From 5f8c74fd1c38724191baabb33c65a5ca83c47a86 Mon Sep 17 00:00:00 2001 From: Mikael CAPELLE Date: Thu, 21 Dec 2023 14:57:09 +0100 Subject: [PATCH] 2023 day 21. --- src/holt59/aoc/2023/day21.py | 89 ++++++++++++- src/holt59/aoc/inputs/holt59/2023/day21.txt | 131 ++++++++++++++++++++ src/holt59/aoc/inputs/tests/2023/day21.txt | 11 ++ 3 files changed, 226 insertions(+), 5 deletions(-) diff --git a/src/holt59/aoc/2023/day21.py b/src/holt59/aoc/2023/day21.py index 992bf35..9618081 100644 --- a/src/holt59/aoc/2023/day21.py +++ b/src/holt59/aoc/2023/day21.py @@ -1,13 +1,92 @@ +import logging +import os import sys -from collections import defaultdict -from dataclasses import dataclass -lines = sys.stdin.read().splitlines() +VERBOSE = os.getenv("AOC_VERBOSE") == "True" +logging.basicConfig(level=logging.INFO if VERBOSE else logging.WARNING) + + +def reachable( + map: list[str], tiles: set[tuple[int, int]], steps: int +) -> set[tuple[int, int]]: + n_rows, n_cols = len(map), len(map[0]) + + for _ in range(steps): + tiles = { + (i + di, j + dj) + for i, j in tiles + for di, dj in ((-1, 0), (+1, 0), (0, -1), (0, +1)) + if map[(i + di) % n_rows][(j + dj) % n_cols] != "#" + } + return tiles + + +map = sys.stdin.read().splitlines() +start = next( + (i, j) for i in range(len(map)) for j in range(len(map[i])) if map[i][j] == "S" +) # part 1 -answer_1 = ... +answer_1 = len(reachable(map, {start}, 6 if len(map) < 20 else 64)) print(f"answer 1 is {answer_1}") # part 2 -answer_2 = ... + +# the initial map is a square and contains an empty rhombus whose diameter is the size +# of the map, and has only empty cells around the middle row and column +# +# after ~n/2 steps, the first map is filled with a rhombus, after that we get a bigger +# rhombus every n steps +# +# we are going to find the number of cells reached for the initial rhombus, n steps +# after and n * 2 steps after, and then interpolate the value to get a 2nd order +# polynomial +# +cycle = len(map) +rhombus = (len(map) - 3) // 2 + 1 + +values: list[int] = [] +values.append(len(tiles := reachable(map, {start}, rhombus))) +values.append(len(tiles := reachable(map, tiles, cycle))) +values.append(len(tiles := reachable(map, tiles, cycle))) + +if logging.root.getEffectiveLevel() == logging.INFO: + n_rows, n_cols = len(map), len(map[0]) + + rows = [ + [ + map[i % n_rows][j % n_cols] if (i, j) not in tiles else "O" + for j in range(-2 * cycle, 3 * cycle + 1) + ] + for i in range(-2 * cycle, 3 * cycle + 1) + ] + + for i in range(len(rows)): + for j in range(len(rows[i])): + if (i // cycle) % 2 == (j // cycle) % 2: + rows[i][j] = f"\033[91m{rows[i][j]}\033[0m" + + print("\n".join("".join(row) for row in rows)) + + +logging.info(f"values to fit: {values}") + +# the value we are interested in (26501365) can be written as R + K * C where R is the +# step at which we find the first rhombus, and K the repeat step, so instead of fitting +# for X values (R, R + K, R + 2 K), we are going to fit for (0, 1, 2), giving us much +# simpler equation for the a, b and c coefficient +# +# we get: +# - (a * 0² + b * 0 + c) = y1 => c = y1 +# - (a * 1² + b * 1 + c) = y2 => a + b = y2 - y1 +# => b = y2 - y1 - a +# - (a * 2² + b * 2 + c) = y3 => 4a + 2b = y3 - y1 +# => 4a + 2(y2 - y1 - a) = y3 - y1 +# => a = (y1 + y3) / 2 - y2 +# +y1, y2, y3 = values +a, b, c = (y1 + y3) // 2 - y2, 2 * y2 - (3 * y1 + y3) // 2, y1 + +n = (26501365 - rhombus) // cycle +answer_2 = a * n * n + b * n + c print(f"answer 2 is {answer_2}") diff --git a/src/holt59/aoc/inputs/holt59/2023/day21.txt b/src/holt59/aoc/inputs/holt59/2023/day21.txt index e69de29..7a37da6 100644 --- a/src/holt59/aoc/inputs/holt59/2023/day21.txt +++ b/src/holt59/aoc/inputs/holt59/2023/day21.txt @@ -0,0 +1,131 @@ +................................................................................................................................... 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