This is pretty much exactly the algorithm that https://www.ioccc.org/2005/aidan/aidan.c https://www.ioccc.org/2005/aidan/aidan.c uses, except obviously much mor

This is pretty much exactly the algorithm that https://www.ioccc.org/2005/aidan/aidan.c https://www.ioccc.org/2005/aidan/aidan.c uses, except obviously much more clearly expressed. There's also a reasonably straightforward extension of this technique that can test for solution uniqueness, and so generate random valid puzzles; I can't remember how it was implemented exactly but it involves continuing the search after finding the first solution and seeing if it succeeds.