经典题：求字典序第m个的序列(2062)

Subset sequence

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 4587    Accepted Submission(s): 2228

Problem Description

Consider the aggregate An= { 1, 2, …, n }. For example, A1={1}, A3={1,2,3}. A subset sequence is defined as a array of a non-empty subset. Sort all the subset sequece of An in lexicography order. Your task is to find the m-th one.

 

Input

The input contains several test cases. Each test case consists of two numbers n and m ( 0< n<= 20, 0< m<= the total number of the subset sequence of An ).

 

Output

For each test case, you should output the m-th subset sequence of An in one line.

 

Sample Input

1 1 2 1 2 2 2 3 2 4 3 10

 

Sample Output

1 1 1 2 2 2 1 2 3 1

设f[i]为1到n的排成的序列的总数，则可由打表发现：f[i]=n*(f[i-1]+1)，这里其实蕴含着递归的思想。我们想要知道序列的具体位置，由规律性：zushu=ceil(m*1.0/(f[n-1]+1))，然后就可以取出首位元素了，剩下的序列可由递归求解，同时，原序列需要更新，元素被取出。然后就要更新内层的组数了：m=m-(zushu-1)*(f[n-1]+1)-1，因为每个序列的最小的那一个就一个元素，其后没有元素，所以需要-1。n还需自减一次。

/*------------------Header Files------------------*/
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include