What is the brute force approach and complexity for Longest Continuous Subarray With Absolute Diff ≤ Limit?

For each start, extend the end while tracking max and min; stop when the spread is too big with time complexity O(N²) and space complexity O(1).

What is the optimal approach and complexity for Longest Continuous Subarray With Absolute Diff ≤ Limit?

Decreasing deque for the max, increasing deque for the min, shrink while max − min > limit with optimal time complexity O(N) and space complexity O(N).

How do you identify the pattern for Longest Continuous Subarray With Absolute Diff ≤ Limit?

Look for key signals in the prompt: "longest contiguous subarray" indicates The answer is a window, and its size is the answer → variable sliding window.; "any two elements differ by at most limit" indicates The worst pair is max and min, so validity is max − min ≤ limit.; "max and min of a changing window" indicates Elements leave from the left, so a single max/min variable won't do → monotonic deques..

Longest Continuous Subarray With Absolute Diff ≤ Limit

Medium·LeetCode #1438 Pro OnlyBasic Reinforcement

LeetCode

Problem Statement

You are given an integer array nums and a number limit.

Find the longest contiguous subarray in which every pair of elements differs by at most limit. In other words, the absolute difference between any two elements of the subarray must be ≤ limit.

Return the length of that subarray.

Input

An integer array nums of length n, and an integer limit.

Output

A single number: the length of the longest subarray where any two elements differ by at most limit.

Example 1

Input: nums = [8, 2, 4, 7], limit = 4

Output: 2

[2, 4] (difference 2) and [4, 7] (difference 3) work. Any subarray of length 3 has a pair that differs by more than 4, e.g. [2, 4, 7] has 7 − 2 = 5.

Example 2

Input: nums = [10, 1, 2, 4, 7, 2], limit = 5

Output: 4

[2, 4, 7, 2] has largest 7 and smallest 2, so the biggest difference is 5, which is allowed.

Example 3

Input: nums = [4, 2, 2, 2, 4, 4, 2, 2], limit = 0

Output: 3

With limit 0, all elements must be equal. The longest run of equal values is [2, 2, 2].

Constraints

• 1 ≤ n ≤ 10^5
• 1 ≤ nums[i] ≤ 10^9
• 0 ≤ limit ≤ 10^9

Pattern Recognition Clues

Recognising these key signals in the problem description immediately identifies the pattern:

“longest contiguous subarray”

→ The answer is a window, and its size is the answer → variable sliding window.

“any two elements differ by at most limit”

→ The worst pair is max and min, so validity is max − min ≤ limit.

“max and min of a changing window”

→ Elements leave from the left, so a single max/min variable won't do → monotonic deques.

Approach Complexity Ladder

Brute Force — every start, grow to the rightO(N²)O(1)

For each start, extend the end while tracking max and min; stop when the spread is too big

Better — sliding window + multisetO(N log N)O(N)

Variable window; a sorted multiset gives the window's min and max

Optimal — sliding window + two monotonic dequesO(N)O(N)

Decreasing deque for the max, increasing deque for the min, shrink while max − min > limit

Brute Force Intuition

Fix a start. Move the end to the right one step at a time, keeping a running max and min. While max − min ≤ limit, the subarray is good — update the answer. As soon as it breaks, stop: a longer subarray from this start can only be worse.

Recognition rule for this sub-pattern:

You need the max or min of the current window at every step. A deque keeps only elements that could still become the max/min.

Remember this · Sliding Window

Trigger

Contiguous subarray / substring + longest, shortest, maximum, count, or "of size K".

Think

Can I keep a valid range and move it, instead of checking every subarray from scratch?

Key question

When is my current window valid?

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