103771: [Atcoder]ABC377 B - Avoid Rook Attack
Description
Score : $200$ points
Problem Statement
There is a grid of $64$ squares with $8$ rows and $8$ columns. Let $(i,j)$ denote the square at the $i$-th row from the top $(1\leq i\leq8)$ and $j$-th column from the left $(1\leq j\leq8)$.
Each square is either empty or has a piece placed on it.
The state of the squares is represented by a sequence $(S_1,S_2,S_3,\ldots,S_8)$ of $8$ strings of length $8$.
Square $(i,j)$ $(1\leq i\leq8,1\leq j\leq8)$ is empty if the $j$-th character of $S_i$ is ., and has a piece if it is #.
You want to place your piece on an empty square in such a way that it cannot be captured by any of the existing pieces.
A piece placed on square $(i,j)$ can capture pieces that satisfy either of the following conditions:
- Placed on a square in row $i$
- Placed on a square in column $j$
For example, a piece placed on square $(4,4)$ can capture pieces placed on the squares shown in blue in the following figure:
How many squares can you place your piece on?
Constraints
- Each $S_i$ is a string of length $8$ consisting of
.and#$(1\leq i\leq 8)$.
Input
The input is given from Standard Input in the following format:
$S_1$ $S_2$ $S_3$ $S_4$ $S_5$ $S_6$ $S_7$ $S_8$
Output
Print the number of empty squares where you can place your piece without it being captured by any existing pieces.
Sample Input 1
...#.... #....... .......# ....#... .#...... ........ ........ ..#.....
Sample Output 1
4
The existing pieces can capture pieces placed on the squares shown in blue in the following figure:
Therefore, you can place your piece without it being captured on $4$ squares: square $(6,6)$, square $(6,7)$, square $(7,6)$, and square $(7,7)$.
Sample Input 2
........ ........ ........ ........ ........ ........ ........ ........
Sample Output 2
64
There may be no pieces on the grid.
Sample Input 3
.#...... ..#..#.. ....#... ........ ..#....# ........ ...#.... ....#...
Sample Output 3
4
Output
得分：200分
问题陈述
有一个由64个方块组成的网格，有8行和8列。 用$(i,j)$表示从顶部第$i$行$(1\leq i\leq8)$和从左边第$j$列$(1\leq j\leq8)$的方块。
每个方块要么是空的，要么上面放了一个棋子。
方块的状态由一个由8个长度为8的字符串组成的序列$(S_1,S_2,S_3,\ldots,S_8)$表示。
如果$S_i$的第$j$个字符是.，那么方块$(i,j)$$(1\leq i\leq8,1\leq j\leq8)$是空的；如果是#，则上面有一个棋子。
你想要在一个空方块上放置你的棋子，以使得它不能被任何现有的棋子捕获。
放在方块$(i,j)$上的棋子可以捕获满足以下任一条件的棋子：
- 放在第$i$行的方块上
- 放在第$j$列的方块上
例如，放在方块$(4,4)$上的棋子可以捕获如下图中蓝色方块上的棋子：
你可以放置多少个方块让你的棋子不被捕获？
约束条件
- 每个$S_i$是一个由
.和#组成的长度为8的字符串$(1\leq i\leq 8)$。
输入
输入从标准输入以下格式给出：
$S_1$ $S_2$ $S_3$ $S_4$ $S_5$ $S_6$ $S_7$ $S_8$
输出
打印出你可以放置棋子而不被任何现有棋子捕获的空方块的数量。
示例输入1
...#.... #....... .......# ....#... .#...... ........ ........ ..#.....
示例输出1
4
现有的棋子可以捕获放在如下图中蓝色方块上的棋子：
因此，你可以放置你的棋子而不被捕获在4个方块上：方块$(6,6)$，方块$(6,7)$，方块$(7,6)$，和方块$(7,7)$。
示例输入2
........ ........ ........ ........ ........ ........ ........ ........
示例输出2
64
网格上可能没有棋子。
示例输入3
.#...... ..#..#.. ....#... ........ ..#....# ........ ...#.... ....#...
示例输出3
4