Day 24.

24.py

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+#!/usr/bin/python3
+
+"""Solution for day 24 of Advent of Code 2016.
+
+Another day, another breadth-first search! I split this problem into two stages: first, computing the distance
+between every combination of points in the maze, and, second, finding the shortest route using those paths.
+
+Finding the distances is just a simple BFS. As we only care about distance, each pair of nodes is only calculated
+once (i.e., it stores a distance for, e.g., (0 -> 2) but not (2 -> 0)). Pairs are stored sorted.
+
+To find all the possible routes, we just need a call to itertools.permutations for the middle section (ignoring '0').
+The '0' stop(s) are then added around the permutation, and the total distance calculated by chunking them into pairs
+and looking them up in the distances table. This is done in the route_length method.
+
+For example, with the example maze with 5 points we compute and store 10 distances:
+  0 -> 1, 0 -> 2, 0 -> 3, 0 -> 4, 1 -> 2, 1 -> 3, 1 -> 4, 2 -> 3, 2-> 4, 3-> 4
+
+Which become tuple keys in our distances dictionary:
+  (0, 1): a, (0, 2): b, ... (3, 4): z
+
+Then to find the route we start with all 24 possible routes:
+  01234, 01243, 01324, 01342, 01423, 01432, 02134, etc...
+
+Each route is chunked into pairs:
+  01234 ==> (0, 1), (1, 2), (2, 3), (3, 4)
+
+And the pairs are then looked up in the dictionary and summed.
+
+The problem could in theory be solved using one large BFS but it would be fairly complicated as you'd need to prevent
+backtracking generally, while still allowing it after reaching a new numbered location. You'd also end up recalculating
+the distances between many places unless you did some clever optimisations. Pre-computing the distances also makes part
+2 very easy.
+"""
+
+import functools
+import itertools
+import operator
+
+
+def find(maze, num):
+    for y, line in enumerate(maze):
+        if num in line:
+            return line.index(num), y
+
+
+def navigable(maze, location):
+    return maze[location[1]][location[0]] != '#'
+
+
+def directions(location):
+    yield (location[0], location[1] + 1)
+    yield (location[0], location[1] - 1)
+    yield (location[0] + 1, location[1])
+    yield (location[0] - 1, location[1])
+
+
+def moves(maze, start):
+    return set(filter(lambda loc: navigable(maze, loc), directions(start)))
+
+
+def distance(maze, start_num, end_num):
+    start = find(maze, start_num)
+    end = find(maze, end_num)
+    visited = set()
+    queue = [start]
+    steps = 0
+    while len(queue):
+        new_queue = functools.reduce(operator.or_, [moves(maze, target) for target in queue])
+        queue = new_queue - visited
+        visited |= queue
+        steps += 1
+        if end in queue:
+            return steps
+
+
+def route_length(distances, route):
+    return sum(map(lambda p: distances[tuple(sorted(p))], (route[i:i +2] for i in range(0, len(route)-1))))
+
+
+with open('data/24.txt', 'r') as file:
+    my_maze = list(map(str.strip, file.readlines()))
+    points = sorted(list(x for x in itertools.chain(*my_maze) if x.isdigit()))
+    distances = dict(((pair, distance(my_maze, *pair)) for pair in itertools.combinations(points, 2)))
+    routes = set(itertools.permutations(points[1:]))
+
+    print('Part one: %s' % min(route_length(distances, ['0'] + [*route]) for route in routes))
+    print('Part two: %s' % min(route_length(distances, ['0'] + [*route] + ['0']) for route in routes))

data/24.txt

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