day 23: solve part 2 via brute force w/ optimized graph

dsa/advent-of-code/2023/day_23.py

@@ -1,6 +1,6 @@
-import sys
 import string
 from itertools import cycle
+from collections import defaultdict
 
 VECTORS = [(0, 1), (0, -1), (-1, 0), (1, 0)]
 VECTOR_BY_CHAR = {
@@ -84,6 +84,54 @@ def is_path(y2, x2):
     return result
 
 
+def precompute_optimized_graph(grid, part):
+    graph = defaultdict(list)  # pos => [(pos, distance)]
+
+    def find_junctions():
+        junctions = set()
+        for y, row in enumerate(grid):
+            for x, _ in enumerate(row):
+                if grid[y][x] == "#":
+                    continue
+                pos = (y, x)
+                if len(neighbors(pos, grid, part)) > 2:
+                    junctions.add(pos)
+        return junctions
+
+    def find_next_junction_or_end(pos, path, step_count=1):
+        if pos == junction:
+            return
+
+        path.add(pos)
+
+        if pos in junctions or pos == end_pos(grid):
+            return (pos, step_count)
+
+        n = [x for x in neighbors(pos, grid, part) if x not in path]
+
+        if len(n) == 0:
+            return
+        if len(n) != 1:
+            print("unexpected condition")
+            exit()
+        return find_next_junction_or_end(n[0], path, step_count + 1)
+
+    junctions = find_junctions()
+
+    # compute distances between all junctions, including end pos
+    for junction in junctions:
+        for neighbor in neighbors(junction, grid, part):
+            next_junction = find_next_junction_or_end(neighbor, {junction})
+            if next_junction is not None:
+                graph[junction].append(next_junction)
+
+    start = start_pos(grid)
+    next_junction = find_next_junction_or_end(neighbors(start, grid, part)[0], {start})
+    graph[start].append(next_junction)
+
+    return graph
+
+
 def find_all_path_lengths(start_pos, end_pos, grid, part):
     all_path_lengths = []
 
@@ -98,6 +146,25 @@ def search(pos, path):
                 new_path.add(adj_pos)
                 search(adj_pos, new_path)
 
+    search(start_pos, path={start_pos})
+
+    return all_path_lengths
+
+
+def find_all_path_lengths_optimized(start_pos, end_pos, graph):
+    all_path_lengths = []
+
+    def search(pos, path, distance=0):
+        if pos == end_pos:
+            all_path_lengths.append(distance)
+            return
+
+        for adj_pos, d in graph[pos]:
+            if adj_pos not in path:
+                new_path = path.copy()
+                new_path.add(adj_pos)
+                search(adj_pos, new_path, distance + d)
+
     path = set()
     path.add(start_pos)
     search(start_pos, path)
@@ -107,15 +174,15 @@ def search(pos, path):
 
 def solution(data, part):
     grid = parsed(data)
+    graph = precompute_optimized_graph(grid, part)
 
-    all_path_lengths = find_all_path_lengths(start_pos(grid), end_pos(grid), grid, part)
-
-    start_node_count = 1
-    print(sorted(all_path_lengths)[-1] - start_node_count)
+    all_path_lengths = find_all_path_lengths_optimized(
+        start_pos(grid), end_pos(grid), graph
+    )
+    print(max(all_path_lengths))
 
 
 if __name__ == "__main__":
-    sys.setrecursionlimit(10000)
     with open("day_23_input.txt", "r") as file:
         data = file.readlines()
-    solution(data, part=1)
+    solution(data, part=2)

dsa/advent-of-code/2023/day_23_sample_with_axes.txt

@@ -0,0 +1,24 @@
+  01234567890123456789012
+0 #.#####################
+1 #.......#########...###
+2 #######.#########.#.###
+3 ###.....#.>X>.###.#.###
+4 ###v#####.#v#.###.#.###
+5 ###X>...#.#.#.....#...#
+6 ###v###.#.#.#########.#
+7 ###...#.#.#.......#...#
+8 #####.#.#.#######.#.###
+9 #.....#.#.#.......#...#
+0 #.#####.#.#.#########v#
+1 #.#...#...#...###...>X#
+2 #.#.#v#######v###.###v#
+3 #...#.>.#...>X>.#.###.#
+4 #####v#.#.###v#.#.###.#
+5 #.....#...#...#.#.#...#
+6 #.#########.###.#.#.###
+7 #...###...#...#...#.###
+8 ###.###.#.###v#####v###
+9 #...#...#.#.>X>.#.>X###
+0 #.###.###.#.###.#.#v###
+1 #.....###...###...#...#
+2 #####################.#