Place the Robots
Time Limit: 5 Seconds Memory Limit: 32768 KB
Robert is a famous engineer. One day he was given a task by his boss. The
background of the task was the following:
Given a map consisting of square blocks. There were three kinds of blocks:
Wall, Grass, and Empty. His boss wanted to place as many robots as possible in
the map. Each robot held a laser weapon which could shoot to four directions
(north, east, south, west) simultaneously. A robot had to stay at the block
where it was initially placed all the time and to keep firing all the time. The
laser beams certainly could pass the grid of Grass, but could not pass the grid
of Wall. A robot could only be placed in an Empty block. Surely the boss would
not want to see one robot hurting another. In other words, two robots must not
be placed in one line (horizontally or vertically) unless there is a Wall
between them.
Now that you are such a smart programmer and one of Robert's best friends, He
is asking you to help him solving this problem. That is, given the description
of a map, compute the maximum number of robots that can be placed in the map.
Input
The first line contains an integer T (<= 11) which is the number of test
cases.
For each test case, the first line contains two integers m and n (1<= m, n
<=50) which are the row and column sizes of the map. Then m lines follow,
each contains n characters of '#', '*', or 'o' which represent Wall, Grass, and
Empty, respectively.
Output
For each test case, first output the case number in one line, in the format:
"Case :id" where id is the test case number, counting from 1. In the
second line just output the maximum number of robots that can be placed in that
map.
Sample Input
2
4 4
o***
*###
oo#o
***o
4 4
#ooo
o#oo
oo#o
***#
Sample Output
Case :1
3
Case :2
5
離散化 + 二分圖匹配 , 匈牙利算法 .
分別把行上和列上能夠連在一起的 ( 中間沒有牆的都算連在一起 ), 都看作二分圖的一個點 , 行和列的離散化的點分別是二分圖的兩部分 , 屬於兩部分的兩點 , 如果它們所代表的行和列的交點上是一塊空地 , 那麼兩點之間就連一條邊 . 求出這兩部分的匹配數 , 就是題目要的結果 ( 這個就不證明了 )
代碼如下 :