Fractal

Time Limit: 1000MS		Memory Limit: 30000K
Total Submissions: 8341		Accepted: 3965

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.

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.

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.

1

2

3

4

-1

-

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

-
递归：
思路很巧妙，把每个左上角的点作为起点；开始递归；
代码：

#include<iostream>

#include<cstdio>

#include<cstring>

#include<cmath>

#include<algorithm>

#include<queue>

using namespace std;

const int INF=0x3f3f3f3f;

#define mem(x,y) memset(x,y,sizeof(x))

#define SI(x) scanf("%d",&x);

char a[2500][2500];

void dfs(int x,int y,int cur){

	if(cur==1){

		a[x][y]='X';

		return;

	}

	int n,m;

	dfs(x,y,cur-1);

	//左上

	m=x;n=y+pow(3,cur-2)*2;

	dfs(m,n,cur-1);

	//右上

	m=x+pow(3,cur-2)*2;n=y;

	dfs(m,n,cur-1);

	//左下

	m=x+pow(3,cur-2)*2;n=y+pow(3,cur-2)*2;

	dfs(m,n,cur-1);

	//右下

	m=x+pow(3,cur-2);n=y+pow(3,cur-2);

	dfs(m,n,cur-1);

	//中

}

int main(){

	int N;

	while(scanf("%d",&N),N!=-1){

		int len=pow(3,N-1);

		for(int i=0;i<len;i++){

			for(int j=0;j<len;j++)

				a[i][j]=' ';

			a[i][len]='\0';

		}

		dfs(0,0,N);

		for(int i=0;i<len;i++){

			printf("%s\n",a[i]);

		}

		puts("-");

	}

	return 0;

}