103752: [Atcoder]ABC375 C - Spiral Rotation
Description
Score : $400$ points
Problem Statement
You are given a grid with $N$ rows and $N$ columns, where $N$ is an even number. Let $(i, j)$ denote the cell at the $i$-th row from the top and $j$-th column from the left.
Each cell is painted black or white. If $A_{i, j} =$ #, cell $(i, j)$ is black; if $A_{i, j} =$ ., it is white.
Find the color of each cell after performing the following operation for $i = 1, 2, \ldots, \frac{N}{2}$ in this order.
- For all pairs of integers $x, y$ between $i$ and $N + 1 - i$, inclusive, replace the color of cell $(y, N + 1 - x)$ with the color of cell $(x, y)$. Perform these replacements simultaneously for all such pairs $x, y$.
Constraints
- $N$ is an even number between $2$ and $3000$, inclusive.
- Each $A_{i, j}$ is
#or..
Input
The input is given from Standard Input in the following format:
$N$
$A_{1,1}A_{1,2}\ldots A_{1,N}$
$A_{2,1}A_{2,2}\ldots A_{2,N}$
$\vdots$
$A_{N,1}A_{N,2}\ldots A_{N,N}$
Output
After all operations, let $B_{i, j} =$ # if cell $(i, j)$ is black, and $B_{i, j} =$ . if it is white. Print the grid in the following format:
$B_{1,1}B_{1,2}\ldots B_{1,N}$
$B_{2,1}B_{2,2}\ldots B_{2,N}$
$\vdots$
$B_{N,1}B_{N,2}\ldots B_{N,N}$
Sample Input 1
8 .......# .......# .####..# .####..# .##....# .##....# .####### .#######
Sample Output 1
........ #######. #.....#. #.###.#. #.#...#. #.#####. #....... ########
The operations change the colors of the grid cells as follows:
.......# ........ ........ ........ ........ .......# ######.. #######. #######. #######. .####..# ######.. #....##. #.....#. #.....#. .####..# → ##..##.. → #....##. → #.##..#. → #.###.#. .##....# ##..##.. #..####. #.##..#. #.#...#. .##....# ##...... #..####. #.#####. #.#####. .####### ##...... #....... #....... #....... .####### ######## ######## ######## ########
Sample Input 2
6 .#.#.# ##.#.. ...### ###... ..#.## #.#.#.
Sample Output 2
#.#.#. .#.#.# #.#.#. .#.#.# #.#.#. .#.#.#
Sample Input 3
12 .......#.### #...#...#..# ###.#..##### ..#.#.#.#... .#.....#.### .......#.#.. #...#..#.... #####....... ...#...#.#.# ..###..#..## #..#.#.#.#.# .####.......
Sample Output 3
.#..##...##. #.#.#.#.#... ###.##..#... #.#.#.#.#... #.#.##...##. ............ ............ .###.###.### ...#...#.#.. .###...#.### ...#...#...# .###...#.###
Output
得分：400分
问题陈述
给定一个有N行和N列的网格，其中N是一个偶数。令$(i, j)$表示从顶部第i行和从左边第j列的单元格。
每个单元格被涂成黑色或白色。如果$A_{i, j} =$ #，单元格$(i, j)$是黑色的；如果$A_{i, j} =$ .，它是白色的。
在按顺序对$i = 1, 2, \ldots, \frac{N}{2}$执行以下操作后，找出每个单元格的颜色。
- 对于所有整数对$x, y$在$i$和$N + 1 - i$之间（包括），将单元格$(y, N + 1 - x)$的颜色更改为单元格$(x, y)$的颜色。对所有这样的对$x, y$同时执行这些替换。
约束条件
- $N$是一个在2到3000之间（包括）的偶数。
- 每个$A_{i, j}$是
#或.。
输入
输入从标准输入以以下格式给出：
$N$
$A_{1,1}A_{1,2}\ldots A_{1,N}$
$A_{2,1}A_{2,2}\ldots A_{2,N}$
$\vdots$
$A_{N,1}A_{N,2}\ldots A_{N,N}$
输出
在所有操作之后，令$B_{i, j} =$ #如果单元格$(i, j)$是黑色的，且$B_{i, j} =$ .如果它是白色的。按以下格式打印网格：
$B_{1,1}B_{1,2}\ldots B_{1,N}$
$B_{2,1}B_{2,2}\ldots B_{2,N}$
$\vdots$
$B_{N,1}B_{N,2}\ldots B_{N,N}$
示例输入1
8 .......# .......# .####..# .####..# .##....# .##....# .####### .#######
示例输出1
........ #######. #.....#. #.###.#. #.#...#. #.#####. #....... ########
操作改变了网格单元格的颜色如下：
.......# ........ ........ ........ ........ .......# ######.. #######. #######. #######. .####..# ######.. #....##. #.....#. #.....#. .####..# → ##..##.. → #....##. → #.##..#. → #.###.#. .##....# ##..##.. #..####. #.##..#. #.#...#. .##....# ##...... #..####. #.#####. #.#####. .####### ##...... #....... #....... #....... .####### ######## ######## ######## ########
示例输入2
6 .#.#.# ##.#.. ...### ###... ..#.## #.#.#.
示例输出2
#.#.#. .#.#.# #.#.#. .#.#.# #.#.#. .#.#.#
示例输入3
12 .......#.### #...#...#..# ###.#..##### ..#.#.#.#... .#.....#.### .......#.#.. #...#..#.... #####....... ...#...#
Sample Input Copy
Sample Output Copy