TOJ 3838: Cow Line -- 排列

3838: Cow Line

Time Limit(Common/Java):2000MS/6000MS     Memory Limit:65536KByte
Total Submit: 25            Accepted:10

Description

The N (1 <= N <= 20) cows conveniently numbered 1...N are playing yet another one of their crazy games with Farmer John. The cows will arrange themselves in a line and ask Farmer John what their line number is. In return, Farmer John can give them a line number and the cows must rearrange themselves into that line.

A line number is assigned by numbering all the permutations of the line in lexicographic order.
Consider this example:
Farmer John has 5 cows and gives them the line number of 3.The permutations of the line in ascending lexicographic order:
1st: 1 2 3 4 5
2nd: 1 2 3 5 4
3rd: 1 2 4 3 5
Therefore, the cows will line themselves in the cow line 1 2 4 3 5.

The cows, in return, line themselves in the configuration "1 2 5 3 4" and ask Farmer John what their line number is.
Continuing with the list:
4th : 1 2 4 5 3
5th : 1 2 5 3 4
Farmer John can see the answer here is 5

Farmer John and the cows would like your help to play their game. They have K (1 <= K <= 10,000) queries that they need help with. Query i has two parts: C_i will be the command, which is either 'P' or 'Q'.

If C_i is 'P', then the second part of the query will be one integer A_i (1 <= A_i <= N!), which is a line number. This is Farmer John
challenging the cows to line up in the correct cow line.

If C_i is 'Q', then the second part of the query will be N distinct integers B_ij (1 <= B_ij <= N). This will denote a cow line. These are the cows challenging Farmer John to find their line number.

 

Input

* Line 1: Two space-separated integers: N and K

* Lines 2..2*K+1: Line 2*i and 2*i+1 will contain a single query.

Line 2*i will contain just one character: 'Q' if the cows are lining up and asking Farmer John for their line number or 'P' if Farmer
John gives the cows a line number.

If the line 2*i is 'Q', then line 2*i+1 will contain N space-separated integers B_ij which represent the cow line. If the line 2*i is 'P',
then line 2*i+1 will contain a single integer A_i which is the line number to solve for.

 

Output

* Lines 1..K: Line i will contain the answer to query i.

If line 2*i of the input was 'Q', then this line will contain a single integer, which is the line number of the cow line in line 2*i+1.

If line 2*i of the input was 'P', then this line will contain N space separated integers giving the cow line of the number in line 2*i+1.

 

Sample Input

5 2P3Q1 2 5 3 4

Sample Output

1 2 4 3 55

Source

USACO Feb 2011

分析：根据排列的序号k（从0开始）求排列时，设共n个数，剩下n - 1个数的全排列个数为fac[n - 1]，那么排列的第一位就是k / fac[n - 1] + 1。接着找剩下的n - 1个数的第k % fac[n - 1]个排列，重复上一过程就好了。

根据排列求排列序号就完全和上面相反。比如共n个数，第一个数为k，那么排列序号 = (k - 1) * fac[n - 1] + 剩下n - 1个数的排列序号。

两个过程都是递归。