**Tags:** optimization programming

Rating: 5.0

# Hack Code

We get a file with a lot of routes (given as lists of routers), and

are asked to find a small subset of routers to tap so that we have at

least one tap on each route. We will ignore the topology of the

network and the order of routers in the paths, and will treat this as

a set cover problem: the routes are sets, and we need to pick a small

set of elements (routers) such that we cover all routes.

We can start with a simple randomised solution: iterate through all

sets, and if no elements in the set are in the current solution, pick

one at random and insert it. This will produce solutions with around

200 elements -- not enough to get any flags, but it is a start.

Next, we can try to improve this (again, at random) with the following

algorithm:

* pick a random router not yet in the solution

* insert it in the solution

* for each other router, see if we can remove it without "breaking"

our solution (so all sets are still covered) and remove it if we can

* if we couldn't remove anything, remove the new router

Sometimes we will add a router and remove multiple old routers, so

this will slowly improve the solution, and after a minute or two we

will have one that is good enough to get the first flag.

A small optimisation to the algorithm will make it run significantly

faster: instead of checking all routers in each iteration, only look

at those for which we could have made a difference -- those that are

in one of the sets covered by the new entry. With this optimisation,

in a few minutes we get a solution with 126 routers, which is enough

to get all flags (and the best the organisers found).

My code that solves this (note: written in a rush during the CTF and

presented here without any cleanup) can be found

[here](https://de298.user.srcf.net/writeups/insa/hackcode.py).