state transition dp Pattern
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Pattern brief
Recognize first
Do you identify both odd and even length palindromes during center expansion?
Solve rhythm
State the active state and invariant first, explain how each update preserves them, then pressure-test with counterexamples.
Most common miss
Forgetting to check even-length palindromes, which requires treating centers between characters.
Recognition signals
- Do you identify both odd and even length palindromes during center expansion?
- Can you explain how previously computed palindromes reduce redundant checks in the DP table?
- Assess understanding of dynamic programming, especially with state transitions.
Solve flow
- 1. Define the active state/window.
- 2. Update state while preserving invariants.
- 3. Validate with edge-heavy examples.
Common misses
- Forgetting to check even-length palindromes, which requires treating centers between characters.
- Failing to handle edge cases like empty string `s` or pattern `p` properly.
- Failing to properly balance the number of opening and closing parentheses during backtracking leads to invalid sequences.
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