math string 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
Check if the candidate handles carry propagation correctly in a digit-by-digit simulation.
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 reverse the input strings before multiplying can misalign digits and produce incorrect results.
Recognition signals
- Check if the candidate handles carry propagation correctly in a digit-by-digit simulation.
- Watch for attempts to convert strings directly to integers, which violates constraints.
- Do you handle carry properly when adding binary digits?
Solve flow
- 1. Define the active state/window.
- 2. Update state while preserving invariants.
- 3. Validate with edge-heavy examples.
Common misses
- Failing to reverse the input strings before multiplying can misalign digits and produce incorrect results.
- Ignoring the carry during addition can lead to incorrect results.
- Forgetting to subtract 1 before modulo leads to incorrect letters for multiples of 26.
Recommended Ladder
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