advent-of-code/2023/day17.py

from __future__ import annotations

import heapq
import os
import sys
from collections import defaultdict
from dataclasses import dataclass
from typing import Literal, TypeAlias

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 = shortest_path(data, 1, 3, lower_bounds=estimates)
print(f"answer 1 is {answer_1}")

# part 2
answer_2 = shortest_path(data, 4, 10, lower_bounds=estimates)
print(f"answer 2 is {answer_2}")