Day 23: LAN Party

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FAQ

  • Gobbel2000
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    8 hours ago

    Rust

    Finding cliques in a graph, which is actually NP-comlete. For part two I did look up how to do it and implemented the Bron-Kerbosch algorithm. Adding the pivoting optimization improved the runtime from 134ms to 7.4ms, so that is definitely worth it (in some sense, of course I already had the correct answer without pivoting).

    Solution
    use rustc_hash::{FxHashMap, FxHashSet};
    
    fn parse(input: &str) -> (Vec<Vec<usize>>, FxHashMap<&str, usize>) {
        let mut graph = Vec::new();
        let mut names: FxHashMap<&str, usize> = FxHashMap::default();
        for l in input.lines() {
            let (vs, ws) = l.split_once('-').unwrap();
            let v = *names.entry(vs).or_insert_with(|| {
                graph.push(vec![]);
                graph.len() - 1
            });
            let w = *names.entry(ws).or_insert_with(|| {
                graph.push(vec![]);
                graph.len() - 1
            });
            graph[v].push(w);
            graph[w].push(v);
        }
        (graph, names)
    }
    
    fn part1(input: String) {
        let (graph, names) = parse(&input);
        let mut triples: FxHashSet<[usize; 3]> = FxHashSet::default();
        for (_, &v) in names.iter().filter(|(name, _)| name.starts_with('t')) {
            for (i, &u) in graph[v].iter().enumerate().skip(1) {
                for w in graph[v].iter().take(i) {
                    if graph[u].contains(w) {
                        let mut triple = [u, v, *w];
                        triple.sort();
                        triples.insert(triple);
                    }
                }
            }
        }
        println!("{}", triples.len());
    }
    
    // Bron-Kerbosch algorithm for finding all maximal cliques in a graph
    fn bron_kerbosch(
        graph: &[Vec<usize>],
        r: &mut Vec<usize>,
        mut p: FxHashSet<usize>,
        mut x: FxHashSet<usize>,
    ) -> Vec<Vec<usize>> {
        if p.is_empty() && x.is_empty() {
            return vec![r.to_vec()];
        }
        let mut maximal_cliques = Vec::new();
        let Some(&u) = p.iter().next() else {
            return maximal_cliques;
        };
        let mut p_pivot = p.clone();
        for w in &graph[u] {
            p_pivot.remove(w);
        }
        for v in p_pivot {
            let pn = graph[v].iter().filter(|w| p.contains(w)).copied().collect();
            let xn = graph[v].iter().filter(|w| x.contains(w)).copied().collect();
            r.push(v);
            let new_cliques = bron_kerbosch(graph, r, pn, xn);
            r.pop();
            maximal_cliques.extend(new_cliques);
            p.remove(&v);
            x.insert(v);
        }
        maximal_cliques
    }
    
    fn part2(input: String) {
        let (graph, names) = parse(&input);
        let p = (0..graph.len()).collect();
        let mut r = Vec::new();
        let maximal_cliques = bron_kerbosch(&graph, &mut r, p, FxHashSet::default());
        let maximum_clique = maximal_cliques
            .iter()
            .max_by_key(|clique| clique.len())
            .unwrap();
        let mut lan_names: Vec<&str> = names
            .iter()
            .filter(|(_, v)| maximum_clique.contains(v))
            .map(|(name, _)| *name)
            .collect();
        lan_names.sort_unstable();
        println!("{}", lan_names.join(","));
    }
    
    util::aoc_main!();
    

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