🐄

VERSION

@@ -1 +1 @@
-🦁
+🐄

y2023/p21.py

@@ -1,35 +1,54 @@
-"""
-5000 steps, he can reach 16733044 garden plots.
+def bfs_twinkle(start, graph, cycles):
+    seen = [set()]
+    state = {start}
+    while len(seen) <= cycles:
+        twinkle = seen[len(seen) - 2]
+        state = {
+            p + s
+            for p in state
+            for s in [1, -1, 1j, -1j]
+            if wrap(p + s) in graph
+            if p + s not in twinkle
+        }
+        seen.append(twinkle | state)
+    return seen
+
+
+def extrapolate_quadratic(y0, y1, y2):
+    a, b, c = (y2 - 2 * y1 + y0) / 2, (-y2 + 4 * y1 - 3 * y0) / 2, y0
+    return lambda x: a * x ** 2 + b * x + c
+
 
-26501365?
-"""
 text = open(0).read()
 graph = {
     complex(x, y): val
     for y, row in enumerate(text.splitlines())
     for x, val in enumerate(row)
+    if val in {'S', '.'}
 }
 
 width = max(int(p.real) for p in graph) + 1
 height = max(int(p.imag) for p in graph) + 1
-block = lambda p: complex(p.real // width, p.imag // height)
-wrap = lambda p: complex(p.real % width, p.imag % height)
+wrap = lambda p: complex(int(p.real % width), int(p.imag % height))
 
 start, = (k for k, v in graph.items() if v == 'S')
-seen = [set(), set()]
-state = {start}
-bops = set()
-for step in range(130):
-    twinkle = seen[step % 2]
-    twinkle |= state
-
-    if step == 64:
-        print(len(twinkle))  # ans1
-
-    state = {
-        p + s
-        for p in state
-        for s in [1, -1, 1j, -1j]
-        if graph[wrap(p + s)] in {'.', 'S'}
-        if p + s not in twinkle
-    }
+seen = bfs_twinkle(start, graph, 327)
+if width < 100:
+    check = len({wrap(p) for p in seen[6]})
+    print(check)
+    exit()
+
+ans1 = len({wrap(p) for p in seen[64]})
+print(ans1)
+
+goal = 26501365
+size, = {height, width}
+offset = goal % size
+
+xs = [offset + size * i for i in range(3)]
+ys = [len(seen[x]) for x in xs]
+yf = extrapolate_quadratic(ys[0], ys[1], ys[2])
+
+x = (goal - offset) / size
+ans2 = int(yf(x))
+print(ans2)