commit5478829a2bdfece833624da2f20828451d70702eparentcc54381e861ab4c06c07210cdfc8b68c88f6f862Author:Eamon Caddigan <eamon.caddigan@gmail.com>Date:Wed, 15 Dec 2021 18:40:50 -0500 New grid_to_distance_matrix is almost 17x fasterDiffstat:

M | day15_part1.py | | | 66 | +++++++++++++++++++++++++----------------------------------------- |

1 file changed, 25 insertions(+), 41 deletions(-)diff --git a/day15_part1.py b/day15_part1.py@@ -32,51 +32,35 @@ def grid_to_distance_matrix(input_array: np.ndarray) -> csr_matrix: # 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]) + # distance matrix will have connections in row 8 at columns 5 and 7. Note + # that this is a _directed_ distance/connectivity/association matrix, + # because the cost of going from #8 to #7 isn't necessarily the same as + # going from #7 to #8. - 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]) + # In the (sparse) distance matrix, data will be stored as: + # Row: node id (row-major indexing), Col: neighbor id + # We'll start off by pretending that every node has four neighbors + dist_row_ids = np.repeat(np.arange(input_array.size, dtype=int), 4) + dist_col_ids = np.empty_like(dist_row_ids) + dist_col_ids[0::4] = dist_row_ids[0::4] - 1 # Left + dist_col_ids[1::4] = dist_row_ids[1::4] + 1 # Right + dist_col_ids[2::4] = dist_row_ids[2::4] - input_array.shape[1] # Top + dist_col_ids[3::4] = dist_row_ids[3::4] + input_array.shape[1] # Bottom - 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]) + # Now we remove the invalid neighbors (at the edges) + grid_col_ids = dist_row_ids % input_array.shape[1] + grid_row_ids = dist_row_ids // input_array.shape[1] + keep_neighbor = np.empty_like(grid_col_ids, dtype=bool) + keep_neighbor[0::4] = grid_col_ids[0::4] >= 1 + keep_neighbor[1::4] = grid_col_ids[1::4] < (input_array.shape[1] - 1) + keep_neighbor[2::4] = grid_row_ids[2::4] >= 1 + keep_neighbor[3::4] = grid_row_ids[3::4] < (input_array.shape[0] - 1) + dist_row_ids = dist_row_ids[keep_neighbor] + dist_col_ids = dist_col_ids[keep_neighbor] # There are a bunch of ways to instantiate a csr_matrix, this is the most - # appropriate for these data - return csr_matrix((dist_data, + # appropriate for this data format + return csr_matrix((np.reshape(input_array, input_array.size)[dist_col_ids], (dist_row_ids, dist_col_ids))) def find_shortest_path(distance_matrix: csr_matrix):