2019: d10: ex2: add solution

2019/d10/ex2/ex2.py

@@ -0,0 +1,86 @@
+#!/usr/bin/env python
+
+import sys
+from cmath import phase
+from itertools import groupby
+from math import gcd, pi
+from typing import NamedTuple, Set, Tuple
+
+
+class Position(NamedTuple):
+    x: int
+    y: int
+
+
+def pos_to_angle_dist(pos: Position) -> Tuple[float, float]:
+    cartesian = complex(*pos)
+    angle = phase(cartesian)
+    if angle < -pi / 2:
+        angle += 2.5 * pi
+    else:
+        angle += pi / 2
+    return (angle, abs(cartesian))
+
+
+def main() -> None:
+    asteroids = [
+        Position(x, y)
+        for y, line in enumerate(sys.stdin.readlines())
+        for x, c in enumerate(line.rstrip())
+        if c == "#"
+    ]
+
+    def count_spotted(x: int, y: int) -> int:
+        seen: Set[Position] = set()
+        ans = 0
+        radius = 1
+
+        while True:
+
+            def is_r_away(pos: Position) -> bool:
+                return max(abs(pos.x - x), abs(pos.y - y)) == radius
+
+            to_visit = list(filter(is_r_away, asteroids))
+            radius += 1
+            if len(to_visit) == 0:
+                break
+            for pos in to_visit:
+                rel = (pos.x - x, pos.y - y)
+                common = gcd(*rel)
+                rel = Position(*(a // common for a in rel))
+                if rel in seen:
+                    continue  # Already have an asteroid on this path
+                seen.add(rel)
+                ans += 1
+
+        return ans
+
+    # We need to find the observatory's position as a prerequisite
+    ans, orig = max((count_spotted(*pos), pos) for pos in asteroids)
+    print(f"({orig.x}, {orig.y}): {ans}")
+
+    def to_rel(p: Position) -> Position:
+        return Position(*(a - o for (a, o) in zip(p, orig)))
+
+    angle_dists = sorted(
+        (pos_to_angle_dist(to_rel(p)), p) for p in asteroids if p != orig
+    )
+    grouped_angle_dists = [
+        [val[1] for val in group]
+        for __, group in groupby(angle_dists, key=lambda x: x[0][0])
+    ]
+
+    def find_n_th(n: int) -> Position:
+        assert 0 < n < len(asteroids)  # Sanity check
+        while n >= len(grouped_angle_dists):
+            for group in grouped_angle_dists:
+                group.pop(0)
+                n -= 1
+        return grouped_angle_dists[n - 1][0]
+
+    x, y = find_n_th(200)
+    print(x * 100 + y)
+
+
+if __name__ == "__main__":
+    main()