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USACO 2017年首轮月赛铂金级题2(翻译)

USACO 2017年首轮月赛铂金级题2(翻译)
USACO 2017年首轮月赛铂金级题2(翻译)

USACO 2017年首轮月赛铂金级题2

推箱子

贝茜和她的朋友们发明了一种新游戏。这个游戏名副其实,但不是特别有创意。他们称做“在不移动草垛的前提下,在谷仓周围推箱子推到指定的位置”的游戏(如果你觉得有点绕口,往下看这个游戏规则时,你应该会想到一些类似的游戏名字)。

这个谷仓可以模式化成一个N×M的矩形网格。有些单元格堆满草垛。贝茜占据了其中一个单元格,一个大木箱在另一个单元格。一个单元格不能同时容纳贝茜和盒子,而且它们也无法进入堆满草垛的单元格。

只要前方没有草垛存在,贝茜可以在东南西北四个方向上移动。如果她要进入有大木箱的房间,这个房间里的木箱将会沿着她进来的方向移到前面的房间。如果前面的那个房间里堆满草垛,贝茜就无法移动了。其中一个特定的单元格作为终点。贝茜的目标是把箱子推到那个地方。

给定谷仓的布局,包括木箱和牛的起始位置,以及木箱的目标位置,判断是否能够赢得这场比赛。

注意:这个问题允许512MB的内存使用,高于默认的256MB。

输入格式(文件pushabox.in):

第一行有三个数字N,M和Q。其中,N代表网格的行数,M代表网格的列数。

1≤N≤1500

1≤Q≤50,000

接下来的N行,其中(.)表示空单元格、(#)表示堆满草垛的单元格、贝西的起始位置(A)和木箱的初始位置(B)。

接下来的Q行,每个行都有一对整数(R,C)。对于每一对坐标,你要判断是否能够从初始状态开始到达谷仓的第R排,第C列的单元格。最上面一行是1,最左边一行是1。

输出格式(文件pushabox.out):

Q行,每一行均为字符串“是”或“否”。

样例输入:

5 5 4

# # .# #

# #. # #

A.B..

# #. # #

# # .# #

3 2

35

1 3

53

样例输出:

NO

YES

NO

NO

把箱子推到(3,5)位置,奶牛只需要向右移动3个空间。其他三个位置均无法实现。

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