[1.0 algorithm] Rework problem 257 interactor scoring (k-based, compressed)

[whuang369]

Tune the "Omkar and Modes" (257) interactive grader so scores discriminate solution quality instead of clustering near full marks:

• Switch the dynamic-scoring thresholds from n-based (k_base=n, k_zero=2n) to k-based, where k = number of distinct value-blocks in the array (k_base = C_BASEk, k_zero = C_ZEROk). This forces solutions to exploit the sorted/mode structure rather than trivially scanning n positions.
• Score on a single unbounded quadratic curve; report the raw (unbounded) value and clip the bounded score to 100. r is floored at 0 before squaring so the curve stays monotonic and non-negative past k_zero.
• Set C_BASE=3, C_ZERO=15 to compress the current solution pool (avg ~65 -> ~44) while keeping the canonical divide-and-conquer solution near the top (~95).

Summary

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

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

[joyemang33]

Hi @whuang369. Thanks for the contribution! Please also attach the harbor trial output for this problem. How are the C_BASE and C_ZERO set here? Can we set them to a lower value so that squeeze the best score a little bit to have more improvement space?

[whuang369]

Hi @joyemang33 , thank you for your advise and information! I've updated the grading parameters for this problem, and ran harbor over this problem. Attached images are the new grading rules and harbor trial!

[joyemang33]

LGTM thanks!