#P1825. [USACO11OPEN] Corn Maze S

    ID: 757 远端评测题 1000ms 512MiB 尝试: 23 已通过: 6 难度: 8 上传者: 标签>广度优先搜索BFS搜索最短路模拟USACO2011

[USACO11OPEN] Corn Maze S

题目描述

This past fall, Farmer John took the cows to visit a corn maze. But this wasn't just any corn maze: it featured several gravity-powered teleporter slides, which cause cows to teleport instantly from one point in the maze to another. The slides work in both directions: a cow can slide from the slide's start to the end instantly, or from the end to the start. If a cow steps on a space that hosts either end of a slide, she must use the slide.

The outside of the corn maze is entirely corn except for a single exit.

The maze can be represented by an N x M (2 <= N <= 300; 2 <= M <= 300) grid. Each grid element contains one of these items:

* Corn (corn grid elements are impassable)

* Grass (easy to pass through!)

* A slide endpoint (which will transport a cow to the other endpoint)

* The exit

A cow can only move from one space to the next if they are adjacent and neither contains corn. Each grassy space has four potential neighbors to which a cow can travel. It takes 1 unit of time to move from a grassy space to an adjacent space; it takes 0 units of time to move from one slide endpoint to the other.

Corn-filled spaces are denoted with an octothorpe (#). Grassy spaces are denoted with a period (.). Pairs of slide endpoints are denoted with the same uppercase letter (A-Z), and no two different slides have endpoints denoted with the same letter. The exit is denoted with the equals sign (=).

Bessie got lost. She knows where she is on the grid, and marked her current grassy space with the 'at' symbol (@). What is the minimum time she needs to move to the exit space?

输入格式

第一行:两个用空格隔开的整数 NNMM

2N+12\sim N+1 行:第 i+1i+1 行描述了迷宫中的第 ii 行的情况(共有MM个字符,每个字符中间没有空格)。

输出格式

一个整数,表示起点到出口所需的最短时间。

题目大意

奶牛们去一个 N×MN\times M 玉米迷宫,2N300,2M3002 \leq N \leq 300,2 \leq M \leq300

迷宫里有一些传送装置,可以将奶牛从一点到另一点进行瞬间转移。这些装置可以双向使用。

如果一头奶牛处在这个装置的起点或者终点,这头奶牛就必须使用这个装置,奶牛在传送过后不会立刻进行第二次传送,即不会卡在传送装置的起点和终点之间来回传送。

玉米迷宫除了唯一的一个出口都被玉米包围。

迷宫中的每个元素都由以下项目中的一项组成:

  1. 玉米,# 表示,这些格子是不可以通过的。
  2. 草地,. 表示,可以简单的通过。
  3. 传送装置,每一对大写字母 A\tt{A}Z\tt{Z} 表示。
  4. 出口,= 表示。
  5. 起点, @ 表示

奶牛能在一格草地上可能存在的四个相邻的格子移动,花费 11 个单位时间。从装置的一个结点到另一个结点不花时间。

5 6
###=##
#.W.##
#.####
#.@W##
######

3

提示

例如以下矩阵,N=5,M=6N=5,M=6

###=##
#.W.##
#.####
#.@W##
######

唯一的一个装置的结点用大写字母 W\tt{W} 表示。

最优方案为:先向右走到装置的结点,花费一个单位时间,再到装置的另一个结点上,花费 00 个单位时间,然后再向右走一个,再向上走一个,到达出口处,总共花费了 33 个单位时间。