2024: d18: ex2: add solution

2024/d18/ex2/ex2.py

@@ -0,0 +1,77 @@
+#!/usr/bin/env python
+
+import heapq
+import sys
+from typing import Iterator, NamedTuple
+
+
+class Point(NamedTuple):
+    x: int
+    y: int
+
+    def neighbours(self) -> Iterator["Point"]:
+        for dx, dy in (
+            (-1, 0),
+            (1, 0),
+            (0, -1),
+            (0, 1),
+        ):
+            yield Point(self.x + dx, self.y + dy)
+
+
+DIMS = Point(70, 70)
+
+
+def solve(input: str) -> str:
+    def parse(input: list[str]) -> list[Point]:
+        return [Point(*map(int, line.split(","))) for line in input]
+
+    def djikstra(start: Point, end: Point, blocks: set[Point]) -> int | None:
+        # Priority queue of (distance, point)
+        queue = [(0, start)]
+        seen: set[Point] = set()
+
+        while len(queue) > 0:
+            cost, p = heapq.heappop(queue)
+            if p == end:
+                return cost
+            # We must have seen p with a smaller distance before
+            if p in seen:
+                continue
+            # First time encountering p, must be the smallest distance to it
+            seen.add(p)
+            # Add all neighbours to be visited
+            for n in p.neighbours():
+                if p in blocks:
+                    continue
+                if not 0 <= p.x <= DIMS.x:
+                    continue
+                if not 0 <= p.y <= DIMS.y:
+                    continue
+                heapq.heappush(queue, (cost + 1, n))
+
+        return None
+
+    def bisect_cutoff(start: Point, end: Point, blocks: list[Point]) -> Point:
+        # Cutting off the path is monotonic: once cut-off, it's never uncut
+        low, high = 0, len(blocks)
+        while low < high:
+            mid = low + (high - low + 1) // 2
+            if djikstra(start, end, set(blocks[:mid])) is None:
+                high = mid - 1
+            else:
+                low = mid
+        return blocks[low]
+
+    coords = parse(input.splitlines())
+    byte = bisect_cutoff(Point(0, 0), DIMS, coords)
+    return f"{byte.x},{byte.y}"
+
+
+def main() -> None:
+    input = sys.stdin.read()
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()