aloalgo.comSliding Window Technique
The sliding window technique transforms brute-force O(n²) solutions into elegant O(n) ones. It's one of the most powerful patterns for array and string problems, and once you recognize it, you'll see it everywhere.1. When to Use Sliding Window
Look for these signals:- The problem involves a contiguous sequence (subarray or substring)
- You need to find min/max/count of something in that sequence
- Keywords: "contiguous", "substring", "subarray", "consecutive", "window"
- Maximum sum of k consecutive elements
- Longest substring without repeating characters
- Smallest subarray with sum ≥ target
- Find all anagrams in a string
2. The Two Types
| Fixed Window | Variable Window | |
|---|---|---|
| Window Size | Constant (given as k) | Changes based on condition |
| Pointers | Move together | Move independently |
| Typical Ask | "Of size k..." | "Longest/shortest that..." |
| Example | Max sum of k elements | Longest substring without repeats |
3. Fixed-Size Window
The window size is given. Slide it across the array, updating your answer as you go.Template
Example: Maximum Sum of K Consecutive Elements
Idea: Initialize the sum of the first k elements, then slide the window by adding the next element and removing the first element of the previous window.- Time: O(n)
- Space: O(1)
Example: Find All Anagrams
Idea: Use a fixed window of size equal to the pattern length. Track character frequencies with a hashmap and compare against the pattern's frequency map as the window slides.- Time: O(n) where n is the length of the string
- Space: O(1) - fixed alphabet size
4. Variable-Size Window
The window expands and contracts based on a condition. This is the more powerful (and trickier) pattern.Template: Find Longest
Template: Find Shortest
Key difference:
- Longest: Expand freely, shrink when invalid, update after shrinking
- Shortest: Expand until valid, shrink while valid, update while shrinking
5. Classic Problems
Longest Substring Without Repeating Characters
Idea: Expand the window by adding characters to a set. When a duplicate is found, shrink from the left until the duplicate is removed. Track the maximum window size seen.- Time: O(n)
- Space: O(min(n, alphabet size))
Minimum Size Subarray Sum
Find the shortest subarray with sum ≥ target.Longest Substring with At Most K Distinct Characters
Maximum Consecutive Ones III
Longest subarray of 1s if you can flip at most k zeros.6. Sliding Window with HashMap
Many problems require tracking character/element frequencies. Use a hashmap to maintain counts.Minimum Window Substring
Find the smallest window in s that contains all characters of t.7. The Mental Model
Think of sliding window as a caterpillar:- Expand the right side (head moves forward)
- Check if window satisfies the condition
- Contract the left side if needed (tail catches up)
- Update the answer
8. Common Mistakes
| Mistake | Problem | Fix |
|---|---|---|
| Updating result at wrong time | Missing valid windows | Longest: after shrink. Shortest: during shrink. |
| Off-by-one in window size | Wrong answer | Window size = right - left + 1 |
| Not cleaning up hashmap | Wrong distinct count | Delete key when count reaches 0 |
| Using if instead of while | Incomplete shrinking | Always use while for contraction |
9. Complexity
| Type | Time | Space |
|---|---|---|
| Fixed window | O(n) | O(1) or O(k) |
| Variable window | O(n) | O(1) or O(unique elements) |
| With hashmap | O(n) | O(alphabet size) |
Both pointers traverse the array once, so total operations = O(2n) = O(n).
10. Practice Problems
Variable WindowRelated PatternsFinal Thoughts
Sliding window is really about maintaining a valid state as you traverse. The window is just the visualization—what matters is knowing what to track, when to expand, and when to contract. Master this pattern and you'll solve a huge category of problems with the same mental framework.Was this helpful?
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