I tried coding LeppyR64's dynamic programming method.
If end up with nested loops
loop r=2...k
for all subsets S of {1...n}
for all subsets T of S
best cover S with r squares =
min(max(cover T with 1 square, cover S-T with r-1 squares)
Alternatively, do a binary search over s asking the question can k squares of
size s cover the n points.
To answer the question, find all maximal subsets T of {1...n} which can be
covered by one square of size s. In practice the number of such subsets seem to
be not much larger than n. Then do a depth first search to see if k of these
subsets can be found to cover {1...n}.
Total time is something like log2(64000) x 2^n x n x smallish function of n.
Lots of loose ends in the above description. More thoughts welcome.
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