string plus enumeration 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
They point out that the expression length is tiny, which is a strong signal to enumerate all parenthesis placements.
Solve rhythm
State the active state and invariant first, explain how each update preserves them, then pressure-test with counterexamples.
Most common miss
Forgetting that an empty prefix or empty suffix should contribute 1, not 0, which breaks cases like (999+999).
Recognition signals
- They point out that the expression length is tiny, which is a strong signal to enumerate all parenthesis placements.
- They ask how multiplication appears after adding parentheses, which hints that outside digits become prefix and suffix multipliers.
- Do you recognize that each '?' position is independent within hour and minute limits?
Solve flow
- 1. Define the active state/window.
- 2. Update state while preserving invariants.
- 3. Validate with edge-heavy examples.
Common misses
- Forgetting that an empty prefix or empty suffix should contribute 1, not 0, which breaks cases like (999+999).
- Replacing '?' without checking hour > 23 leads to invalid counts.
- Failing to check the bounds of valid hours and minutes when replacing '?' characters.
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