Day 3

day3.py

@@ -0,0 +1,94 @@
+puzzle_input = 0 # TODO
+
+def cardinals(distance):
+    d = 0
+    distance[1] = d
+    yield 1
+
+    d += 1
+    distance[2] = d
+    yield 2
+
+    while True:
+        v = (2*d)**2 - (d-1)
+        distance[v] = d
+        yield v
+
+        v = (2*d)**2 + (d+1)
+        distance[v] = d
+        yield v
+
+        v = (2*d + 1)**2 - d
+        distance[v] = d
+        yield v
+
+        v = (2*d + 1)**2 + (d+1)
+        distance[v] = d + 1
+        yield v
+
+        d += 1
+
+def closest_cardinals(n, distance):
+    cs = cardinals(distance)
+    lo = next(cs)
+    hi = next(cs)
+    while not lo <= n <= hi:
+        lo, hi = hi, next(cs)
+    return lo, hi
+
+def manhattan_to_center(n):
+    distance = {}
+    best = sorted(closest_cardinals(n, distance), key=lambda x: abs(n - x))[0]
+    return distance[best] + abs(n - best)
+
+for inp, expected in [
+    (1, 0),
+    (2, 1),
+    (12, 3),
+    (23, 2),
+    (1024, 31),
+]:
+    actual = manhattan_to_center(inp)
+    assert actual == expected, f'Expected {expected} got {actual}'
+
+print(manhattan_to_center(puzzle_input))
+
+def walking_order():
+    start = (0, 0)
+    R, D, L, U = [(+1, 0), (0, -1), (-1, 0), (0, +1)]
+
+    yield R
+    yield U
+
+    count = 2
+    while True:
+        for deltas in [(L, D), (R, U)]:
+            for delta in deltas:
+                for _ in range(count):
+                    yield delta
+            count += 1
+
+def neighbors(cell):
+    x, y = cell
+    for dx in range(-1, 2):
+        for dy in range(-1, 2):
+            if dx == dy == 0: continue
+            yield (x+dx, y+dy)
+
+def sum_neighbors_until(limit):
+    grid = {}
+    deltas = walking_order()
+
+    cell = (0, 0)
+    grid[cell] = 1
+
+    while True:
+        x, y = cell
+        dx, dy = next(deltas)
+        cell = (x+dx, y+dy)
+        value = sum(grid.get(n, 0) for n in neighbors(cell))
+        grid[cell] = value
+        if value > limit:
+            return value
+
+print(sum_neighbors_until(puzzle_input))