Fix Set Covering: Update doc (pre-compilng) and variables

[SciCodePhy]

1. Update the variables interface;
2. Fix the typo of doc (pre-compiling part);

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 88.67%. Comparing base (e735c83) to head (8960106).

Additional details and impacted files

@@           Coverage Diff           @@
##             main      #52   +/-   ##
=======================================
  Coverage   88.67%   88.67%           
=======================================
  Files          16       16           
  Lines         680      680           
=======================================
  Hits          603      603           
  Misses         77       77           

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