Bug fix drive subissue 41

[Priyangshu-Mandal]

Implements subissue #41: Problem Engine, Submission Integrity & Code Runner.

Changes

• Added local C++/Python code runner support in contest rooms.
• Loaded contest problem statements, specifications, constraints, and sample cases.
• Persisted problem content during room provisioning.
• Added sample test cases to the local runner.
• Fixed Codeforces problem URL generation for IDs such as 1678B1.
• Strengthened submission validation:
  • Requires a verified Codeforces handle.
  • Validates room and team membership.
  • Validates assigned/revealed problems.
  • Rejects submissions after the room is inactive.
  • Persists accepted submissions for match results.

Testing

• Focused tests passed.
• Contest integration tests passed: 7/7.
• Problem-content and contest tests passed: 15/15.
• ESLint passed for changed files.
• Docker Compose configuration validated.
• MongoDB replica set and Redis services verified successfully.