Implement time complexity-based scoring with cascading closure

[Copilot]

Scoring now awards points only for the first submission at each time complexity level. When a complexity is solved, that level and all easier complexities are closed from future scoring.

Changes

Database Schema

• Added ProblemComplexitySolve table with unique constraint on (problem_id, complexity) to track first solver per complexity level
• Added execution_times and detected_complexity to Submission model
• Added optimal_complexity to Problem model

Complexity Management (bemo/complexity.py)

• Defined hierarchy: O(1) < O(log n) < O(n) < O(n log n) < O(n²) < O(n³) < O(2^n) < O(n!)
• is_complexity_open_for_scoring() checks if complexity already solved or closed by easier solution
• record_complexity_solve() atomically records first solver via database constraint
• calculate_complexity_bonus() awards scaled points (O(1)=8×, O(n)=6×, O(n²)=4×)

Scoring Logic (bemo/routes.py)

• Capture execution times from Judge0 API during submission check
• Estimate complexity from execution time and problem rating
• Award bonus only if record_complexity_solve() succeeds (handles races)
• Store detected complexity in submission for display

UI

• Problem page displays open/closed status for all complexity levels with color-coded badges
• Submission page shows detected complexity and whether bonus was awarded

Example

Problem (rating 1000): All complexities initially open

Alice solves O(n²) → +400 bonus, closes [O(n²), O(n³), O(2^n), O(n!)]
Bob solves O(n) → +600 bonus, closes [O(n), O(log n), O(1)]
Carol solves O(n²) → 0 bonus (already solved)
Dave solves O(n log n) → +500 bonus (still open between O(n) and O(n²))

Migration

python migrate_complexity_tracking.py

Adds new fields and tables. Idempotent, backward compatible.

Original prompt

Pull Request: #5 address the feedback
The scoring system should only apply to the first submission of an open time complexity. Once a time complexity is solves, it and all easier complexities are closed from scoring.

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