advent-of-code/src/holt59/aoc/2024/day20.py

import itertools
from collections import Counter
from typing import Any, Callable, Iterable, Iterator, Sequence, TypeAlias

from ..base import BaseSolver
from ..tools.graphs import dijkstra, make_neighbors_grid_fn

Node: TypeAlias = tuple[int, int]


def make_neighbors_fn(grid: list[str], cheat_length: int):
    n_rows, n_cols = len(grid), len(grid[0])

    def _fn(node: Node):
        row, col = node
        return (
            ((row_n, col_n), abs(row_n - row) + abs(col_n - col))
            for row_d in range(-cheat_length, cheat_length + 1)
            for col_d in range(
                -cheat_length + abs(row_d), cheat_length - abs(row_d) + 1
            )
            if 0 <= (row_n := row + row_d) < n_rows
            and 0 <= (col_n := col + col_d) < n_cols
            and grid[row_n][col_n] != "#"
        )

    return _fn


class Solver(BaseSolver):
    def find_cheats(
        self,
        path: Sequence[Node],
        cost: float,
        costs_to_target: dict[Node, float],
        neighbors_fn: Callable[[Node], Iterable[tuple[Node, float]]],
    ):
        cheats: dict[tuple[tuple[int, int], tuple[int, int]], float] = {}

        for i_node, node in enumerate(self.progress.wrap(path)):
            for reach_node, reach_cost in neighbors_fn(node):
                n_cost = (
                    i_node + reach_cost + costs_to_target.get(reach_node, float("inf"))
                )
                if n_cost < cost:
                    cheats[node, reach_node] = cost - n_cost

        return cheats

    def solve(self, input: str) -> Iterator[Any]:
        grid = input.splitlines()
        n_rows, n_cols = len(grid), len(grid[0])
        start = next(
            (i, j) for i in range(n_rows) for j in range(n_cols) if grid[i][j] == "S"
        )
        target = next(
            (i, j) for i in range(n_rows) for j in range(n_cols) if grid[i][j] == "E"
        )

        reachable = dijkstra(
            target,
            None,
            make_neighbors_grid_fn(
                n_rows,
                n_cols,
                excluded=(
                    (i, j)
                    for i in range(n_rows)
                    for j in range(n_cols)
                    if grid[i][j] == "#"
                ),
            ),
        )

        # note: path is inverted here
        path, cost = reachable[start]
        costs_to_target = {k: c for k, (_, c) in reachable.items()}

        self.logger.info(f"found past from start to target with cost {cost}")

        for cheat_length in (2, 20):
            cheats = self.find_cheats(
                list(reversed(path)),
                cost,
                costs_to_target,
                make_neighbors_fn(grid, cheat_length),
            )

            for saving, count in sorted(Counter(cheats.values()).items()):
                self.logger.debug(
                    f"There are {count} cheats that save {saving} picoseconds."
                )

            target_saving = 100 if len(grid) > 20 else 50
            yield sum(saving >= target_saving for saving in cheats.values())