math plus rejection sampling 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
Will your solution maintain uniform distribution for all outputs?
Solve rhythm
State the active state and invariant first, explain how each update preserves them, then pressure-test with counterexamples.
Most common miss
Using rand7() % 10 directly introduces bias.
Recognition signals
- Will your solution maintain uniform distribution for all outputs?
- How can you reduce the expected number of rand7() calls in your mapping?
Solve flow
- 1. Define the active state/window.
- 2. Update state while preserving invariants.
- 3. Validate with edge-heavy examples.
Common misses
- Using rand7() % 10 directly introduces bias.
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