Day 16

16/input

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+Valve AP has flow rate=0; tunnels lead to valves AA, ON
+Valve QN has flow rate=21; tunnels lead to valves RI, CG
+Valve LK has flow rate=0; tunnels lead to valves XM, AA
+Valve HA has flow rate=0; tunnels lead to valves WH, KF
+Valve DS has flow rate=16; tunnel leads to valve II
+Valve KD has flow rate=0; tunnels lead to valves KG, QB
+Valve JW has flow rate=0; tunnels lead to valves AD, KF
+Valve HU has flow rate=0; tunnels lead to valves UK, CO
+Valve AE has flow rate=10; tunnels lead to valves IR, PT, UV
+Valve XA has flow rate=0; tunnels lead to valves CG, EU
+Valve SE has flow rate=17; tunnels lead to valves YR, AD
+Valve TR has flow rate=0; tunnels lead to valves AL, CS
+Valve BS has flow rate=0; tunnels lead to valves YH, XM
+Valve IJ has flow rate=24; tunnels lead to valves XN, WE
+Valve AA has flow rate=0; tunnels lead to valves LK, AP, IZ, PC, QD
+Valve KG has flow rate=0; tunnels lead to valves KD, CS
+Valve QV has flow rate=0; tunnels lead to valves XM, II
+Valve PC has flow rate=0; tunnels lead to valves AA, YF
+Valve GJ has flow rate=20; tunnel leads to valve RI
+Valve UV has flow rate=0; tunnels lead to valves UK, AE
+Valve IR has flow rate=0; tunnels lead to valves EU, AE
+Valve EU has flow rate=13; tunnels lead to valves IR, DT, XA, ON
+Valve ED has flow rate=0; tunnels lead to valves XN, CO
+Valve DT has flow rate=0; tunnels lead to valves EU, UK
+Valve YE has flow rate=0; tunnels lead to valves XM, WS
+Valve AD has flow rate=0; tunnels lead to valves JW, SE
+Valve WE has flow rate=0; tunnels lead to valves IJ, NA
+Valve UK has flow rate=5; tunnels lead to valves UV, DT, QD, HU
+Valve YR has flow rate=0; tunnels lead to valves OS, SE
+Valve II has flow rate=0; tunnels lead to valves QV, DS
+Valve GT has flow rate=0; tunnels lead to valves CS, MN
+Valve YH has flow rate=0; tunnels lead to valves BS, QB
+Valve BQ has flow rate=0; tunnels lead to valves XM, KF
+Valve OS has flow rate=0; tunnels lead to valves YR, NA
+Valve WH has flow rate=0; tunnels lead to valves QB, HA
+Valve QB has flow rate=4; tunnels lead to valves WH, KD, YH, IZ
+Valve ON has flow rate=0; tunnels lead to valves AP, EU
+Valve IZ has flow rate=0; tunnels lead to valves AA, QB
+Valve MN has flow rate=25; tunnel leads to valve GT
+Valve CG has flow rate=0; tunnels lead to valves XA, QN
+Valve QD has flow rate=0; tunnels lead to valves UK, AA
+Valve AL has flow rate=0; tunnels lead to valves KF, TR
+Valve XN has flow rate=0; tunnels lead to valves ED, IJ
+Valve WS has flow rate=0; tunnels lead to valves YE, CS
+Valve CO has flow rate=18; tunnels lead to valves ED, PT, HU
+Valve PT has flow rate=0; tunnels lead to valves CO, AE
+Valve RI has flow rate=0; tunnels lead to valves QN, GJ
+Valve CS has flow rate=9; tunnels lead to valves YF, GT, WS, TR, KG
+Valve YF has flow rate=0; tunnels lead to valves PC, CS
+Valve NA has flow rate=23; tunnels lead to valves OS, WE
+Valve KF has flow rate=12; tunnels lead to valves HA, AL, JW, BQ
+Valve XM has flow rate=3; tunnels lead to valves LK, QV, YE, BS, BQ

16/solution.mjs

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+
+import { readFileSync } from 'node:fs';
+
+const input = readFileSync('input', 'utf-8');
+
+
+const valves = new Map(input
+  .split('\n')
+  .filter(Boolean)
+  .map(line => {
+    const valve = line.match(/Valve (\w+)/)[1];
+    const rate = parseInt(line.match(/rate=(\d+)/)[1]);
+    const to = line.match(/valves? (.*)/)[1].split(', ');
+    return [valve, {valve, rate, to}];
+  })
+);
+
+function shortestPath(v, vDest, path=[]) {
+  const valve = valves.get(v);
+
+  if (valve.to.includes(vDest)) {
+    return [...path, v, vDest];
+  }
+  return valve.to
+    .filter(to => !path.includes(to))
+    .map(to => shortestPath(to, vDest, [...path, v]))
+    .filter(Boolean)
+    .sort((p1, p2) => p1.length - p2.length)[0];
+}
+
+// Add a property to all valves containing links to all other valves with a
+// flow rate greater than 0 and the time it will take to reach them
+const valvesWithFlow = [...valves.values()]
+  .filter(valve => valve.rate > 0);
+for (const valve of valves.values()) {
+  valve.usefulTo = valvesWithFlow
+    .filter(vDest => vDest.valve !== valve.valve)
+    .map(vDest => ({
+      valve: vDest.valve,
+      time: shortestPath(valve.valve, vDest.valve).length - 1,
+      rate: vDest.rate
+    }));
+}
+
+function product(...arrs) {
+  if (!arrs.length) return [];
+  return arrs.reduce((result, arr) =>
+    result.flatMap(r =>
+      arr.map(a => [...r, a])
+    ),
+    [[]]
+  )
+}
+
+// General solution for n players
+function solve(players, rate=0) {
+  for (const player of players) {
+    const valve = valves.get(player.path[player.path.length - 1]);
+
+    if (valve.rate > 0 && !player.opened) {
+      player.opened = true;
+      player.timeRemaining -= 1;
+      rate += valve.rate * Math.max(0, player.timeRemaining);
+    }
+  }
+
+  // Array of valve names which haven't been visited
+  const unvisitedValves = valvesWithFlow
+    .map(v => v.valve)
+    .filter(valve => !players.find(p => p.path.includes(valve)));
+
+  // Exit conditions
+  if (
+    unvisitedValves.length === 0 ||
+    players.every(player => player.timeRemaining <= 0)
+  ) {
+    return [rate, players];
+  }
+
+  // Decide who is moving
+  const maxTimeRemaining = players.reduce(
+    (max, player) => Math.max(max, player.timeRemaining),
+    0
+  );
+  const movingPlayers = players.filter(
+    player => player.timeRemaining === maxTimeRemaining
+  );
+  const nonMovingPlayers = players.filter(
+    player => !movingPlayers.includes(player)
+  );
+
+  const playerMoves = product(...movingPlayers
+    .map(player => {
+      const valve = valves.get(player.path[player.path.length - 1]);
+      const destinations = valve.usefulTo
+        .filter(to => unvisitedValves.includes(to.valve))
+        .filter((to, _, tos) => !tos.find((otherTo) =>
+          otherTo.rate > to.rate &&
+          otherTo.time <= to.time
+        ));
+      if (destinations.length < movingPlayers.length) {
+        destinations.push(undefined);
+      }
+      return destinations;
+    })
+  ).filter(moves => {
+    const valves = moves.filter(Boolean).map(to => to.valve);
+    return (
+      valves.length !== 0 &&
+      new Set(valves).size === valves.length
+    );
+  });
+
+  return playerMoves
+    .map(moves => {
+      const movedPlayers = moves.map((to, i) => {
+        const player = movingPlayers[i];
+        if (to === undefined) {
+          // Not moving
+          return player;
+        }
+        return {
+          timeRemaining: player.timeRemaining - to.time,
+          opened: false,
+          path: [...player.path, to.valve]
+        };
+      });
+
+      return solve([...nonMovingPlayers, ...movedPlayers], rate);
+    })
+    .filter(Boolean)
+    .sort(([rate1], [rate2]) => rate2 - rate1)[0];
+}
+
+
+const solution1 = solve([{
+  timeRemaining: 30,
+  opened: false,
+  path: ['AA']
+}]);
+console.log(`Max pressure released in 30 minutes: ${solution1[0]}`);
+
+const solution2 = solve([{
+  timeRemaining: 26,
+  opened: false,
+  path: ['AA']
+}, {
+  timeRemaining: 26,
+  opened: false,
+  path: ['AA']
+}]);
+console.log(`Max pressure released with elephant: ${solution2[0]}`);