Fractal

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本文介绍了一种使用递归算法绘制分形盒子的方法。通过定义不同级别的分形盒子，并利用递归的思想来绘制这些图案，文章提供了一个具体的实现案例，包括输入输出格式及样例。

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Description

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales.
A box fractal is defined as below :

A box fractal of degree 1 is simply
X
A box fractal of degree 2 is
X X
X
X X
If using B(n - 1) to represent the box fractal of degree n - 1, then a box fractal of degree n is defined recursively as following
```
B(n - 1)        B(n - 1)

        B(n - 1)

B(n - 1)        B(n - 1)
```

Your task is to draw a box fractal of degree n.

Input

The input consists of several test cases. Each line of the input contains a positive integer n which is no greater than 7. The last line of input is a negative integer −1 indicating the end of input.

Output

For each test case, output the box fractal using the 'X' notation. Please notice that 'X' is an uppercase letter. Print a line with only a single dash after each test case.

Sample Input

-1

Sample Output

X X

X X X X

X X

X X X X

X X

X X X X

X X

X X X X

思路：采用分治思想，将同一类型的问题分解成规模更小的问题，用深搜解决

代码如下：

#include <cstdio>
#define Max 729 + 5
char matrix[Max][Max];
void DFS(int n,int x,int y)
{
	if (n == 1)
	{
		matrix[x][y] = 'X';
		return;
	}
	else
	{
		int size = 1;
		for (int i = 2; i < n; i++)
			size *= 3;
		DFS(n - 1,x,y);//左上角
		DFS(n - 1,x,y + 2 * size);//右上角
		DFS(n - 1,x + size,y + size);//中间
		DFS(n - 1,x + 2 * size,y);//左下角
		DFS(n - 1,x + 2 * size,y + 2 * size);//右下角
	}
}
int main()
{
	int n;
	while (scanf("%d",&n) == 1 && (n + 1))
	{
		int size = 1;
		for (int i = 1; i < n; i++)
			size *= 3;
		for (int j = 0; j < size; j++)//初始化
		{
			for (int k = 0; k < size; k++)
				matrix[j][k] = ' ';
			matrix[j][size] = '\0';
		}
		DFS(n,0,0);
		for (int k = 0; k < size; k++)
			printf("%s\n",matrix[k]);
		printf("-\n");
	}
	return 0;
}