P3014 [USACO11FEB]牛线Cow Line

题目背景

征求翻译。如果你能提供翻译或者题意简述，请直接发讨论，感谢你的贡献。

题目描述

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.

输入输出格式

输入格式：

• 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.

输出格式：

• 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.

输入输出样例

5 2
P
3
Q
1 2 5 3 4

1 2 4 3 5
5 

#include<map>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
int n,m,vis[21];
long long num[21];
int main(){//freopen("permutation.in","r",stdin);//freopen("permutation.out","w",stdout);scanf("%d%d",&n,&m);for(int i=1;i<=21;i++)    num[i]=1;for(int i=2;i<=n;i++)    num[n-i+1]=i*num[n-i+2];for(int k=1;k<=m;k++){char c;long long x;cin>>c;memset(vis,0,sizeof(vis));if(c=='P'){cin>>x;long long k=x;int flag=1;for(int i=1;i<=n;i++){int ans;if(k>=num[i+1]){long long a=k/num[i+1];long long nn=k%num[i+1];if(nn)    flag=1;else flag=0;int bns=0;for(int j=1;j<=n;j++){if(!vis[j])    bns++;if(bns-flag==a){ans=j;vis[j]=1;break;}}k=nn;}else{if(flag==1){for(int j=1;j<=n;j++)if(!vis[j]){ans=j;vis[j]=1;break;}    }else{for(int j=n;j>=1;j--)if(!vis[j]){ans=j;vis[j]=1;break;}}}cout<<ans<<" ";}cout<<endl;}else{long long ans=0;for(int i=1;i<=n;i++){cin>>x;int bns=0;for(int j=1;j<=n;j++){if(!vis[j])    bns++;if(j==x)    break;}bns--;vis[x]=1;ans+=(long long)bns*num[i+1];}cout<<ans+1<<endl;}}
}