[konnjags] Difficulty of pattern unlock

For a given Android pattern unlock pattern, determine its difficulty.  We are particularly concerned about segments like a knight's move, which involve threading the finger between two intervening dots, being careful not to touch either of them.  However, if one or both of those two intervening dots have already been consumed in a previous part of the path, then a knight's move is easy: go over the consumed dot again, because a path cannot consume a dot more than once.  More generally, the easiest path between two dots, the one requiring the least fine dexterity, might not be the shortest path.

Consider improving pattern unlock by providing a wide empty margin through which the finger can easily travel between any of the 8 dots on the edge of the square, via a roundabout path.  And of course, traveling from the edge to the center dot or vice versa is always easy.

Previously, octagon.