diff --git a/2022/src/bin/day16.rs b/2022/src/bin/day16.rs
new file mode 100644
index 0000000..f0cf6c7
--- /dev/null
+++ b/2022/src/bin/day16.rs
@@ -0,0 +1,361 @@
+use std::{
+    collections::{BinaryHeap, HashMap, HashSet},
+    str::FromStr,
+};
+
+use regex::Regex;
+
+const INPUT: &str = include_str!("../../input/day16.txt");
+
+fn main() {
+    println!("{}", part1(INPUT));
+}
+
+fn part1(input: &str) -> u32 {
+    let graph = Graph::parse(input);
+
+    graph.max_flow(30)
+}
+
+// I really want this to be Copy, so here's a hack to avoid strings.
+#[derive(Debug, Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
+struct Valve(u64);
+
+impl FromStr for Valve {
+    type Err = String;
+
+    fn from_str(s: &str) -> Result<Self, Self::Err> {
+        if s.len() != 2 {
+            return Err(s.to_string());
+        }
+
+        let u = s
+            .chars()
+            .rev()
+            .enumerate()
+            .map(|(i, c)| (c as u64) << (8 * i))
+            .sum();
+
+        Ok(Self(u))
+    }
+}
+
+impl From<&str> for Valve {
+    fn from(value: &str) -> Self {
+        Self::from_str(value).unwrap()
+    }
+}
+
+impl std::fmt::Display for Valve {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        let u = self.0;
+        write!(
+            f,
+            "{}{}",
+            char::from_u32((u >> 8).try_into().unwrap()).unwrap(),
+            char::from_u32((u & 0xff).try_into().unwrap()).unwrap()
+        )
+    }
+}
+
+type Flow = u32;
+type Pressure = u32;
+
+#[derive(Debug, Clone)]
+struct Graph {
+    valves: HashMap<Valve, Pressure>,
+    tunnels: HashMap<Valve, Vec<Valve>>,
+}
+
+impl Graph {
+    fn parse(text: &str) -> Self {
+        let mut valves = HashMap::new();
+        let mut tunnels: HashMap<Valve, Vec<Valve>> = HashMap::new();
+
+        let re = Regex::new(r"^Valve (.*) has flow rate=(.*); tunnels? leads? to valves? (.*)$")
+            .unwrap();
+
+        for line in aoc::lines(text) {
+            let caps = re.captures(line).unwrap();
+
+            let valve = Valve::from_str(&caps[1]).unwrap();
+            let flow_rate: u32 = caps[2].parse().unwrap();
+            let neighbors: Vec<Valve> =
+                caps[3].split(", ").map(|s| s.try_into().unwrap()).collect();
+
+            valves.insert(valve, flow_rate);
+            for n in neighbors {
+                tunnels
+                    .entry(valve)
+                    .and_modify(|dests| dests.push(n))
+                    .or_insert_with(|| vec![n]);
+            }
+        }
+
+        Self { valves, tunnels }
+    }
+}
+
+#[derive(Debug, Clone, PartialEq, Eq, Hash)]
+enum Action {
+    MoveTo(Valve),
+    Open(Valve),
+}
+
+#[derive(Debug, Clone, PartialEq, Eq, Hash)]
+struct Path(Vec<Action>);
+
+impl Path {
+    fn current_location(&self) -> Valve {
+        match self.0.last() {
+            None => Valve::from("AA"),
+            Some(Action::MoveTo(v)) => *v,
+            Some(Action::Open(v)) => *v,
+        }
+    }
+
+    fn minutes_elapsed(&self) -> usize {
+        self.0.len()
+    }
+
+    fn successors(
+        &self,
+        valves: &HashMap<Valve, Pressure>,
+        paths: &HashMap<(Valve, Valve), Option<ShortestPath<Valve>>>,
+    ) -> Vec<Vec<Action>> {
+        let here = self.current_location();
+
+        let open_valves: HashSet<Valve> = self
+            .0
+            .iter()
+            .cloned()
+            .filter_map(|a| match a {
+                Action::Open(v) => Some(v),
+                Action::MoveTo(_) => None,
+            })
+            .collect();
+
+        let mut suffixes = vec![];
+
+        for (&dest, &pressure) in valves {
+            if pressure == 0 {
+                continue;
+            }
+            if open_valves.contains(&dest) {
+                continue;
+            }
+
+            let Some(ref sp) = paths[&(here, dest)] else {
+                continue;
+            };
+
+            let mut actions = vec![];
+            for &node in &sp.nodes[1..] {
+                // skip self start
+                actions.push(Action::MoveTo(node));
+            }
+            actions.push(Action::Open(dest));
+
+            suffixes.push(actions);
+        }
+
+        suffixes
+    }
+
+    fn flow(&self, valves: &HashMap<Valve, Pressure>, total_minutes: usize) -> Flow {
+        self.0
+            .iter()
+            .enumerate()
+            .map(|(i, a)| {
+                let pressure = match a {
+                    Action::MoveTo(_) => 0,
+                    Action::Open(ref v) => valves[v],
+                };
+                let minutes_left = total_minutes - i - 1;
+                pressure * (minutes_left as u32)
+            })
+            .sum()
+    }
+}
+
+#[derive(Debug, Clone, Eq, PartialEq)]
+struct State {
+    path: Path,
+    flow: Flow,
+}
+
+impl PartialOrd for State {
+    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+impl Ord for State {
+    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
+        // BinaryHeap is a **MAX-HEAP**. To get a min-heap, we run the comparisons backwards.
+
+        let self_minutes = self.path.minutes_elapsed();
+        let other_minutes = other.path.minutes_elapsed();
+
+        // Sort more remaining time first...
+        let cmp_minutes = self_minutes.cmp(&other_minutes);
+
+        // ... and break ties by higher flow.
+        cmp_minutes.then_with(|| other.flow.cmp(&self.flow))
+    }
+}
+
+impl Graph {
+    fn max_flow(&self, total_minutes: usize) -> Flow {
+        let paths = {
+            let nodes: Vec<Valve> = self.valves.keys().cloned().collect();
+            let mut edges: HashMap<(Valve, Valve), u64> = HashMap::new();
+            for (&from, tos) in &self.tunnels {
+                for &to in tos {
+                    edges.insert((from, to), 1);
+                }
+            }
+            all_pairs_shortest_paths(nodes, edges)
+        };
+
+        let mut queue: BinaryHeap<State> = BinaryHeap::new();
+        let mut expanded: HashSet<Valve> = HashSet::new();
+
+        let start = State {
+            path: Path(vec![]),
+            flow: 0,
+        };
+
+        queue.push(start.clone());
+
+        let mut best: State = start;
+
+        while let Some(state) = queue.pop() {
+            let here = state.path.current_location();
+            expanded.insert(here);
+
+            if state.flow > best.flow {
+                best = state.clone();
+            }
+
+            for actions in state.path.successors(&self.valves, &paths) {
+                let path = {
+                    let mut aa = state.path.0.clone();
+                    aa.extend(actions);
+                    Path(aa)
+                };
+
+                if path.minutes_elapsed() > total_minutes {
+                    // 🌋🌋🌋
+                    continue;
+                }
+
+                let flow = path.flow(&self.valves, total_minutes);
+
+                queue.push(State { path, flow });
+            }
+        }
+
+        best.flow
+    }
+}
+
+#[derive(Debug, Clone)]
+struct ShortestPath<V> {
+    nodes: Vec<V>,
+}
+
+fn all_pairs_shortest_paths<V>(
+    nodes: Vec<V>,
+    edges: HashMap<(V, V), u64>,
+) -> HashMap<(V, V), Option<ShortestPath<V>>>
+where
+    V: Eq + std::hash::Hash + Copy + core::fmt::Debug,
+{
+    let mut dist: HashMap<(V, V), u64> = HashMap::new();
+    let mut next: HashMap<(V, V), V> = HashMap::new();
+
+    for (&(u, v), &w) in &edges {
+        dist.insert((u, v), w);
+        next.insert((u, v), v);
+        next.insert((v, u), u);
+    }
+    for &v in &nodes {
+        dist.insert((v, v), 0);
+        next.insert((v, v), v);
+    }
+
+    for &k in &nodes {
+        for &i in &nodes {
+            for &j in &nodes {
+                let Some(d_ik) = dist.get(&(i,k)) else { continue };
+                let Some(d_kj) = dist.get(&(k,j)) else { continue };
+                let d_ikj = d_ik + d_kj;
+
+                let Some(&d_ij) = dist.get(&(i,j)) else {
+                    dist.insert((i, j) , d_ikj);
+                    next.insert((i, j) , next[&(i,k)]);
+                    continue;
+                };
+
+                if d_ij > d_ikj {
+                    dist.insert((i, j), d_ikj);
+                    next.insert((i, j), next[&(i, k)]);
+                }
+            }
+        }
+    }
+
+    let mut paths: HashMap<(V, V), Option<ShortestPath<V>>> = HashMap::new();
+
+    let find_path = |mut u: V, v: V| -> Option<Vec<V>> {
+        let mut path = vec![u];
+
+        while u != v {
+            let Some(&k) = next.get(&(u, v)) else {
+                return None
+            };
+
+            u = k;
+            path.push(u);
+        }
+        Some(path)
+    };
+
+    for &i in &nodes {
+        for &j in &nodes {
+            let Some(nodes) = find_path(i, j) else {
+                continue;
+            };
+            paths.insert((i, j), Some(ShortestPath { nodes }));
+        }
+    }
+
+    paths
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn heap_order() {
+        let mut queue: BinaryHeap<State> = BinaryHeap::new();
+
+        let worse = State {
+            path: Path(vec![Action::MoveTo("DD".into()), Action::Open("DD".into())]),
+            flow: 560,
+        };
+        let better = State {
+            path: Path(vec![
+                Action::MoveTo("DD".into()),
+                Action::MoveTo("BB".into()),
+            ]),
+            flow: 0,
+        };
+        queue.push(worse);
+        queue.push(better.clone());
+
+        assert_eq!(better, queue.pop().unwrap());
+    }
+}