ravel wrote:I called a set of puzzles a family with distance n, when all puzzles have a pairwise distance less equal n.
Similar to Gordon's idea above i also thought about clusters of puzzles, where a cluster of distance n could be defined this way:
1. Any set A with a single puzzle is a cluster
2. Set A remains to be a cluster of distance n, when a puzzle is added, that has distance less equal n to any puzzle in A.
I just posted n2-2007-05-23.dat.gz
which contains 3 fields
puzzle cluster-id gfroyle-ordinal
for a -gn2c neighborhood tour (size 2 neighborhood tour in my solver)
puzzles with the same cluster-id are in the same size 2 neighborhood
a size 2 neighborhood tour is similar to 2-off + 2-on except that off+on are done in pairs
and each pair must produce a valid puzzle
this does much more pruning that a pure 2-off + 2-on tour like havard is doing,
but the search space is a bit more tractable (-go2c for a pure 2-off +2-on in my solver)
I also added a hamming-style distance based on the sudoku space thread discussions
the distance is biased towards minimizing clue position differences first, then minimizing cell value differences
the -C option compares each pair of puzzles on the input (1 with 2, 2 with 3, etc.), lists the
distance, the first puzzle, and the second puzzle mapped to show a minimum distance mapping
ravel wrote:Now i wondered, what distance the cluster of known 17-clues has. To get a feeling, i looked at Ocean's puzzle
May 16, where he mentioned, that it does not have another 17 within 2 off/2 on. I found 4 puzzles in the old list
with the lowest distance 6 and 31 with highest distance 16.
that's a good idea
do a pairwise distance to find the min and max distance
in graph theoretic terms the max distance would be the diameter of the known 17 space
3 off 1 on is pretty quick I hope?