| Criteria | Exemplary | Proficient | Developing | Beginning |
|---|---|---|---|---|
| Correctness & Proof | Provides rigorous correctness proof with loop invariants or induction as appropriate. | Demonstrates correctness with reasonable justification. | Correctness argument is incomplete or has logical gaps. | No correctness proof or argument provided. |
| Complexity Analysis | Provides tight Big-O, Big-Omega, and Big-Theta bounds with detailed derivation. | Correctly identifies Big-O complexity with adequate explanation. | Complexity analysis is attempted but contains errors. | No complexity analysis provided. |
| Optimization | Identifies and implements optimal solution with comparison to alternatives. | Proposes a reasonable optimization or discusses trade-offs. | Mentions optimization but does not implement or analyze it. | No consideration of efficiency or optimization. |
| Presentation & Clarity | Analysis is exceptionally clear with proper mathematical notation and diagrams. | Presentation is organized with appropriate notation. | Presentation is somewhat unclear; notation is inconsistent. | Presentation is disorganized and difficult to follow. |
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