Fractal

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

2

3

-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 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 + 5char 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;}