- Fractal(3.4.1)

C - Fractal(3.4.1)

Time Limit:1000MS    Memory Limit:30000KB    64bit IO Format:%I64d
& %I64u

SubmitStatus

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
4
-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
-
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 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
             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   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 X
-
#include <iostream>
#include <string>
#include <cstring>
#include <cmath>
using namespace std;
#define M 1000
char s[M][M];
void print( int n, int x, int y)
{
    int m;//m 表示方盒子规模 即边长
	double t=3;
    if( n == 1 )
    {
        s[x][y] = 'X';   //回溯，当n=1时，为（x，y）坐标赋值'X'
        return ;
    }
    else if( n > 1 )
    {
        m = pow( t, n - 2 );  //计算盒子规模
        print( n - 1, x, y );   //左上角第一个图形进行递归打印，第一个图形左上角坐标为（x，y）
        print( n - 1, x, y + 2 * m ); //右上角第二个图形进行递归打印，第二个图形左上角坐标为（x，y+2*m）
        print( n - 1, x + m, y + m );  //中间第三个图形进行递归打印，第三个图形左上角坐标为（x+m,y+m）
        print( n - 1, x + 2 * m, y );  //左下角第四个图形进行递归打印，第四个图形左下角坐标为（x+2*m,y）
        print( n - 1, x + 2 * m, y + 2 * m);//右下角第五个图形进行递归打印，第五个图形右下角坐标为（x+2*m,y+2*m）
    }
}  

int main()
{
    int n, i, p; double t=3;
    while(cin >> n && n != -1 )
    {
        p = pow( t, n - 1 );  //计算方盒子规模
        for( i = 0; i < p; i++ )   //对数组进行初始化
        {
            memset( s + i, ' ', p );   //每一行均初始化为空格
            s[i][p] = '\n';     //每一行最后一列初始化为换行,如果不这样做，会出错，图形无法输出
        }
        print( n, 0, 0 );   //从左上角（x，y）坐标开始打印
        for( i = 0; i < p; i++)
            cout << s[i] ;     //输出图形
        cout << '-' << endl;
    }
    return 0;
}