently track the maximum and minimum values in the current window. By expanding and contracting the window based on the absolute difference condition, you can find the longest valid subarray.
Examples
Example 1
Input: nums = [8,2,4,7], limit = 4
Output: 2
All subarrays are: [8] with maximum absolute diff |8-8| = 0 4. [8,2,4] with maximum absolute diff |8-2| = 6 > 4. [8,2,4,7] with maximum absolute diff |8-2| = 6 > 4. [2] with maximum absolute diff |2-2| = 0 4. [4] with maximum absolute diff |4-4| = 0 <= 4. [4,7] with maximum absolute diff |4-7| = 3 <= 4. [7] with maximum absolute diff |7-7| = 0 <= 4. Therefore, the size of the longest subarray is 2.
Example 2
Input: nums = [10,1,2,4,7,2], limit = 5
Output: 4
The subarray [2,4,7,2] is the longest since the maximum absolute diff is |2-7| = 5 <= 5.
Example 3
Input: nums = [4,2,2,2,4,4,2,2], limit = 0
Output: 3
Example details omitted.
Constraints
- 1 <= nums.length <= 105
- 1 <= nums[i] <= 109
- 0 <= limit <= 109
Solution Approach
Sliding Window with Maximum and Minimum Tracking
Use a sliding window to maintain a dynamic range of numbers where the absolute difference between the maximum and minimum is within the given limit. As the window slides, track the maximum and minimum values using data structures like a deque or multiset, and adjust the window's size accordingly.
Efficient Window Expansion and Contraction
As the window expands to include new elements, check whether the difference between the maximum and minimum exceeds the limit. If it does, contract the window from the left side until the condition is met again. This allows the algorithm to process elements in O(n) time.
Using Deque or Multiset for Tracking
To maintain the maximum and minimum elements efficiently, use a deque (double-ended queue) or a multiset (in C++) to quickly access the current maximum and minimum values within the window. These structures allow you to keep the time complexity of updating the window within bounds.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | O(n) |
| Space | O(n) |
The time complexity is O(n) because each element is added and removed from the sliding window at most once. The space complexity is O(n) due to the additional space required for the data structures used to track the window's maximum and minimum values.
What Interviewers Usually Probe
- Look for understanding of sliding window techniques.
- Evaluate how efficiently the candidate handles window adjustments and tracking of max/min values.
- Assess the ability to explain why O(n) time complexity is achievable.
Common Pitfalls or Variants
Common pitfalls
- Failing to update the window correctly when the absolute difference exceeds the limit.
- Using inefficient data structures for tracking max/min values, leading to suboptimal time complexity.
- Not handling edge cases such as very small arrays or large limit values properly.
Follow-up variants
- Allowing the subarray to contain negative numbers and adjusting the absolute difference condition.
- Extending the problem to find the sum of elements in the longest subarray that meets the condition.
- Modifying the condition to check for differences in specific positions within the subarray instead of all pairs.
How GhostInterview Helps
- GhostInterview can help you practice solving this problem with time-efficient techniques and data structures for maintaining a sliding window.
- By using the sliding window approach and understanding the time complexity, GhostInterview helps you grasp the trade-offs between different data structures.
- GhostInterview walks you through handling window adjustments and tracking the maximum and minimum values in an optimal way.
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 best approach to solve Longest Continuous Subarray With Absolute Diff Less Than or Equal to Limit?
The best approach is using a sliding window technique that maintains the maximum and minimum values of the current subarray, expanding and contracting the window based on the absolute difference condition.
How do I handle large arrays efficiently for this problem?
For large arrays, you should use a sliding window approach with data structures like deques or multisets that allow for efficient tracking of the window's maximum and minimum values in O(1) time.
Why is the sliding window approach optimal for this problem?
The sliding window approach ensures that each element is processed only once, leading to an O(n) time complexity. This is much more efficient than checking every pair of elements directly.
What are some common mistakes in solving this problem?
Common mistakes include not correctly adjusting the window when the absolute difference exceeds the limit, and using inefficient data structures for tracking the max/min values.
How can GhostInterview help me solve problems like Longest Continuous Subarray With Absolute Diff Less Than or Equal to Limit?
GhostInterview provides targeted practice on sliding window techniques and helps you master optimal data structures for maintaining dynamic ranges in problems like this.
Need direct help with Longest Continuous Subarray With Absolute Diff Less Than or Equal to Limit instead of spending more time grinding it?
Download GhostInterview when you want a LeetCode solver, not another long practice loop. Capture Longest Continuous Subarray With Absolute Diff Less Than or Equal to Limit from a screenshot, get the answer path and complexity, and use supported stealth workflows that stay outside captured layers.
Capture the prompt fast instead of rewriting the problem by hand.
Get the solution path, trade-offs, and complexity summary in one pass.
Stay outside captured layers on supported screen-share workflows.
Stay in the same pattern family
Solve the Constrained Subsequence Sum problem using dynamic programming, sliding window, and priority queues to maximize subsequence sum with constraints.
Open problem page#862 Shortest Subarray with Sum at Least KFind the shortest subarray with a sum of at least k using binary search and sliding window techniques.
Open problem page#2398 Maximum Number of Robots Within BudgetDetermine the maximum number of consecutive robots you can operate without exceeding a given budget using efficient binary search techniques.
Open problem page