Optimizing Sliding Window Algorithms with Dynamic Expansion

Variable-Size Sliding Window: When to Expand vs Contract Unlike fixed-size windows, finding the longest substring without repeating characters requires dynamic window adjustment. The key insight: expand greedily by advancing the right pointer, but when a duplicate is encountered, contract from the left until the window is valid again. A HashSet tracks current window contents, enabling O(1) duplicate detection and removal. This pattern of "expand until invalid, then contract until valid" is foundational to constraint-based window problems. Why This Works: The right pointer moves exactly n times, and the left pointer also moves at most n times across the entire execution (never backtracks). Amortized analysis shows each character enters and exits the window at most once, yielding O(n) total operations despite the nested loop appearance. This amortized complexity analysis is critical for understanding why certain "nested loop" solutions are actually linear. Time: O(n) amortized | Space: O(min(n, charset_size)) #SlidingWindow #AmortizedAnalysis #HashSet #SubstringProblems #Python #AlgorithmOptimization #CodingInterview #SoftwareEngineering

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