2023 day 17.

2023-12-17 09:37:31 +01:00 · 2023-12-17 09:37:31 +01:00 · 5b30cc00d5
commit 5b30cc00d5
parent 3a7f8e83dc
3 changed files with 377 additions and 3 deletions
--- a/2023/day17.py
+++ b/2023/day17.py
@ -1,13 +1,233 @@
+from __future__ import annotations
+
+import heapq
+import os
 import sys
 from collections import defaultdict
 from dataclasses import dataclass
+from typing import Literal, TypeAlias

-lines = sys.stdin.read().splitlines()
+VERBOSE = os.getenv("AOC_VERBOSE") == "True"
+
+Direction: TypeAlias = Literal[">", "<", "^", "v"]
+
+
+@dataclass(frozen=True, order=True)
+class Label:
+    row: int
+    col: int
+
+    direction: Direction
+    count: int
+
+    parent: Label | None = None
+
+
+# mappings from direction to row shift / col shift / opposite direction
+MAPPINGS: dict[Direction, tuple[int, int, Direction]] = {
+    ">": (0, +1, "<"),
+    "<": (0, -1, ">"),
+    "v": (+1, 0, "^"),
+    "^": (-1, 0, "v"),
+}
+
+
+def print_shortest_path(
+    grid: list[list[int]],
+    target: tuple[int, int],
+    per_cell: dict[tuple[int, int], list[tuple[Label, int]]],
+):
+    assert len(per_cell[target]) == 1
+    label = per_cell[target][0][0]
+
+    path: list[Label] = []
+    while True:
+        path.insert(0, label)
+        if label.parent is None:
+            break
+        label = label.parent
+
+    p_grid = [[str(c) for c in r] for r in grid]
+
+    for i in range(len(grid)):
+        for j in range(len(grid[0])):
+            if per_cell[i, j]:
+                p_grid[i][j] = f"\033[94m{grid[i][j]}\033[0m"
+
+    prev_label = path[0]
+    for label in path[1:]:
+        for r in range(
+            min(prev_label.row, label.row), max(prev_label.row, label.row) + 1
+        ):
+            for c in range(
+                min(prev_label.col, label.col),
+                max(prev_label.col, label.col) + 1,
+            ):
+                if (r, c) != (prev_label.row, prev_label.col):
+                    p_grid[r][c] = f"\033[93m{grid[r][c]}\033[0m"
+
+        p_grid[label.row][label.col] = f"\033[91m{grid[label.row][label.col]}\033[0m"
+
+        prev_label = label
+
+    p_grid[0][0] = f"\033[92m{grid[0][0]}\033[0m"
+
+    print("\n".join("".join(row) for row in p_grid))
+
+
+def shortest_many_paths(grid: list[list[int]]) -> dict[tuple[int, int], int]:
+    n_rows, n_cols = len(grid), len(grid[0])
+
+    visited: dict[tuple[int, int], tuple[Label, int]] = {}
+
+    queue: list[tuple[int, Label]] = [
+        (0, Label(row=n_rows - 1, col=n_cols - 1, direction="^", count=0))
+    ]
+
+    while queue and len(visited) != n_rows * n_cols:
+        distance, label = heapq.heappop(queue)
+
+        if (label.row, label.col) in visited:
+            continue
+
+        visited[label.row, label.col] = (label, distance)
+
+        for direction, (c_row, c_col, i_direction) in MAPPINGS.items():
+            if label.direction == i_direction:
+                continue
+            else:
+                row, col = (label.row + c_row, label.col + c_col)
+
+            # exclude labels outside the grid or with too many moves in the same
+            # direction
+            if row not in range(0, n_rows) or col not in range(0, n_cols):
+                continue
+
+            heapq.heappush(
+                queue,
+                (
+                    distance
+                    + sum(
+                        grid[r][c]
+                        for r in range(min(row, label.row), max(row, label.row) + 1)
+                        for c in range(min(col, label.col), max(col, label.col) + 1)
+                    )
+                    - grid[row][col],
+                    Label(
+                        row=row,
+                        col=col,
+                        direction=direction,
+                        count=0,
+                        parent=label,
+                    ),
+                ),
+            )
+
+    return {(r, c): visited[r, c][1] for r in range(n_rows) for c in range(n_cols)}
+
+
+def shortest_path(
+    grid: list[list[int]],
+    min_straight: int,
+    max_straight: int,
+    lower_bounds: dict[tuple[int, int], int],
+) -> int:
+    n_rows, n_cols = len(grid), len(grid[0])
+
+    target = (len(grid) - 1, len(grid[0]) - 1)
+
+    # for each tuple (row, col, direction, count), the associated label when visited
+    visited: dict[tuple[int, int, str, int], Label] = {}
+
+    # list of all visited labels for a cell (with associated distance)
+    per_cell: dict[tuple[int, int], list[tuple[Label, int]]] = defaultdict(list)
+
+    # need to add two start labels, otherwise one of the two possible direction will
+    # not be possible
+    queue: list[tuple[int, int, Label]] = [
+        (lower_bounds[0, 0], 0, Label(row=0, col=0, direction="^", count=0)),
+        (lower_bounds[0, 0], 0, Label(row=0, col=0, direction="<", count=0)),
+    ]
+
+    while queue:
+        _, distance, label = heapq.heappop(queue)
+
+        if (label.row, label.col, label.direction, label.count) in visited:
+            continue
+
+        visited[label.row, label.col, label.direction, label.count] = label
+        per_cell[label.row, label.col].append((label, distance))
+
+        if (label.row, label.col) == target:
+            break
+
+        for direction, (c_row, c_col, i_direction) in MAPPINGS.items():
+            # cannot move in the opposite direction
+            if label.direction == i_direction:
+                continue
+
+            # other direction, move 'min_straight' in the new direction
+            elif label.direction != direction:
+                row, col, count = (
+                    label.row + min_straight * c_row,
+                    label.col + min_straight * c_col,
+                    min_straight,
+                )
+
+            # same direction, too many count
+            elif label.count == max_straight:
+                continue
+
+            # same direction, keep going and increment count
+            else:
+                row, col, count = (
+                    label.row + c_row,
+                    label.col + c_col,
+                    label.count + 1,
+                )
+            # exclude labels outside the grid or with too many moves in the same
+            # direction
+            if row not in range(0, n_rows) or col not in range(0, n_cols):
+                continue
+
+            distance_to = (
+                distance
+                + sum(
+                    grid[r][c]
+                    for r in range(min(row, label.row), max(row, label.row) + 1)
+                    for c in range(min(col, label.col), max(col, label.col) + 1)
+                )
+                - grid[label.row][label.col]
+            )
+
+            heapq.heappush(
+                queue,
+                (
+                    distance_to + lower_bounds[row, col],
+                    distance_to,
+                    Label(
+                        row=row,
+                        col=col,
+                        direction=direction,
+                        count=count,
+                        parent=label,
+                    ),
+                ),
+            )
+
+    if VERBOSE:
+        print_shortest_path(grid, target, per_cell)
+
+    return per_cell[target][0][1]
+
+
+data = [[int(c) for c in r] for r in sys.stdin.read().splitlines()]
+estimates = shortest_many_paths(data)

 # part 1
-answer_1 = ...
+answer_1 = shortest_path(data, 1, 3, lower_bounds=estimates)
 print(f"answer 1 is {answer_1}")

 # part 2
-answer_2 = ...
+answer_2 = shortest_path(data, 4, 10, lower_bounds=estimates)
 print(f"answer 2 is {answer_2}")
--- a/2023/inputs/day17.txt
+++ b/2023/inputs/day17.txt
@ -0,0 +1,141 @@
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--- a/2023/tests/day17.txt
+++ b/2023/tests/day17.txt
@ -0,0 +1,13 @@
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