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Add solution to 2023-12-21
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‎2023/day21/input

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‎2023/day21/solutions.py

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from collections import deque
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from scipy.optimize import curve_fit
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with open("input") as f:
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ls = f.read().strip().split()
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N = len(ls)
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blocked = set()
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for i, l in enumerate(ls):
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for j, x in enumerate(l):
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if x == "S":
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start = i + 1j * j
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elif x == "#":
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blocked.add(i + 1j * j)
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def counts():
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q = deque([(start, 0)])
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curr_dist = None
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evens = 1
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odds = 0
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seen = {start}
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while True:
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z, dist = q.popleft()
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if dist != curr_dist:
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curr_dist = dist
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yield (curr_dist, odds if curr_dist % 2 else evens)
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for dz in (-1, 1, -1j, 1j):
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w = z + dz
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w_mod_N = (w.real % N) + 1j * (w.imag % N)
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if w_mod_N in blocked or w in seen:
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continue
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seen.add(w)
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q.append((w, dist + 1))
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if dist % 2:
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evens += 1
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else:
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odds += 1
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# For part 2, by looking at how the output of counts evolves for the test input,
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# one quickly finds that it has behavior periodic with the size of the grid. By
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# looking at the counts for each remainder, one finds that they are all quadratic
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# polynomials after some initial noise. (This is easiest to see for the test input
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# by looking at the counts that show up after all numbers of steps that are 0 mod 11.
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# As such, we keep track of the counts for the residue class belong to our target,
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# fit a quadratic polynomial, and once the predictions have stabilized for the
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# actual input, we assume that we have the right answer.
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def f(x, a, b, c):
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return a * x**2 + b * x + c
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gen = counts()
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to_hit = 26501365
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period = N
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preds = []
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data = []
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for i, num_locs in gen:
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# Part 1
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if i == 64:
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print(num_locs)
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# Part 2
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if i % period == to_hit % period:
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data.append((i, num_locs))
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if len(data) < 3:
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continue
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last_seen = data[-3:]
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fa, fb, fc = curve_fit(f, *zip(*last_seen))[0]
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pred = round(f(to_hit, fa, fb, fc))
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preds.append(pred)
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# We assume that we have converged if the same prediction shows up
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# three times in a row
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if len(preds) > 3 and len(set(preds[-3:])) == 1:
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print(preds[-1])
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break

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