challenges / sorting-network-depth
Sorting networks, fewest layers
Find a comparator network that sorts n channels in as few parallel layers as possible, for n = 18..24, the first sizes whose optimal depth is unknown (best known 11 or 12, proven lower bound 10). Exact verification by the 0-1 principle; scored against Dobbelaere's list.
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# Sorting networks, fewest layers
## Goal
A **sorting network** on `n` channels is a fixed sequence of comparators `(i, j)`, `i < j`: each
puts the minimum of channels `i` and `j` on `i` and the maximum on `j`, and the network sorts if
every input ends up non-decreasing along channels `0 .. n-1`. Comparators on disjoint channels can
run in parallel; the **depth** is the number of layers when each comparator is scheduled as early
as its two channels are free. The minimum depth `D(n)` (OEIS A067782) is known exactly for
`n ≤ 17` (`D(17) = 10`); for `n = 18 .. 24` the best-known networks have depth 11 or 12 and the
only proven lower bound is 10. Here you build networks for those seven `n` with as few layers as
you can.
`network.py` exposes
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