Optimize schedule generation algorithm

Yes, the branch is called sceduler-improvements. Yes it is missing h.

This PR optimizes the core algorithm, adds a result cap, and rewrites the test suite.

Algorithm changes

1. Range-mask formula in binaryMeetingTime.ts - Replaced per-slot bit loop with (1n << numSlots) - 1n shifted into place. One expression instead of a tight loop.

2. Prefix mask array in generateCombinations.ts - Instead of rechecking the whole schedule from scratch each iteration, a prefixMasks array maintains the running OR of all accepted masks. Conflict detection goes from O(n) to O(1) per position, and the prefix state is reused when only the last index advances.

3. Precomputed optional masks in generateSchedules.ts - Optional section masks are computed once before the main loop instead of once per locked schedule. addOptionalCourses threads a single combined bigint mask through recursion instead of an array, and uses push/pop instead of array spreading.

4. MAX_RESULTS cap (100) - Prevents runaway generation when many non-conflicting sections exist. This was the primary cause of the hour-long runtime.

Bug fixes

5. Empty course guard - Added early return when any course has zero sections. Previously this would silently produce wrong results.

6. Single-course maxResults - The single-course fast path now respects the maxResults cap via .slice(). Previously it was ignored.

Test improvements

7. Rewrote generateSchedules.test.ts - The old tests tested local shadow copies of the logic, not the actual production functions. The new file imports and tests the real implementations. Covers locked-only, optional-only, mixed, numCourses edge cases, MAX_RESULTS capping, and conflict invariants.

8. New addOptionalCourses.test.ts - Full coverage for the new function: skip/include choices, conflict filtering, multi-meeting sections, numCourses combinations, maxResults capping, and push/pop array isolation safety.

9. New unit tests in binaryMeetingTime.test.ts - New tests covering incrementIndex carry/overflow, meetingTimesToBinaryMask edge cases (zero-duration, multi-day, multi-block, back-to-back), masksConflict, and generateCombinationsOptimized (empty course guard, mask correctness, single-course cap).

10. Benchmark suite - Before/after comparison across 13 scenarios including adversarial, edge case, and uncapped exhaustion tests. File is named benchmark.bench.ts (not .test.ts) so it won't run during normal CI test runs. Run manually with npx tsx --test apps/searchneu/lib/scheduler/binaryMeetingTimeTests/benchmark.bench.ts.

Benchmark results (69 unit tests + 21 benchmarks, all passing)

┌─ small  (4 × 8,    4,096 brute force)
│  original :           100 results         0.3 ms
│  optimized:           100 results         0.2 ms   (1.2x faster)
└────────────────────────────────────────────────────────────

┌─ medium (6 × 10,  1,000,000 brute force)
│  original :           100 results         0.8 ms
│  optimized:           100 results         0.5 ms   (1.6x faster)
└────────────────────────────────────────────────────────────

┌─ large  (8 × 12,  429,981,696 brute force)
│  original :           100 results         1.3 ms
│  optimized:           100 results         0.2 ms   (6.6x faster)
└────────────────────────────────────────────────────────────

┌─ massive (10 × 15, 576,650,390,625 brute force)
│  original :           100 results         4.9 ms
│  optimized:           100 results         0.1 ms   (37.5x faster)
└────────────────────────────────────────────────────────────

┌─ deep   (12 × 10, 1e12 brute force - overconstrained)
│  original :             0 results      4936.9 ms
│  optimized:             0 results       141.4 ms   (34.9x faster)
└────────────────────────────────────────────────────────────

┌─ uncapped (8 × 12, no cap - full exhaustion)
│  original :       2419200 results      8575.8 ms
│  optimized:       2419200 results      1560.1 ms   (5.5x faster)
└────────────────────────────────────────────────────────────