tso wrote:Are you able to find the Almost Locked Sets and the other complex implication chains you found by hand? Is there a human-implemental algorithm you could describe?
The algorithm first searches for all the single-step links in the candidate grid - strong links, weak links, extended links and links that involve Almost Locked Sets - then attempts to join these links together to form cyclic chains. It continues to look for cyclic chains until it exhausts all possible chains or it finds a chain that, after its associated elimination, leaves just a single candidate for a cell or a sector (i.e. a row, column or box).
I think the algorithm is similar to the procedure described by
Jeff, except that most humans probably have to restrict their searches to strong links. The main benefit of computational power is the ability to consider a greater number of link types.
I like to post chains in order that they might be 'shot down' by the more talented human solvers, which enables me to 'improve' (this term is necessarily slightly subjective - some people prefer longer chains made from straightforward link types whereas others prefer shorter chains that involve Almost Locked Sets) the chains the solver presents. For instance, recent work by
bennys et al has led me to lean towards shorter, more complicated, chains.