# Algorithmic Problem Domain

## Approach
- Model the problem state explicitly (structs/enums), separate from I/O.
- Define invariants and validate inputs before solving.
- Choose algorithm by constraints: brute force (small), BFS/DFS, IDA*, A*, dynamic programming, greedy, heuristic search.
- Provide a reference/naive implementation for correctness checking.
- Benchmark with criterion; profile before optimizing.

## Common Patterns
- State-space search with visited set and pruning.
- Backtracking with constraint propagation.
- Memoization / DP tables.
- Bitmask representations for small state spaces.
- Move generation + undo (for puzzles/games).

## Testing
- Unit tests for move/invariant correctness.
- Property tests (proptest) for round-trip moves.
- Known-answer tests (Kociemba, IDA* expected lengths).
- Fuzz input parsing.

## Pitfalls
- Off-by-one in move indexing.
- Forgetting parity/invariant checks (illegal states "solve").
- Heuristic not admissible → wrong shortest path.
- State representation mismatch (cubie vs sticker).
- Overflow in depth/counters.
- Non-deterministic ordering breaking reproducibility.

## Libraries (Rust)
- (none required) pure std; optional: rand (scrambles), criterion (bench), proptest (tests).
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