166 lines
4.3 KiB
Python
166 lines
4.3 KiB
Python
# -*- encoding: utf-8 -*-
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import heapq
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import sys
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from typing import Callable, Iterator, TypeVar
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Node = TypeVar("Node")
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def dijkstra(
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start: Node,
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neighbors: Callable[[Node], Iterator[Node]],
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cost: Callable[[Node, Node], float],
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) -> tuple[dict[Node, float], dict[Node, Node]]:
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"""
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Compute shortest paths from one node to all reachable ones.
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Args:
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start: Starting node.
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neighbors: Function returning the neighbors of a node.
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cost: Function to compute the cost of an edge.
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Returns:
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A tuple (lengths, parents) where lengths is a mapping from Node to distance
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(from the starting node) and parents a mapping from parents Node (in the
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shortest path). If keyset of lengths and parents is the same. If a Node is not
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in the mapping, it cannot be reached from the starting node.
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"""
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queue: list[tuple[float, Node]] = []
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visited: set[Node] = set()
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lengths: dict[Node, float] = {start: 0}
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parents: dict[Node, Node] = {}
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heapq.heappush(queue, (0, start))
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while queue:
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length, current = heapq.heappop(queue)
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if current in visited:
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continue
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visited.add(current)
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for neighbor in neighbors(current):
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if neighbor in visited:
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continue
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neighbor_cost = length + cost(current, neighbor)
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if neighbor_cost < lengths.get(neighbor, float("inf")):
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lengths[neighbor] = neighbor_cost
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parents[neighbor] = current
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heapq.heappush(queue, (neighbor_cost, neighbor))
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return lengths, parents
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def make_path(parents: dict[Node, Node], start: Node, end: Node) -> list[Node] | None:
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if end not in parents:
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return None
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path: list[Node] = [end]
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while path[-1] is not start:
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path.append(parents[path[-1]])
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return list(reversed(path))
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def print_path(path: list[tuple[int, int]], n_rows: int, n_cols: int) -> None:
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end = path[-1]
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graph = [["." for _c in range(n_cols)] for _r in range(n_rows)]
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graph[end[0]][end[1]] = "E"
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for i in range(0, len(path) - 1):
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cr, cc = path[i]
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nr, nc = path[i + 1]
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if cr == nr and nc == cc - 1:
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graph[cr][cc] = "<"
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elif cr == nr and nc == cc + 1:
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graph[cr][cc] = ">"
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elif cr == nr - 1 and nc == cc:
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graph[cr][cc] = "v"
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elif cr == nr + 1 and nc == cc:
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graph[cr][cc] = "^"
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else:
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assert False, "{} -> {} infeasible".format(path[i], path[i + 1])
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print("\n".join("".join(row) for row in graph))
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def neighbors(
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grid: list[list[int]], node: tuple[int, int], up: bool
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) -> Iterator[tuple[int, int]]:
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n_rows = len(grid)
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n_cols = len(grid[0])
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c_row, c_col = node
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for n_row, n_col in (
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(c_row - 1, c_col),
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(c_row + 1, c_col),
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(c_row, c_col - 1),
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(c_row, c_col + 1),
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):
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if not (n_row >= 0 and n_row < n_rows and n_col >= 0 and n_col < n_cols):
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continue
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if up and grid[n_row][n_col] > grid[c_row][c_col] + 1:
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continue
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elif not up and grid[n_row][n_col] < grid[c_row][c_col] - 1:
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continue
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yield n_row, n_col
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# === main code ===
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lines = sys.stdin.read().splitlines()
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grid = [[ord(cell) - ord("a") for cell in line] for line in lines]
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start: tuple[int, int]
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end: tuple[int, int]
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# for part 2
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start_s: list[tuple[int, int]] = []
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for i_row, row in enumerate(grid):
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for i_col, col in enumerate(row):
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if chr(col + ord("a")) == "S":
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start = (i_row, i_col)
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start_s.append(start)
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elif chr(col + ord("a")) == "E":
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end = (i_row, i_col)
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elif col == 0:
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start_s.append((i_row, i_col))
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# fix values
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grid[start[0]][start[1]] = 0
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grid[end[0]][end[1]] = ord("z") - ord("a")
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lengths_1, parents_1 = dijkstra(
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start=start, neighbors=lambda n: neighbors(grid, n, True), cost=lambda lhs, rhs: 1
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)
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path_1 = make_path(parents_1, start, end)
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assert path_1 is not None
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print_path(path_1, n_rows=len(grid), n_cols=len(grid[0]))
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print(f"answer 1 is {lengths_1[end] - 1}")
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lengths_2, parents_2 = dijkstra(
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start=end, neighbors=lambda n: neighbors(grid, n, False), cost=lambda lhs, rhs: 1
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)
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answer_2 = min(lengths_2.get(start, float("inf")) for start in start_s)
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print(f"answer 2 is {answer_2}")
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