POJ 2083 Fractal

Fractal

Time Limit: 1000MS Memory Limit: 30000KTotal Submissions: 8719 Accepted: 4133

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

1234-1

Sample Output

X-X X XX X-X X   X X X     XX X   X X   X X    X   X XX X   X X X     XX X   X X-X X   X X         X X   X X X     X           X     XX X   X X         X X   X X   X X               X X    X                 X   X X               X XX X   X X         X X   X X X     X           X     XX X   X X         X X   X X         X X   X X          X     X         X X   X X            X X             X            X X         X X   X X          X     X         X X   X XX X   X X         X X   X X X     X           X     XX X   X X         X X   X X   X X               X X    X                 X   X X               X XX X   X X         X X   X X X     X           X     XX X   X X         X X   X X-

题解：这道题的意识是当输入1时，输出“X”，当输入2时输出以1的形态输出三行如上所示

按照n-1的形式进行输出。

采用了递归的方法，一行一行的输出一层一层的输出

采用分治算法，将大的问题先化为一个个小的问题，由一个个小的结果组合在一起组成大问题的结果，（递归）一层层的~~

这道题虽只有七组数据但如果用printf输出一个个地字符，会超时，改用putchar（）来输出。

代码：

#include<cstdio>#include<cstring>char ans[750][750];int l[8] = {0, 1};///递归void print(int i, int j, int n){    if (n == 1)    {        ans[i][j] = 'X';        return;    }    print(i, j, n - 1);    print(i, j + (l[n - 1] <<1), n - 1);    print(i + l[n - 1], j + l[n - 1], n - 1);    print(i + (l[n - 1] <<1 ), j, n - 1);    print(i + (l[n - 1] <<1 ), j + (l[n - 1] << 1), n - 1);}int main(void){    int n, i, j;    for (int i = 2; i <= 7; ++i)        l[i] = l[i - 1] * 3;    while (scanf("%d", &n), ~n)    {        memset(ans, ' ', sizeof(ans));///空格填充        print(0, 0, n);         for (i = 0; i < l[n]; i++)        {            for (j = 0; j < l[n]; ++j)                putchar(ans[i][j]);///此处应该用putchar();若用printf则会超时。            putchar(10);///相当于printf("\n");        }        puts("-");///相当于printf("-\n");    }    return 0;}