math recursion 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
Recognizes negative exponent handling is required.
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 handle n = INT_MIN correctly when negating.
Recognition signals
- Recognizes negative exponent handling is required.
- Uses recursion to optimize repeated multiplications.
- Look for understanding of recursion and factorials.
Solve flow
- 1. Define the active state/window.
- 2. Update state while preserving invariants.
- 3. Validate with edge-heavy examples.
Common misses
- Failing to handle n = INT_MIN correctly when negating.
- Misunderstanding how factorials divide the problem into smaller sections, leading to incorrect permutation generation.
- Not handling negative numbers or zero correctly, which can lead to incorrect answers.
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