Fix #210: [Model] Partition

[GiggleLiu]

Summary

Add the Partition problem model — a classical NP-complete satisfaction problem (Karp #20, Garey & Johnson SP12). Given a multiset of positive integers, decide whether it can be partitioned into two subsets of equal sum.

Implements the full model with brute-force solver support, canonical example, unit tests (>95% coverage), trait consistency, and paper entry.

Fixes #210

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.93%. Comparing base (9a2b2b7) to head (f3f9ed2).

Additional details and impacted files

@@           Coverage Diff            @@
##             main     #664    +/-   ##
========================================
  Coverage   96.92%   96.93%            
========================================
  Files         271      273     +2     
  Lines       36298    36416   +118     
========================================
+ Hits        35182    35299   +117     
- Misses       1116     1117     +1     

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[GiggleLiu]

Implementation Summary

Changes

• src/models/misc/partition.rs — New Partition satisfaction problem model (Metric = bool, Vec<u64> sizes, evaluate checks selected_sum * 2 == total_sum)
• src/unit_tests/models/misc/partition.rs — 14 unit tests covering basic accessors, satisfying/unsatisfying evaluation, edge cases (odd total, single element, two elements), solver integration, serialization, and panic paths
• src/models/misc/mod.rs — Module registration + canonical example spec wiring
• src/models/mod.rs — Re-export Partition
• src/lib.rs — Added Partition to prelude
• src/unit_tests/trait_consistency.rs — Added check_problem_trait entry
• src/example_db/fixtures/examples.json — Regenerated (32 → 33 model examples)
• docs/paper/reductions.typ — Added display-name entry + problem-def block after SubsetSum
• docs/src/reductions/problem_schemas.json — Regenerated (41 → 42 schemas)
• docs/src/reductions/reduction_graph.json — Regenerated

Deviations from Plan

• None

Open Questions

• None

[Copilot]

Pull request overview

Adds the Partition satisfaction problem model to the misc model catalog, integrating it into the registry/docs/example DB and ensuring it participates in the project’s shared solver + trait infrastructure.

Changes:

• Introduces Partition model (Problem<Metric=bool>) with schema registration, variant declaration, and canonical example specs.
• Adds a dedicated unit test suite for Partition and wires it into trait-consistency checks.
• Updates generated documentation artifacts (problem schemas, reduction graph), paper catalog entry, and example DB fixtures.

Reviewed changes

Copilot reviewed 10 out of 10 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
src/unit_tests/trait_consistency.rs	Adds Partition to the cross-model trait sanity test.
src/unit_tests/models/misc/partition.rs	New unit tests for Partition behavior, solver integration, and serialization.
src/models/mod.rs	Re-exports Partition from models::misc.
src/models/misc/partition.rs	New Partition model implementation, schema inventory entry, variants, and example spec hook.
src/models/misc/mod.rs	Registers the new module and exposes Partition in misc.
src/lib.rs	Adds Partition to the public prelude exports.
src/example_db/fixtures/examples.json	Adds canonical Partition fixture (samples + satisfying set).
docs/src/reductions/reduction_graph.json	Adds Partition node and shifts indices accordingly (generated artifact).
docs/src/reductions/problem_schemas.json	Adds Partition schema entry (generated artifact).
docs/paper/reductions.typ	Adds Partition to the paper’s problem catalog and definition section.

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