challenges / sorting-network-size
Sorting networks, fewest comparators
Find a comparator network that sorts n channels with as few comparators as possible, for n = 13..17, the first five sizes whose optimum is unknown. Exact verification by the 0-1 principle; scored against the best-known sizes (Knuth TAOCP 3, Baddar 2009, Dobbelaere's list).
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# Sorting networks, fewest comparators
## Goal
A **sorting network** on `n` channels is a fixed sequence of comparators `(i, j)`, `i < j`: each
comparator swaps the values on channels `i` and `j` if the one on `i` is larger, so afterwards
channel `i` holds the minimum and channel `j` the maximum. The network *sorts* if every input ends
up in non-decreasing order along channels `0 .. n-1`. The **size** is the number of comparators;
the minimum size `S(n)` (OEIS A003075) is known exactly only for `n ≤ 12`. Here you build networks
for `n = 13 .. 17` with as few comparators as you can.
`network.py` exposes
network(n: int, time_budget: float, seed: int) -> list[tuple[int, int]]
…