Advanced · Module 21 · Lesson 1 of 4
Linear Patterns: Two Pointers vs. Sliding Window vs. Prefix Sum + Hash Map
Disambiguate contiguous subarray and pair problems instantly: when non-negative elements unlock a O(1)-space Sliding Window, when negative numbers require Prefix Sum + Hash Map, and when range updates call for a Difference Array.
By the end you can
- Distinguish Sliding Window from Prefix Sum + Hash Map based on whether the window metric is monotonic (non-negative weights)
- Apply Fixed-Size and Variable-Size Sliding Window templates with an explicit validity invariant
- Convert Q range-addition updates [L, R] += val from O(Q * N) into O(Q + N) using a 1D or 2D Difference Array
Builds on Two pointers, Sliding window, Prefix sums.
01 · A question first
Two subarray-sum problems look 99% identical: 'longest subarray with sum <= K' and 'number of subarrays with sum == K'. When the array contains negative numbers, Sliding Window completely breaks on both—yet Prefix Sum + Hash Map solves the second in O(N) time. How do you spot that trap in 10 seconds?
Make a guess before you read on.
02 · The idea
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What's inside
- Intuitive Explanation & Real-World Analogy
- Core Concepts & Visual Walkthrough
- Pseudocode
- Multi-Language Implementations (C++, Java, Python)
- Time & Auxiliary Space Complexity Derivation
- Edge Cases & Common Beginner Mistakes
- Alternative Approaches (Brute Force vs. Optimal)
- Pattern Recognition Guide & Three-Stage Practice Plan
03 · Practice
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