9 karma · joined April 14, 2024
https://alpha.twizzle.net/explore/?alg=%28U+R%29105
Unless by "same direction" you mean "opposite direction", in which case 63 works:
It (using the address of the nodes as arguments) can serve as a tiebreaker in a Cartesian tree (such as one implementing a first-fit memory allocator) or even to replace the random priority value in a treap (meaning you need neither storage nor computation for the priority node of the treap).
And then after that: what use can this be put to?
To explore the entire state space of possible initial positions, I use a number of tricks; I'll be writing that up pretty soon. I've explored through n=12 already, and expect to finish n=13 and n=14 pretty soon. I'm not sure if I'll be able to do n=15.
And by the way, I've found a position for n=14 that requires 206 moves to solve.
6: 14 7: 26 8: 74 9: 86 10: 126 11: 106 (?) (full state space not explored) 12: 130 (?) (full state space not explored)