[GradTrak] Optimal course-to-requirement matching with double major overlap enforcement

[ethanransing]

Summary

Introduces optimal course-to-requirement matching for GradTrak, which replaces greedy assignment with algorithms that optimally assign courses to requirements within a program (e.g. L&S's 7 Breadths), and also handle Berkeley's upper-division overlap policy for double majors.

Changes

1. Bipartite matching for breadth/count requirements. Replaces greedy matching
2. Unit-threshold buckets (ex. >= X units of UD classes): Course assignment uses backtracking w/ pruning to optimally fulfill buckets
3. Joint matching across double majors (see L&S, CDSS, CoE policies): Backtracking w/ pruning to assign upper division classes to major A, major B, both (if overlap cap isn't exceeded), or none
4. Testing: Unit tests in packages/BtLL/src/test.ts covers
5. UX change: hide DS domain emphasis subrequirements by default

Limitations

1. Joint majors aren't handled. These don't have the same overlap restrictions as double majors
2. This CoE double major restriction isn't encoded: "Each major must include at least 5 upper division technical courses, of at least 3 units each, that do not overlap with the other major."
3. 3+ majors aren't supported

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[chatgpt-codex-connector]

Respect OR semantics when extracting joint leaves

extractLeaves flattens OrRequirement exactly like AndRequirement, so all leaves inside every OR branch are treated as simultaneously optimizable constraints. Because runJointAssignment maximizes satisfied leaf count, it can allocate courses to multiple sibling OR alternatives and starve required leaves elsewhere, producing a final tree where an And parent is false even though a satisfying assignment exists (e.g., satisfying several OR siblings instead of a required sibling node).

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[chatgpt-codex-connector]

Preserve course number when hydrating inputs from URL

URL parsing now constructs hydrated inputs with courseNumber: "", and this value is propagated into loaded outputs. The Grades UI uses input.courseNumber for rendering and edit state, so opening/reloading shared URLs can produce blank or invalid course identities in cards/edit flows until the user manually reselects a course. Parse should retain or recover the real course number instead of hardcoding an empty value.

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