Add solution to 2023-12-21

2023/day21/input

@@ -0,0 +1,131 @@
+...................................................................................................................................
+..............#............#..#......#.##.....#..##..##.#...............#.........#......#....#..#.......#............#.#..........
+.......##.......#..#..................#.......#...#..##.##.................##......#.......#..#.....##........##..#.....#......###.
+.......#...#..#...........#............#..#..........#.#..#................#.....#......#.................###.....#.#....#.........
+...........#......#....#...#...#........#.............#....................#......#...............#..#..........#..............#...
+...#.#..#.#............................#.....##........#........#..................#.#....##.............#.##...#......###.........
+..#......#.........#...........#....#.....#..........#.................................#.................#............#..#......##.
+.##...#...#....#................#.#.#.....#..................................................#...#.....#...#..#...............##...
+.......#.............#.#..#........#.#...........#.#............#..#...........##.#....##...........#.........#..#.....#...........
+......#......#...............#........#.....#...##.#...........................#....#..#.#......#....#.....#...#....#.........#....
+..................##.#.......#.....#.......#......#...........#.#...............#.....#.##..#....#....#..............#.#..#...#....
+...........#..........#......................#.............#...##......##...............#.......##.......#.......#..#....#.........
+.....#..................#............#...#.......#...........#.......#................#..#...#....#.......##...#.....#........#....
+...#...........#..............##...##.....#.#..#...............#....................#.......#..#..#.....#..#...#.............#..#..
+.#......#.......................#......#.#..#.#...............#...............................#.#..#......#..........#....#....#...
+..........#........#.........##.#...#.....................#.......#...#...............#...#..#......#..#.#........#...#...#........
+.##.....#..#...............#............................#.............#..................#.....#...#.#....#......#.....#...........
+....#...#..#.##.#........#..#.............................#..............#....#............#.....#.....#.#...#...#.......#....#.#..
+......#.......#..#........#...........##............#.....##...##.............#........#....................#......#.......#.......
+.#......#............#...#..#..#..##..................#...#...............#...............#.............#..#..#.##..#......#..#....
+............#.............#...#.......#..........#....#..##....#...#...#.#.....#..............#...#....##..........................
+...##...#.......#........#.#...#....#...#................................#.....#.#........#.......#.....#..........................
+.#......#.......#...##.#..##.......#.......................#.#.....#.......................#.....#.......#.........#..........#.#..
+.........#...........#...........................#.........##.......#......##..#............#..#.........#.......#....#............
+......................#....##..................#.......#..........#..#...#.##.#.....................#.#...#....#.......#.......##..
+..##.##...........#....#...#...#..#.#........##.....#.........#...#......#.#........#.............................#...#............
+...........###...#..##.....#..................................#....##........#.#....#..............#...#..##.....#.....#......#..#.
+....#....##.#........#.........##...............#............#....#..........#.....................#................#.#............
+.#..##.#....#...............##.#.............#..#..............#......###.....#.#......................#.....##.........##.......#.
+...#............#.......#..#...#...........#........#....#......#..............#.....................#..#..........................
+.#...................#........#.........#.#.................#............#............#.#..................#...#....#....#.........
+.......#..#........#..........#..........#.#.....#..##.........#..............#......#........................##.....#.#...........
+............#.............................###........#.........#...#......#...#.#.....#...............#....##...#....##..##....#...
+....#...#.##.......#.#..............##..................###..##......#........#.....#.#...................#...#......#........#..#.
+..............##...#....##................###....###.#...#........#.....#..................#..............#...#.....#...#..........
+..##......#.##......##....#........#...#..#...#............#...#....#..#.............#........#..................#........#........
+..#....................#.#........#....#.....................#............#......#...#.....##.............#..........#..........#..
+.........#...##..#........................#.##.....#...............#..##...#.....#..#............................#...#..##.#.....#.
+.......................#........#.#.........#..#.......##..........................#..#.....#..................##..................
+...............#...............#...#.........##......#.........#..#......#..#.........#....#...................#..#.#...###........
+..#.#...#..#......##.......................#...#......#..............#......................#..#...............##..................
+...........#.................#.....#..........##.........#..........#.....#............#....#.........................#.....#......
+.........#..##....#..............#...#..........#......#..#.#.#..........#..#....#............##..#............#........#.#....#...
+.....#.#..###....#.........#...#.....#........#..#.....##...#......#.................##...............#................#.....#.....
+.......#....#..............#.#...#........#.....#...............#..#..#................#.........#...................##.....#......
+......#...#.................#.#...........#.#.................................#.#.##.......#......#...#..#...................#.##..
+..#...........#........#...#...#.....#...#.......#........##...#.......#...................................#..........#............
+......#..#..#..........#..#...#......#..............#..#....#.....#.#....#........#.###.......#..#.#.....................#...#.....
+..#..................#..#........#...#..........#..#.#....#...........#.#...#...#..#..#.#........#..#.......##...................#.
+..#......##.............#.........#......#.##...##.#.#...#...........#.........#.##...#..#.....#...#....#..........................
+................................##............#..#.............#...........#........#.##.......#.#...#..#...#.#........#.......#...
+..........................#.........................#..........#....#.....#......#.#.......#.#..#.....#.....#..#.................#.
+...#.............#...#...#...#...#.....#.........#.................#...##.....#......................#.....#.#.#.........##....#...
+.....#...........#.##.#...#...#.#.#....#......#...#..#..#...#...#.#.#.#.##.......#.........#..........#...................#....##..
+......#..................##..##.#.......#..............#.#...............#.#...#...##.......#.......#.....#....#...............#...
+...#.........................#........##........#....#...#.....#....................#......#..#...........#.#.##..............#....
+.............#........#....####..##..........#.#..............#...#............#.............##...####..........##...........##....
+................#.....##..........#........#..##.#................#.......#.##....#.......#..#...##......##........................
+.#.........#...#.......#.#.#....#.....#..................##.#.......#......#......#....#.......#...#.....#...#.....#...#.......#...
+..........#...#..............#....#..#..#...............##.....#.......#...............#................#.#.#.#.........#..........
+..............#.#...........#.......#............#..#..#.#..............#....#..##.#.#........#...#................#...#.#.........
+.................................#............#...#................#...#......#.#...#..#............#............#.................
+..............##....#........#............#.#...#.#....#...##..##........#.#.#....................#.#..........#.#....#....#.......
+..........#.......#...#...#...#.#..#..#......#.......#..........#.........#..#.....................#........#....#..#.....#........
+.....#....#........................#...#.#..#.....#...#.#.........#..........#.....#..#..#..###..#..............#..................
+.................................................................S.................................................................
+...............#................#.........#....#.#...........##.....#........................#.......#..#.#.....###..##.#..........
+..........#....#........#...#..#.......#.#.........#.........#..#.....###......#.........#...#........#....#...#....##.............
+.......##..............#........##.........#........#..#.#......#..........#........#....#............##.#........#....#..#........
+.........##...........#....#.#.....#.........#.#....#.....##..#.....#.......#..#.#..................#.#......#.....................
+..........##....##....#......##.......#...........#............#.......###.......##..#.#.#..#....#...#.........#.###.#.#...........
+.................#.#..........#...#...#........#........#..###..............#....#............#.........#.......#.#....##..........
+.##...............................#..#.#.......#...#....#...#............#......#........#....#.#....#..#.......#..#...............
+................#..................#.......###..#..........#.#.................#..##......##.#........#......####..................
+.....#...............................#..#.#.#....#.#............#....#....................##....#..............................#...
+..#............#.#...#...........#.........#......#.................##.#...#.......................##..#...........................
+................#......#....#...##..#........##..#.##..#.......#........#..........#................#..............................
+.................................#..###..........#.....##............##.....##.......#.#.#....#..#.............#..#............#...
+..#...#..............#............###...........#.#.#.#..#....#.#..#...#.....#..........................#....#...........#.#..#..#.
+.#.###...#........#..............#.#........#.......#.......#.........#.....#...#..###...##..##..#....#.#......#.........#......#..
+..........#.........#.......#..##.#.....#.##..#.........#..#...#.....#.#.##....#.........#.#.....#......#..............#...#.......
+..#..#..#...#.........#..##...#..#...#......#.............#.#.........#.#...##.....#.....#...#..#.....#..##...........#........#...
+..#....#....#................###...#......#.....#..#....#..........#.........#.#..#.................#.#..#............#.....##..#..
+....#.......##........##...#..##........#........#..##............#.........#..##...#.....#..#...#.......#.............#........#..
+.#...#...##.............#........##...#.....#.##....#...#.....#..........##..............#................................##.#.#...
+.....#.......##.........#.....#.....#..#.###..#......#......##..............#................#..##..................##......###..#.
+.##...####.......#..........#.........#...#........................##....#......#.......#........#.....#.........#..........#.#....
+..................#...........#..#.....#..#........#...................#............#..........#..#.#...........#.#....#....#......
+........#..#....................................#..................#.#................#..#....#.#.......................#....#.....
+.#..............##..............##.##....##..##...#...##......##......#......#..........#....#..................................#..
+.#....#.....#....##..............#.##..##...#.......#.##.......##..#.............#.#.....#...#......#............#..........##.....
+..................##............#...##.................#...#.##...#.........#....#....#....#..#.....#........#..........#...#.#..#.
+.##.......#........#.#.........#......................#.#..#.#........#.....................#.#.............###........#.#.........
+.#..........#....#.....#...........#....#..........###................#.#.#...#.##......#...................#....#.....#.......#...
+...#....#..#..#.......#.#..............#........#........###.#.....#....#...#.....##.......................#....#...........#....#.
+..#.................................#.....###......#......##...#...#.......#............##.....#........#.#........................
+.#...........#....#......#.......................#........##........#.........#.....#.....#....#............###..#...#.#....#......
+.......#.#......#.#....................#.##................#.#...........#...........#.#...##........................#.............
+....#......#....#.......#.....................#.#..#........#..........#..#..#.......#.#..............#......#..............#......
+.....#......#.......#....................#.......#..#...####.##....#...#.#.......##...#.#...........#..............#..........#....
+..#.........#........##....#.............##.#.#.........#....##........#..#........................#...#.#..#....#.................
+.#....#..#.##.......#..#..#...##............##.##..#..#......#.##.......#.................#......................##.....#........#.
+..................#.........#............#...##......................#...............#...........#................#.....#....#.#...
+..#......##............#.......#.#................#.....#..........................#..#...................#....#....#.........#....
+.#.#........#....#..##..#.....#.#...............#.......##..#.........#.....#........#...............##............................
+..#.........##...................#.#........##......#.#.......##......##.#..#....#.#.#...........#..##...................#.......#.
+....#.#.##.....###..#..........#....#..............#.###....#......##.............##...........#........#...........#...........##.
+.#...##..#......##....#........##.#..............#.......##..#.....#....##.....................#...##..#............#..........#...
+....#...#..........#...........#.#.#..............##.#.#.....###..................#.............#....#.....####....................
+........#..#.........###........................#.#..#..........#.............................#...#......#.............##..........
+.....#...#.............#.....#....#...#..............##.##........#..#...##.....#...............#..............#....#...#....#.....
+....#.#...........#...#.##.....##....#.#...........##....#.....#...............................#.#.#...#.....#..#........#.........
+...##...........................##..##.................##....#........#.....#...........#....#.....#............##.......#.........
+............#.....#.....#......##...........................................#.........#.....#......#............#........#.#.#.....
+......##...#....#...#...#.......#...........................#..#...#.#................#..........#...#.##..........#....##.#.......
+.....#...#.#..###.#.#.........#.#..........#...........#.....#.............................#..#.#....#.#.....#.....#..#......#.....
+.#.....#...#....................#...............................#.....#.............#.##.....####..##.....#.###....#..#............
+....#...#.............#.#....#.....#..#..#...#.............#.......................#.#........#..#...#.................#...#.#...#.
+..........#..#...#.....#..........#...#....#.#.....................#............................#....#.#......#.#.............#....
+..##.....#...#......#.#....#....#.##.#....#......#........##........#...........#..#........#......#.#.....................#.#.....
+......#...####.......#......#..##..###.......#...............#........#.........#....#.#.............##........##..#.#......#......
+....##.##..........#.#.#.#.#..#.....##......................#.....#.#......................#....#.................#...........#....
+.......#..##.#.#..##...#...........................#............................#....##.......#........#......#..........#.#.......
+.....#.##.......#................#...#........#...#.............................#..#........#......###.###....#...##.............#.
+.......#............##..........##..#.#.....#...................#................................#..#...#...#........#....#......#.
+.#.#.#.#..#...#...........#.#.....#...................#.#......................#......##.....#..................#...##..#.#........
+............#...............#...#........##....#..#...........................#.#..#.....#.##.................#...#....#......#....
+.....#.......#.............................#......#..#.#..#.....................#...........#...#........#.#........#....#.........
+.#.##..#............#..#.................................................#...#..###................##........##.#..#......#......#.
+.........#...............##......#............#.....#...........................#.............##.#.#.#.......###.....#..........#..
+...................................................................................................................................

2023/day21/solutions.py

@@ -0,0 +1,76 @@
+from collections import deque
+
+from scipy.optimize import curve_fit
+
+with open("input") as f:
+    ls = f.read().strip().split()
+
+N = len(ls)
+blocked = set()
+for i, l in enumerate(ls):
+    for j, x in enumerate(l):
+        if x == "S":
+            start = i + 1j * j
+        elif x == "#":
+            blocked.add(i + 1j * j)
+
+
+def counts():
+    q = deque([(start, 0)])
+    curr_dist = None
+    evens = 1
+    odds = 0
+    seen = {start}
+    while True:
+        z, dist = q.popleft()
+        if dist != curr_dist:
+            curr_dist = dist
+            yield (curr_dist, odds if curr_dist % 2 else evens)
+        for dz in (-1, 1, -1j, 1j):
+            w = z + dz
+            w_mod_N = (w.real % N) + 1j * (w.imag % N)
+            if w_mod_N in blocked or w in seen:
+                continue
+            seen.add(w)
+            q.append((w, dist + 1))
+            if dist % 2:
+                evens += 1
+            else:
+                odds += 1
+
+
+# For part 2, by looking at how the output of counts evolves for the test input,
+# one quickly finds that it has behavior periodic with the size of the grid. By
+# looking at the counts for each remainder, one finds that they are all quadratic
+# polynomials after some initial noise. (This is easiest to see for the test input
+# by looking at the counts that show up after all numbers of steps that are 0 mod 11.
+# As such, we keep track of the counts for the residue class belong to our target,
+# fit a quadratic polynomial, and once the predictions have stabilized for the
+# actual input, we assume that we have the right answer.
+def f(x, a, b, c):
+    return a * x**2 + b * x + c
+
+
+gen = counts()
+to_hit = 26501365
+period = N
+preds = []
+data = []
+for i, num_locs in gen:
+    # Part 1
+    if i == 64:
+        print(num_locs)
+    # Part 2
+    if i % period == to_hit % period:
+        data.append((i, num_locs))
+        if len(data) < 3:
+            continue
+        last_seen = data[-3:]
+        fa, fb, fc = curve_fit(f, *zip(*last_seen))[0]
+        pred = round(f(to_hit, fa, fb, fc))
+        preds.append(pred)
+        # We assume that we have converged if the same prediction shows up
+        # three times in a row
+        if len(preds) > 3 and len(set(preds[-3:])) == 1:
+            print(preds[-1])
+            break