Fractal(递归，好题)

Fractal

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

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 OutputX

-
X X
 X
X X
-
X X   X X
 X     X
X X   X X
   X X
    X
   X X
X X   X X
 X     X
X X   X X
-
X X   X X         X X   X X
 X     X           X     X
X X   X X         X X   X X
   X X               X X
    X                 X
   X X               X X
X X   X X         X X   X X
 X     X           X     X
X X   X X         X X   X X
         X X   X X
          X     X
         X X   X X
            X X
             X
            X X
         X X   X X
          X     X
         X X   X X
X X   X X         X X   X X
 X     X           X     X
X X   X X         X X   X X
   X X               X X
    X                 X
   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]='';
		}
		dfs(0,0,N);
		for(int i=0;i<len;i++){
			printf("%s
",a[i]);
		} 
		puts("-");
	}
	return 0;
}