From 51527eee9de32fb85d35cc8125752f3cb53b4b8c Mon Sep 17 00:00:00 2001
From: Bruno BELANYI <bruno@belanyi.fr>
Date: Mon, 12 Dec 2022 16:14:58 +0100
Subject: [PATCH] 2022: d12: ex2: add solution

---
 2022/d12/ex2/ex2.py | 96 +++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 96 insertions(+)
 create mode 100755 2022/d12/ex2/ex2.py

diff --git a/2022/d12/ex2/ex2.py b/2022/d12/ex2/ex2.py
new file mode 100755
index 0000000..657f807
--- /dev/null
+++ b/2022/d12/ex2/ex2.py
@@ -0,0 +1,96 @@
+#!/usr/bin/env python
+
+import dataclasses
+import heapq
+import sys
+from collections.abc import Iterator
+from typing import NamedTuple
+
+
+class Point(NamedTuple):
+    x: int
+    y: int
+
+
+@dataclasses.dataclass
+class HeightMap:
+    heights: list[list[int]]
+    start: Point
+    end: Point
+
+    def reachable_neighbours(self, p: Point) -> Iterator[Point]:
+        reachable_height = self.heights[p.x][p.y] + 1
+        for (dx, dy) in ((-1, 0), (1, 0), (0, -1), (0, 1)):
+            x, y = p.x + dx, p.y + dy
+            if x < 0 or x >= len(self.heights):
+                continue
+            if y < 0 or y >= len(self.heights[0]):
+                continue
+            if self.heights[x][y] > reachable_height:
+                continue
+            yield Point(x, y)
+
+
+def solve(input: list[str]) -> int:
+    def to_height_map(input: list[str]) -> HeightMap:
+        start, end = None, None
+        heights = [[0 for _ in range(len(input[0]))] for _ in range(len(input))]
+
+        for i, line in enumerate(input):
+            for j, c in enumerate(line):
+                height = ord(c)
+                if c == "S":
+                    height = ord("a")
+                    start = Point(i, j)
+                if c == "E":
+                    height = ord("z")
+                    end = Point(i, j)
+                heights[i][j] = height - ord("a")
+
+        assert start is not None  # Sanity check
+        assert end is not None  # Sanity check
+        return HeightMap(heights, start, end)
+
+    def djikstra(map: HeightMap) -> int:
+        # Priority queue of (distance, point)
+        queue = [(0, map.start)]
+        seen: set[Point] = set()
+
+        while len(queue) > 0:
+            dist, p = heapq.heappop(queue)
+            if p == map.end:
+                return dist
+            # 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 map.reachable_neighbours(p):
+                heapq.heappush(queue, (dist + 1, n))
+
+        # There is no solution, return value larger than the map
+        return len(map.heights) * len(map.heights[0]) + 1
+
+    def hike_distances(map: HeightMap) -> Iterator[int]:
+        starts = (
+            Point(i, j)
+            for i in range(len(map.heights))
+            for j in range(len(map.heights[0]))
+            if map.heights[i][j] == 0
+        )
+        for start in starts:
+            map.start = start
+            yield djikstra(map)
+
+    map = to_height_map(input)
+    return min(hike_distances(map))
+
+
+def main() -> None:
+    input = sys.stdin.read().splitlines()
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()