1085:Fractal（分治法）

1085:Fractal

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时间限制: 

1000ms

  内存限制: 

65536kB

描述

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.

输入

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.

输出

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.

实验源码（OpenJudge提交通过）

#include <stdio.h>

char box[730][730]={"",""};

void drawFractalBox(int n,int x,int y)//x为行，y为列

{

int i=n;

int c=1;

while(--i)

c=c*3; 

//首先计算打印的行数和列数 C

if(c==1)

{

box[x][y]='X'; 

return;

}

else

{

drawFractalBox(n-1,x,y); //左上

drawFractalBox(n-1,x,(c*2)/3+y); //右上

drawFractalBox(n-1,c/3+x,c/3+y); //中间

drawFractalBox(n-1,(c*2)/3+x,y); //左下

drawFractalBox(n-1,(2*c)/3+x,y+(2*c)/3); //右下

}

}

int main()

{

int i,j,n;

scanf("%d",&n);

while(n!=-1)

{

int num=1;

int t=n;

while(--t)

num=num*3; //得到行列数

for(i=1;i<=num;i++)

for(j=1;j<=num;j++)

box[i][j]=' '; //初始化

drawFractalBox(n,1,1); //填充

for(i=1;i<=num;i++)

{

for(j=1;j<=num;j++)

printf("%c",box[i][j]);

printf("\n");

}//输出

printf("-\n");

scanf("%d",&n);//输入下一个

}

return 0;

}

运行结果截图：