Solution to problem 16 in Python

src/Year_2022/Day16.py

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+# --- Day 16: Proboscidea Volcanium ---
+
+# The sensors have led you to the origin of the distress signal: yet another
+# handheld device, just like the one the Elves gave you. However, you don't see
+# any Elves around; instead, the device is surrounded by elephants! They must
+# have gotten lost in these tunnels, and one of the elephants apparently figured
+# out how to turn on the distress signal.
+
+# The ground rumbles again, much stronger this time. What kind of cave is this,
+# exactly? You scan the cave with your handheld device; it reports mostly
+# igneous rock, some ash, pockets of pressurized gas, magma... this isn't just a
+# cave, it's a volcano!
+
+# You need to get the elephants out of here, quickly. Your device estimates that
+# you have 30 minutes before the volcano erupts, so you don't have time to go
+# back out the way you came in.
+
+# You scan the cave for other options and discover a network of pipes and
+# pressure-release valves. You aren't sure how such a system got into a volcano,
+# but you don't have time to complain; your device produces a report (your
+# puzzle input) of each valve's flow rate if it were opened (in pressure per
+# minute) and the tunnels you could use to move between the valves.
+
+# There's even a valve in the room you and the elephants are currently standing
+# in labeled AA. You estimate it will take you one minute to open a single valve
+# and one minute to follow any tunnel from one valve to another. What is the
+# most pressure you could release?
+
+# For example, suppose you had the following scan output:
+
+# Valve AA has flow rate=0; tunnels lead to valves DD, II, BB
+# Valve BB has flow rate=13; tunnels lead to valves CC, AA
+# Valve CC has flow rate=2; tunnels lead to valves DD, BB
+# Valve DD has flow rate=20; tunnels lead to valves CC, AA, EE
+# Valve EE has flow rate=3; tunnels lead to valves FF, DD
+# Valve FF has flow rate=0; tunnels lead to valves EE, GG
+# Valve GG has flow rate=0; tunnels lead to valves FF, HH
+# Valve HH has flow rate=22; tunnel leads to valve GG
+# Valve II has flow rate=0; tunnels lead to valves AA, JJ
+# Valve JJ has flow rate=21; tunnel leads to valve II
+
+# All of the valves begin closed. You start at valve AA, but it must be damaged
+# or jammed or something: its flow rate is 0, so there's no point in opening it.
+# However, you could spend one minute moving to valve BB and another minute
+# opening it; doing so would release pressure during the remaining 28 minutes at
+# a flow rate of 13, a total eventual pressure release of 28 * 13 = 364. Then,
+# you could spend your third minute moving to valve CC and your fourth minute
+# opening it, providing an additional 26 minutes of eventual pressure release at
+# a flow rate of 2, or 52 total pressure released by valve CC.
+
+# Making your way through the tunnels like this, you could probably open many or
+# all of the valves by the time 30 minutes have elapsed. However, you need to
+# release as much pressure as possible, so you'll need to be methodical.
+# Instead, consider this approach:
+
+# == Minute 1 ==
+# No valves are open.
+# You move to valve DD.
+
+# == Minute 2 ==
+# No valves are open.
+# You open valve DD.
+
+# == Minute 3 ==
+# Valve DD is open, releasing 20 pressure.
+# You move to valve CC.
+
+# == Minute 4 ==
+# Valve DD is open, releasing 20 pressure.
+# You move to valve BB.
+
+# == Minute 5 ==
+# Valve DD is open, releasing 20 pressure.
+# You open valve BB.
+
+# == Minute 6 ==
+# Valves BB and DD are open, releasing 33 pressure.
+# You move to valve AA.
+
+# == Minute 7 ==
+# Valves BB and DD are open, releasing 33 pressure.
+# You move to valve II.
+
+# == Minute 8 ==
+# Valves BB and DD are open, releasing 33 pressure.
+# You move to valve JJ.
+
+# == Minute 9 ==
+# Valves BB and DD are open, releasing 33 pressure.
+# You open valve JJ.
+
+# == Minute 10 ==
+# Valves BB, DD, and JJ are open, releasing 54 pressure.
+# You move to valve II.
+
+# == Minute 11 ==
+# Valves BB, DD, and JJ are open, releasing 54 pressure.
+# You move to valve AA.
+
+# == Minute 12 ==
+# Valves BB, DD, and JJ are open, releasing 54 pressure.
+# You move to valve DD.
+
+# == Minute 13 ==
+# Valves BB, DD, and JJ are open, releasing 54 pressure.
+# You move to valve EE.
+
+# == Minute 14 ==
+# Valves BB, DD, and JJ are open, releasing 54 pressure.
+# You move to valve FF.
+
+# == Minute 15 ==
+# Valves BB, DD, and JJ are open, releasing 54 pressure.
+# You move to valve GG.
+
+# == Minute 16 ==
+# Valves BB, DD, and JJ are open, releasing 54 pressure.
+# You move to valve HH.
+
+# == Minute 17 ==
+# Valves BB, DD, and JJ are open, releasing 54 pressure.
+# You open valve HH.
+
+# == Minute 18 ==
+# Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
+# You move to valve GG.
+
+# == Minute 19 ==
+# Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
+# You move to valve FF.
+
+# == Minute 20 ==
+# Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
+# You move to valve EE.
+
+# == Minute 21 ==
+# Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
+# You open valve EE.
+
+# == Minute 22 ==
+# Valves BB, DD, EE, HH, and JJ are open, releasing 79 pressure.
+# You move to valve DD.
+
+# == Minute 23 ==
+# Valves BB, DD, EE, HH, and JJ are open, releasing 79 pressure.
+# You move to valve CC.
+
+# == Minute 24 ==
+# Valves BB, DD, EE, HH, and JJ are open, releasing 79 pressure.
+# You open valve CC.
+
+# == Minute 25 ==
+# Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
+
+# == Minute 26 ==
+# Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
+
+# == Minute 27 ==
+# Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
+
+# == Minute 28 ==
+# Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
+
+# == Minute 29 ==
+# Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
+
+# == Minute 30 ==
+# Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
+
+# This approach lets you release the most pressure possible in 30 minutes with
+# this valve layout, 1651.
+
+# Work out the steps to release the most pressure in 30 minutes. What is the
+# most pressure you can release?
+
+
+import re
+from collections import deque
+
+with open("files/P16.txt") as f:
+    data = f.read().splitlines()
+    rates = {}
+    tunnels = {}
+    for line in data:
+        parts = line.split()
+        valve = parts[1]
+        rate = int(re.search("\d+", line).group())
+        if rate:
+            rates[valve] = rate
+        tunnel_list = re.search(r"valves? (.+)$", line).group(1)
+        tunnels[valve] = tunnel_list.split(", ")
+
+
+def bfs(tunnels, start, targets):
+    dist = {start: 0}
+    seen = {start}
+    queue = deque([start])
+    while queue and any(target not in dist for target in targets):
+        path = queue.popleft()
+        for route in tunnels[path]:
+            if route not in seen:
+                seen.add(route)
+                dist[route] = dist[path] + 1
+                queue.append(route)
+    return dist
+
+
+def find_paths(dist, rates, time):
+    pressures = []
+    paths = []
+    stack = [(time, 0, ["AA"])]
+    while stack:
+        time, p, path = stack.pop()
+        cur = path[-1]
+        new = []
+        for n, d in dist[cur].items():
+            if d > time - 2 or n in path:
+                continue
+            tt = time - d - 1
+            pp = p + rates[n] * tt
+            s = tt, pp, path + [n]
+            new.append(s)
+        if new:
+            stack.extend(new)
+        else:
+            pressures.append(p)
+            # paths always start at AA, so no need to keep first location
+            paths.append(path[1:])
+    return pressures, paths
+
+
+def get_distances():
+    dist = {}
+    for start in ("AA", *rates):
+        dist[start] = {}
+        d = bfs(tunnels, start, rates)
+        for rate in rates:
+            if rate != start and rate in d:
+                dist[start][rate] = d[rate]
+
+    return dist
+
+
+def part_1():
+    dist = get_distances()
+    p, _ = find_paths(dist, rates, 30)
+    print(f"One can release up to {max(p)} pressure")
+
+
+# --- Part Two ---
+
+# You're worried that even with an optimal approach, the pressure released won't
+# be enough. What if you got one of the elephants to help you?
+
+# It would take you 4 minutes to teach an elephant how to open the right valves
+# in the right order, leaving you with only 26 minutes to actually execute your
+# plan. Would having two of you working together be better, even if it means
+# having less time? (Assume that you teach the elephant before opening any
+# valves yourself, giving you both the same full 26 minutes.)
+
+# In the example above, you could teach the elephant to help you as follows:
+
+# == Minute 1 ==
+# No valves are open.
+# You move to valve II.
+# The elephant moves to valve DD.
+
+# == Minute 2 ==
+# No valves are open.
+# You move to valve JJ.
+# The elephant opens valve DD.
+
+# == Minute 3 ==
+# Valve DD is open, releasing 20 pressure.
+# You open valve JJ.
+# The elephant moves to valve EE.
+
+# == Minute 4 ==
+# Valves DD and JJ are open, releasing 41 pressure.
+# You move to valve II.
+# The elephant moves to valve FF.
+
+# == Minute 5 ==
+# Valves DD and JJ are open, releasing 41 pressure.
+# You move to valve AA.
+# The elephant moves to valve GG.
+
+# == Minute 6 ==
+# Valves DD and JJ are open, releasing 41 pressure.
+# You move to valve BB.
+# The elephant moves to valve HH.
+
+# == Minute 7 ==
+# Valves DD and JJ are open, releasing 41 pressure.
+# You open valve BB.
+# The elephant opens valve HH.
+
+# == Minute 8 ==
+# Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
+# You move to valve CC.
+# The elephant moves to valve GG.
+
+# == Minute 9 ==
+# Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
+# You open valve CC.
+# The elephant moves to valve FF.
+
+# == Minute 10 ==
+# Valves BB, CC, DD, HH, and JJ are open, releasing 78 pressure.
+# The elephant moves to valve EE.
+
+# == Minute 11 ==
+# Valves BB, CC, DD, HH, and JJ are open, releasing 78 pressure.
+# The elephant opens valve EE.
+
+# (At this point, all valves are open.)
+
+# == Minute 12 ==
+# Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
+
+# ...
+
+# == Minute 20 ==
+# Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
+
+# ...
+
+# == Minute 26 ==
+# Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
+
+# With the elephant helping, after 26 minutes, the best you could do would
+# release a total of 1707 pressure.
+
+# With you and an elephant working together for 26 minutes, what is the most
+# pressure you could release?
+
+
+def part_2():
+    dist = get_distances()
+    all_paths = list(zip(*find_paths(dist, rates, 26)))
+    p, paths = zip(*sorted(all_paths, reverse=True))
+
+    i, j = 0, 1
+    while any(path in paths[j] for path in paths[i]):
+        j += 1
+    # lower bound
+    combined_p = p[i] + p[j]
+    # since p[i] can only decrease, j cannot exceed this
+    j_max = j
+    for i in range(1, j_max):
+        for j in range(i + 1, j_max + 1):
+            if any(path in paths[j] for path in paths[i]):
+                continue
+            combined_p = max(combined_p, p[i] + p[j])
+
+    print(f"An elephant and me could release up to {combined_p} pressure")
+
+
+if __name__ == "__main__":
+    part_1()
+    part_2()

src/Year_2022/files/P16.txt

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+Valve VR has flow rate=11; tunnels lead to valves LH, KV, BP
+Valve UV has flow rate=0; tunnels lead to valves GH, RO
+Valve OH has flow rate=0; tunnels lead to valves AJ, NY
+Valve GD has flow rate=0; tunnels lead to valves TX, PW
+Valve NS has flow rate=0; tunnels lead to valves AJ, AA
+Valve KZ has flow rate=18; tunnels lead to valves KO, VK, PJ
+Valve AH has flow rate=0; tunnels lead to valves ZP, DI
+Valve SA has flow rate=0; tunnels lead to valves VG, JF
+Valve VK has flow rate=0; tunnels lead to valves RO, KZ
+Valve GB has flow rate=0; tunnels lead to valves XH, AA
+Valve AJ has flow rate=6; tunnels lead to valves IC, OH, ZR, NS, EM
+Valve PJ has flow rate=0; tunnels lead to valves KZ, SP
+Valve KO has flow rate=0; tunnels lead to valves KZ, LE
+Valve AA has flow rate=0; tunnels lead to valves TW, GB, TI, NS, UL
+Valve TW has flow rate=0; tunnels lead to valves TU, AA
+Valve VG has flow rate=25; tunnel leads to valve SA
+Valve BP has flow rate=0; tunnels lead to valves RO, VR
+Valve XH has flow rate=0; tunnels lead to valves GB, RI
+Valve TX has flow rate=0; tunnels lead to valves RI, GD
+Valve IR has flow rate=10; tunnels lead to valves TN, NY, JF
+Valve TU has flow rate=0; tunnels lead to valves JD, TW
+Valve KC has flow rate=0; tunnels lead to valves SP, RO
+Valve LN has flow rate=0; tunnels lead to valves EM, RI
+Valve HD has flow rate=0; tunnels lead to valves FE, SC
+Valve KE has flow rate=0; tunnels lead to valves OM, RI
+Valve VY has flow rate=0; tunnels lead to valves PW, BS
+Valve LH has flow rate=0; tunnels lead to valves OM, VR
+Valve EM has flow rate=0; tunnels lead to valves AJ, LN
+Valve SO has flow rate=22; tunnels lead to valves ZP, FE
+Valve EC has flow rate=0; tunnels lead to valves OM, UL
+Valve KV has flow rate=0; tunnels lead to valves SP, VR
+Valve FE has flow rate=0; tunnels lead to valves SO, HD
+Valve TI has flow rate=0; tunnels lead to valves AA, PW
+Valve SC has flow rate=14; tunnel leads to valve HD
+Valve ZP has flow rate=0; tunnels lead to valves SO, AH
+Valve RO has flow rate=19; tunnels lead to valves UV, BP, VK, KC
+Valve ZR has flow rate=0; tunnels lead to valves OM, AJ
+Valve JL has flow rate=21; tunnels lead to valves GN, TN
+Valve PW has flow rate=9; tunnels lead to valves TI, GN, VY, GD, IC
+Valve UL has flow rate=0; tunnels lead to valves EC, AA
+Valve GN has flow rate=0; tunnels lead to valves JL, PW
+Valve TN has flow rate=0; tunnels lead to valves JL, IR
+Valve NV has flow rate=0; tunnels lead to valves RI, JD
+Valve DI has flow rate=23; tunnels lead to valves LE, AH
+Valve IC has flow rate=0; tunnels lead to valves PW, AJ
+Valve JF has flow rate=0; tunnels lead to valves SA, IR
+Valve LE has flow rate=0; tunnels lead to valves DI, KO
+Valve BS has flow rate=0; tunnels lead to valves JD, VY
+Valve JD has flow rate=15; tunnels lead to valves NV, TU, BS
+Valve SP has flow rate=24; tunnels lead to valves KC, KV, PJ
+Valve NY has flow rate=0; tunnels lead to valves IR, OH
+Valve OM has flow rate=7; tunnels lead to valves EC, GH, KE, ZR, LH
+Valve GH has flow rate=0; tunnels lead to valves OM, UV
+Valve RI has flow rate=3; tunnels lead to valves NV, KE, LN, XH, TX