two pointer invariant Pattern
Pattern hubs are for building transferable solving frames. Learn the recognition signals first, then drill state definition, update rules, and edge explanation until the pattern feels stable.
Pattern brief
Recognize first
Do you understand the two-pointer technique and how it helps reduce the time complexity of this problem?
Solve rhythm
State the active state and invariant first, explain how each update preserves them, then pressure-test with counterexamples.
Most common miss
Failing to optimize the solution and instead using a brute-force approach that simulates all pairs, leading to O(n^2) time complexity.
Recognition signals
- Do you understand the two-pointer technique and how it helps reduce the time complexity of this problem?
- Can you explain why we always move the pointer pointing to the shorter line in the two-pointer approach?
- Do you see how sorting simplifies duplicate management in two-pointer scanning?
Solve flow
- 1. Define the active state/window.
- 2. Update state while preserving invariants.
- 3. Validate with edge-heavy examples.
Common misses
- Failing to optimize the solution and instead using a brute-force approach that simulates all pairs, leading to O(n^2) time complexity.
- Failing to skip duplicate fixed elements leads to repeated triplets in output.
- Forgetting to sort the array first, which can lead to inefficient solutions or missed results.
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