commit 154c34ba3b80eae475fec44d1601030b3bf68063
parent d98128cf7c4865fe421b3d688eaf25cad34819fc
Author: Eamon Caddigan <eamon.caddigan@gmail.com>
Date: Wed, 15 Dec 2021 14:35:38 -0500
Solution to day 15, part 1
Diffstat:
| A | day15_part1.py | | | 111 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
1 file changed, 111 insertions(+), 0 deletions(-)
diff --git a/day15_part1.py b/day15_part1.py
@@ -0,0 +1,111 @@
+#!/usr/bin/env python
+"""Advent of Code 2021, day 15 (part 1): Chiton
+Another graph search problem, but this one requires a bit more care"""
+
+# Since I'm not TRYING to reinvent the wheel, I'm going to see if any of
+# scipy's graph search algorithms can handle this. I'll implement A* myself if
+# I have to, but I'll try to avoid it.
+
+#from typing import List, Tuple, cast
+import numpy as np
+from scipy.sparse import csr_matrix
+from scipy.sparse.csgraph import dijkstra
+from utils import get_puzzle_input, convert_input_to_array
+
+EXAMPLE_INPUT = \
+"""1163751742
+1381373672
+2136511328
+3694931569
+7463417111
+1319128137
+1359912421
+3125421639
+1293138521
+2311944581
+"""
+
+def grid_to_distance_matrix(input_array: np.ndarray) -> csr_matrix:
+ """Given a n x m grid of node values, return a sparse array (representing
+ [n x m] x [n x m] associations) giving the connectivity/distance matrix"""
+ # Remember that numpy stores data in row-major order, so I'm preserving the
+ # indicies into the original 2d array in the distance matrix: e.g., the
+ # last element in a 3x3 array has index 8 (thanks to zero-indexing), and is
+ # connected to index 7 (to its left) and index 5 (above it), so the sparse
+ # distance matrix will have connections in row 8 at columns 5 and 7. I
+ # believe that this function could be much more efficient by being smart
+ # with divmod, but it's only run once per solution, so the easier-to-debug
+ # implementation wins the day. Also note that this is a _directed_
+ # distance/connectivity/association matrix, because the cost of going from
+ # #8 to #7 isn't necessarily teh same as going from #7 to #8.
+ dist_row_ids = []
+ dist_col_ids = []
+ dist_data = []
+ for grid_row_id in range(input_array.shape[0]):
+ for grid_col_id in range(input_array.shape[1]):
+ dist_row_id = grid_row_id * input_array.shape[1] + grid_col_id
+ if grid_row_id >= 1:
+ # Top neighbor
+ dist_row_ids.append(dist_row_id)
+ dist_col_ids.append(dist_row_id - \
+ input_array.shape[1])
+ dist_data.append(input_array[grid_row_id - 1,
+ grid_col_id])
+
+ if grid_row_id < (input_array.shape[0] - 1):
+ # Bottom neighbor
+ dist_row_ids.append(dist_row_id)
+ dist_col_ids.append(dist_row_id + \
+ input_array.shape[1])
+ dist_data.append(input_array[grid_row_id + 1,
+ grid_col_id])
+
+ if grid_col_id >= 1:
+ # Left neighbor
+ dist_row_ids.append(dist_row_id)
+ dist_col_ids.append(dist_row_id - 1)
+ dist_data.append(input_array[grid_row_id,
+ grid_col_id - 1])
+
+ if grid_col_id < (input_array.shape[1] - 1):
+ # Right neighbor
+ dist_row_ids.append(dist_row_id)
+ dist_col_ids.append(dist_row_id + 1)
+ dist_data.append(input_array[grid_row_id,
+ grid_col_id + 1])
+
+ # There are a bunch of ways to instantiate a csr_matrix, this is the most
+ # appropriate for these data
+ return csr_matrix((dist_data,
+ (dist_row_ids, dist_col_ids)))
+
+def find_shortest_path(distance_matrix: csr_matrix):
+ """Runs scipy's implementation of Dijkstra's algorithm (which isn't as fast
+ as A* in theory, but since this is optimized and my hacked together A*
+ wouldn't be, probably is faster in practice) and returns the distance from
+ the starting point to all other points, and the index of the preceding
+ point"""
+ return dijkstra(distance_matrix,
+ directed=True, # This is a directed graph
+ indices=0, # Find the distance from here
+ return_predecessors=True, # Reconstructable path
+ min_only=True)[0:2] # Just want this distance
+
+def solve_puzzle(input_string: str) -> int:
+ """Return the numeric solution to the puzzle"""
+ return int(
+ find_shortest_path(
+ grid_to_distance_matrix(
+ convert_input_to_array(input_string)
+ )
+ )[0][-1]
+ )
+
+def main() -> None:
+ """Run when the file is called as a script"""
+ assert solve_puzzle(EXAMPLE_INPUT) == 40
+ print("Total risk of best path:",
+ solve_puzzle(get_puzzle_input(15)))
+
+if __name__ == "__main__":
+ main()
