Sierpinski carpet

题目描述

For a non-negative integer $K$, we define a level-$K$ carpet as follows:

A level-$0$ carpet is a $1 \times 1$ grid consisting of a single black cell. For K > 0, a level-$K$ carpet is a $3^K \times 3^K$ grid. When this grid is divided into nine $3^{K-1} \times 3^{K-1}$ blocks: The central block consists entirely of white cells. The other eight blocks are level-$(K-1)$ carpets.

You are given a non-negative integer $N$.
Print a level-$N$ carpet according to the specified format.

输入格式

The input is given from Standard Input in the following format: $N$

输出格式

Print $3^N$ lines.
The $i$-th line ($1 \leq i \leq 3^N$) should contain a string $S_i$ of length $3^N$ consisting of $.$ and #.
The $j$-th character of $S_i$ ($1 \leq j \leq 3^N$) should be # if the cell at the $i$-th row from the top and $j$-th column from the left of a level-$N$ carpet is black, and $.$ if it is white.

1

###
#.#
###

2

#########
#.##.##.#
#########
###...###
#.#...#.#
###...###
#########
#.##.##.#
#########

提示

$0 \leq N \leq 6$ $N$ is an integer.A level-$1$ carpet is a $3 \times 3$ grid as follows: When output according to the specified format, it looks like the sample output.
A level-$2$ carpet is a $9 \times 9$ grid.

标签: AtCoder|abc357C

来源

AtCoder|abc357C