[algorithmic] Clarify and rescore Number Loop construction

[joyemang33]

Summary

Clarifies algorithmic problem 145 as a self-contained Number Loop construction task and updates the checker to provide continuous partial credit.

The revised scoring first buckets by the number of valid loop solutions, then uses the number of 1 clues as the within-bucket optimization objective. The checker now emits Ratio: and RatioUnbounded: fields so the algorithmic judge correctly parses partial scores.

Please read CONTRIBUTING.md before submitting.

Type of Change

• New research problem
• New algorithmic problem
• New Frontier-CS 2.0 problem
• Bug fix
• Documentation update
• Other:

Testing

• Compiled algorithmic/problems/145/checker.cpp locally with g++ -std=gnu++17 -O2 -I algorithmic/judge/include.
• Ran the checker against both bundled official answers.
• Confirmed both cases report Ratio: 0.5892857143 RatioUnbounded: 0.5892857143 under the new unique-solution plus 1-count scoring.
• Ran a regenerated Harbor trial for problem 145 and confirmed iterative submissions now surface parsed partial scores.

Checklist

• Code follows the project structure and conventions
• Self-review completed
• Documentation updated (if applicable)

CI Validation (for new problems)

When adding new problems, CI will automatically validate that your reference solution achieves score > 0.

• Algorithmic problems: Include reference.cpp in your problem directory
• Research problems: Include reference.py (or reference.cpp if language: cpp in config.yaml)
• 2.0 problems: Include reference.py unless the problem config declares another language