Sliding window is a technique used to efficiently process subarrays or substrings within a larger dataset. It avoids unnecessary recomputation by maintaining a "window" of elements that slides across the input. This approach is widely used in problems involving sums, averages, or frequency counts within a specific range.
The sliding window pattern is a powerful optimization technique for iterating through subsets of a sequence—usually an array or string. Instead of using nested loops to examine every possible subarray, this method uses a "window" that dynamically shifts to maintain optimal performance.
A fixed-length sliding window is ideal for problems where the size of the subset is constant—such as finding the maximum sum of k consecutive elements.
As the window slides forward, the element entering is added and the element exiting is subtracted, maintaining an O(n) time complexity.
In variable-length sliding windows, the window adjusts its size based on conditions. This is useful in problems like "longest substring without repeating characters" where the window expands and contracts based on validity.
The sliding window technique transforms brute-force O(n²) solutions into linear time O(n) algorithms.
It’s an essential tool for working efficiently with intervals and substrings in competitive programming and real-world scenarios.
The Sliding Window Algorithm is an efficient pattern used in Data Structures and Algorithms (DSA), particularly for solving problems involving arrays or strings that require examining contiguous subarrays or substrings. It allows for optimized solutions with O(N) time complexity and is commonly implemented in Python.
The Variable Length Sliding Window technique is used when the size of the window can change dynamically depending on certain conditions. The goal is often to find the longest or shortest subarray or substring that satisfies a particular requirement.
L (left) and R (right) to define the window boundaries.R to grow the window while the condition (e.g., no duplicates) remains valid.L and removing elements from the set until the condition is valid again.R - L + 1.O(N) — Both L and R only move forward across the array.O(N) — A set or map may store up to N elements depending on the input.The Fixed Length Sliding Window technique applies when the size of the window is predetermined and constant throughout the algorithm. It is typically used when evaluating every subarray or substring of a specific length.
K elements to initialize the window.O(N) — One complete pass through the array.O(1) — Only a few variables are used to track window metrics.| Feature | Fixed Length | Variable Length |
|---|---|---|
| Window Size | Constant (Predefined) | Dynamic (Adjusts Based on Condition) |
| Use Case | Evaluate all windows of a fixed size | Find the optimal window size that meets a condition |
| Space Complexity | O(1) | O(N) (may use a set or map) |
| Time Complexity | O(N) | O(N) |