How to Recognize Sliding Window Problems Instantly (Pattern Triggers)

In an interview, speed matters. You don't have 10 minutes to wonder if it's DP or Sliding Window. You need to recognize the pattern instantly.

Sliding Window problems have a very specific "DNA". Once you learn to spot these markers, you will trigger the solution template automatically.

TL;DR — The 4-Step Recognition Algorithm

1. Contiguous? (Subarray/Substring) $\to$ If No, STOP.
2. Optimization? (Max/Min/Longest) $\to$ Strong Signal.
3. Constraint? (Sum $\le$ K, Distinct $\le$ K) $\to$ Strong Signal.
4. Monotonic? (No negatives) $\to$ If Yes, Sliding Window. If No, Prefix Sum.

Key signals in problem statements

Look for these exact phrases. If you see them, there is a 90% chance it's Sliding Window.

1. "Contiguous Subarray" or "Substring"
   • Signal: The answer must be a continuous block, not a subsequence.
2. "Longest" or "Shortest" or "Minimum/Maximum length"
   • Signal: It's an optimization problem.
3. "With at most K..." or "Sum is at least S"
   • Signal: There is a constraint that defines the window validity.
4. "Window of size K"
   • Signal: Explicit Fixed Window.

Typical constraints

• Input Size: $N=10^5$ or $10^6$.
• Time Limit: implied $O(N)$ or $O(N\log N)$.
• Deduction: $O(N^2)$ brute force will TLE (Time Limit Exceeded). You need a linear pass.

Common disguises

Sometimes the problem hides the window.

• "Find the maximum number of fruits you can pick..." -> Longest subarray with at most 2 distinct types.
• "Find the minimum operations to reduce x to 0..." -> Longest subarray with sum = TotalSum - x. (Inverted thinking!).

Mindset checklist before solving

Before you code, ask these 3 questions:

1. Is the data contiguous?
   • Yes $\to$ Candidate for Window.
   • No $\to$ DP or Backtracking.
2. Is the condition monotonic?
   • Does adding an element always make the window "bigger/heavier"?
   • Does removing an element always make it "smaller/lighter"?
   • Yes $\to$ Sliding Window.
   • No (Negative numbers) $\to$ Prefix Sum.
3. Can I shrink?
   • If I have a valid window, can I make it smaller and still potentially be valid (or invalid)?

Illustrative examples

• LeetCode 3: Longest Substring Without Repeating Characters
  • Keywords: "Substring", "Longest", "Without repeating".
• LeetCode 209: Minimum Size Subarray Sum
  • Keywords: "Subarray", "Minimal length", "Sum $\ge$ target".
• LeetCode 438: Find All Anagrams in a String
  • Keywords: "Substring", "Anagram" (Fixed size).

Red Herrings: What looks like Sliding Window but isn't?

1. "Longest Increasing Subsequence"
   • Trap: "Subsequence" means non-contiguous.
   • Solution: Dynamic Programming ($O(N^2)$) or Patience Sorting ($O(NlogN)$).
2. "Subarray Sum Equals K" (with negatives)
   • Trap: "Subarray" is correct, but negative numbers break the greedy expansion.
   • Solution: Prefix Sum.
3. "Knapsack Problem"
   • Trap: Selecting items to maximize value.
   • Solution: Dynamic Programming.

FAQ

Q: What if the problem asks for the number of subarrays?
A: Standard Sliding Window is for finding the best one. For counting all valid subarrays, you usually need Two Pointers (if monotonic) or Prefix Sums (if not). However, for "at most K" problems, Sliding Window can count by adding right - left + 1 at each step.

Q: Can Sliding Window work with $O(NlogN)$?
A: Yes! If the "check" condition involves a sorted data structure (like a TreeMap or SortedList) to find the median or max in the window, the complexity becomes $O(NlogK)$.

Summary

If you see "Contiguous" + "Optimization (Max/Min)", it is almost certainly Sliding Window.
Verify Monotonicity (no negatives).
Then choose Fixed vs Dynamic (See Fixed vs Dynamic).

Next Step:
What happens when the "Monotonicity" check fails? Read Sliding Window for Negative Numbers.

For a broader look at pattern recognition, read Stop Grinding Blind 75: A Pattern-First Approach.