Refactor 2.0

[GiggleLiu]

• Refactor the variables interface. Now variables are forced to be 1:num_variables.
• Rewrite the SAT to 3-SAT reduction to make it more general.

[codecov]

Codecov Report

Attention: Patch coverage is 98.47909% with 4 lines in your changes missing coverage. Please review.

Project coverage is 94.32%. Comparing base (ea50b96) to head (d946121).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/reduction_path.jl	60.00%	2 Missing ⚠️
src/models/models.jl	98.07%	1 Missing ⚠️
src/rules/sat_3sat.jl	96.87%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #116      +/-   ##
==========================================
- Coverage   95.51%   94.32%   -1.20%     
==========================================
  Files          34       33       -1     
  Lines        1450     1444       -6     
==========================================
- Hits         1385     1362      -23     
- Misses         65       82      +17     

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[GiggleLiu]

@c-allergic I refactored the interfaces for ConstraintSatisfactionProblem a bit so that it can be converted to tensor networks easier. Now we can use energy_terms to generate tensors.

julia> ProblemReductions.energy_terms(IndependentSet(smallgraph(:petersen)))
25-element Vector{ProblemReductions.EnergyTerm{Int64, 2, Int64, Int64}}:
 EnergyTerm
┌───┬───┬────────────┐
│ 1 │ 2 │     energy │
├───┼───┼────────────┤
│ 0 │ 0 │          0 │
│ 1 │ 0 │          0 │
│ 0 │ 1 │          0 │
│ 1 │ 1 │ 3037000500 │
└───┴───┴────────────┘

 EnergyTerm
┌───┬───┬────────────┐
│ 1 │ 5 │     energy │
├───┼───┼────────────┤
│ 0 │ 0 │          0 │
│ 1 │ 0 │          0 │
│ 0 │ 1 │          0 │
│ 1 │ 1 │ 3037000500 │
└───┴───┴────────────┘

 EnergyTerm
┌───┬───┬────────────┐
│ 1 │ 6 │     energy │
├───┼───┼────────────┤
│ 0 │ 0 │          0 │
│ 1 │ 0 │          0 │
│ 0 │ 1 │          0 │
│ 1 │ 1 │ 3037000500 │
└───┴───┴────────────┘

 EnergyTerm
┌───┬───┬────────────┐
│ 2 │ 3 │     energy │
├───┼───┼────────────┤
│ 0 │ 0 │          0 │
│ 1 │ 0 │          0 │
│ 0 │ 1 │          0 │
│ 1 │ 1 │ 3037000500 │
└───┴───┴────────────┘

 EnergyTerm
┌───┬───┬────────────┐
│ 2 │ 7 │     energy │
├───┼───┼────────────┤
│ 0 │ 0 │          0 │
│ 1 │ 0 │          0 │
│ 0 │ 1 │          0 │
│ 1 │ 1 │ 3037000500 │
└───┴───┴────────────┘

 EnergyTerm
┌───┬───┬────────────┐
│ 3 │ 4 │     energy │
├───┼───┼────────────┤
│ 0 │ 0 │          0 │
│ 1 │ 0 │          0 │
│ 0 │ 1 │          0 │
│ 1 │ 1 │ 3037000500 │
└───┴───┴────────────┘

 EnergyTerm
┌───┬───┬────────────┐
│ 3 │ 8 │     energy │
├───┼───┼────────────┤
│ 0 │ 0 │          0 │
│ 1 │ 0 │          0 │
│ 0 │ 1 │          0 │
│ 1 │ 1 │ 3037000500 │
└───┴───┴────────────┘

 EnergyTerm
┌───┬───┬────────────┐
│ 4 │ 5 │     energy │
├───┼───┼────────────┤
│ 0 │ 0 │          0 │
│ 1 │ 0 │          0 │
│ 0 │ 1 │          0 │
│ 1 │ 1 │ 3037000500 │
└───┴───┴────────────┘

 ⋮
 EnergyTerm
┌───┬────────┐
│ 3 │ energy │
├───┼────────┤
│ 0 │      0 │
│ 1 │     -1 │
└───┴────────┘

 EnergyTerm
┌───┬────────┐
│ 4 │ energy │
├───┼────────┤
│ 0 │      0 │
│ 1 │     -1 │
└───┴────────┘

 EnergyTerm
┌───┬────────┐
│ 5 │ energy │
├───┼────────┤
│ 0 │      0 │
│ 1 │     -1 │
└───┴────────┘

 EnergyTerm
┌───┬────────┐
│ 6 │ energy │
├───┼────────┤
│ 0 │      0 │
│ 1 │     -1 │
└───┴────────┘

 EnergyTerm
┌───┬────────┐
│ 7 │ energy │
├───┼────────┤
│ 0 │      0 │
│ 1 │     -1 │
└───┴────────┘

 EnergyTerm
┌───┬────────┐
│ 8 │ energy │
├───┼────────┤
│ 0 │      0 │
│ 1 │     -1 │
└───┴────────┘

 EnergyTerm
┌───┬────────┐
│ 9 │ energy │
├───┼────────┤
│ 0 │      0 │
│ 1 │     -1 │
└───┴────────┘

 EnergyTerm
┌────┬────────┐
│ 10 │ energy │
├────┼────────┤
│  0 │      0 │
│  1 │     -1 │
└────┴────────┘