Hidoku Solver in Python: branch cutting, intelligent successor generation and some simplifications

Hidoku Sample

In this post we are implementing a Hidoku solver (Hidoku is yet another fine number puzzle) that uses a depth first search, branch cutting, limited (intelligent) successor generation and some automatic simplification. Usually, a Hidoku is a quadratic board consisting of n x n fields - but rectangular or other forms would be possible as well. With each Hidoku, some fields are already pre-filled with numbers at the beginning. The game goal is to fill in all other numbers so that an ascending number queue is built: each number has to be adjacent to it's successor, with adjacent meaning in an adjacent horizontal, vertical or diagonal field.