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| ......##................#.#.......#............#..#......##.#.......................#........#.#.#...#.....#.........#...#.#....... | ||
| ................................................................................................................................... |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,44 @@ | ||
| with open("input") as f: | ||
| inp = f.read().strip().split("\n") | ||
|
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| R, C = len(inp), len(inp[0]) | ||
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| grid = {i+j*1j: inp[j][i] for i in range(C) for j in range(R)} | ||
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| for p, c in grid.items(): | ||
| if c == "S": | ||
| start = p | ||
| grid[p] = "." | ||
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| ps = set() | ||
| ps.add(start) | ||
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| # Let f(n) be the number of gardens after n steps. Let R = C be the height/width of the grid. | ||
| # The number of steps is 26501365 = 202300*R + 65. We anticipate that g(m) = f(65+m*R) is quadratic, | ||
| # so we find g(m), for m = 0, 1, 2, and fit a quadratic polynomial to (m, g(m)) [m = 0, 1, 2]. | ||
| # This happens to fit perfectly. | ||
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| steps = 26501365 | ||
| rest = steps % R | ||
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| for m in range(rest+2*R): | ||
| new_ps = set() | ||
| for p in ps: | ||
| for dp in [-1, 1, 1j, -1j]: | ||
| new_p = p + dp | ||
| cor_p = (new_p.real % C) + (new_p.imag % R)*1j | ||
| if grid[cor_p] == ".": | ||
| new_ps.add(new_p) | ||
| ps = new_ps | ||
| if m == 63: | ||
| print(len(ps)) # Part 1 | ||
| if (m+1) % R == rest: | ||
| print((m+1)//R, m+1, len(ps)) # Points to fit | ||
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| # This is the corresponding polynomial. | ||
| def n_gardens(steps): | ||
| return 3738+14836*steps+14696*steps**2 | ||
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||
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| print(n_gardens(steps // R)) |