Add solution to 2023-12-20

2023/day20/input

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+%vg -> lf, vd
+%dr -> kg
+%cn -> mv, pt
+%rq -> bk, gr
+%vp -> lp, bk
+%kg -> lv
+%lv -> jc, tp
+%sj -> rm, vd
+%jc -> tp, qr
+%km -> tp, dr
+%jx -> cn
+&vd -> tf, lf, nb, cx, hx, lr
+%lp -> jt, bk
+%vj -> ps
+broadcaster -> km, lr, xh, rf
+%dj -> pt, gc
+%cg -> vd, hx
+&ln -> tg
+%fl -> pt, sk
+%lm -> tr, bk
+%lr -> vd, vg
+&pt -> vq, rf, cm, jx, rg
+%cx -> gp
+%gp -> vd, sj
+&db -> tg
+%st -> vd
+%jt -> bk
+%jh -> lm, bk
+%xf -> bd, tp
+%gc -> cm, pt
+&tp -> dr, km, kg, db, vj, qr
+%ps -> xf, tp
+%rf -> pt, dj
+%lf -> nb
+%bd -> tp, gg
+%dk -> tp, vj
+%mn -> jh, bk
+&tg -> rx
+%ql -> bk, zx
+%tr -> bk, vp
+%sk -> pt
+%nb -> cg
+%sb -> vd, cx
+%qr -> dk
+%xh -> bk, ql
+%rg -> sd
+%hx -> sb
+%sd -> pt, jx
+%gr -> bk, mn
+%gg -> tp
+%zx -> rq
+&bk -> xh, ln, zx
+%rm -> st, vd
+%hq -> fl, pt
+&vq -> tg
+%cm -> rg
+&tf -> tg
+%mv -> pt, hq

2023/day20/solutions.py

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+from collections import defaultdict, deque
+from itertools import count
+from math import lcm, prod
+
+with open("input") as f:
+    ws = [l.split() for l in f.read().strip().replace(",", "").split("\n")]
+
+flips = {w[1:] for w, *_ in ws if w[0] == "%"}
+
+parents = defaultdict(dict)
+children = defaultdict(list)
+
+for w, _, *regs in ws:
+    for reg in regs:
+        parents[reg][w.strip("&%")] = False
+        children[w.strip("&%")].append(reg)
+
+
+def press_button(states, sent, periods, i):
+    q = deque([("broadcaster", "button", False)])
+
+    def send(sender, signal):
+        for c in children[sender]:
+            q.append((c, sender, signal))
+
+    while q:
+        receiver, sender, signal = q.popleft()
+        sent[signal] += 1
+        if receiver == "broadcaster":
+            send("broadcaster", signal)
+        elif receiver in flips:
+            if not signal:
+                states[receiver] = not states[receiver]
+                send(receiver, states[receiver])
+        else:
+            if signal and receiver == "tg" and sender not in periods:  # For part 2
+                periods[sender] = i
+            parents[receiver][sender] = signal
+            send(receiver, not all(parents[receiver].values()))
+    return states, sent, periods
+
+
+# Part 1
+states = defaultdict(bool)
+sent = defaultdict(int)
+
+for _ in range(1000):
+    states, sent, _ = press_button(states, sent, {}, 0)
+
+print(prod(sent.values()))
+
+# Part 2
+# For part 2, we manually inspect the output. We find that rx depends only on tg,
+# and that tg depends on four other registers. By watching the changes in those,
+# we find that they are cyclic, so the earliest time tg could possible be set is
+# at a button click count corresponding to the least common multiple of the cycle
+# lengths for the four other registers.
+states = defaultdict(bool)
+sent = defaultdict(int)
+periods = {}
+
+for i in count(1):
+    states, _, periods = press_button(states, sent, periods, i)
+    if len(periods) == 4:
+        print(lcm(*periods.values()))
+        break