https://www.luogu.org/problem/show?pid=3014
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
输入样例#1：
5 2 P 3 Q 1 2 5 3 4
输出样例#1：
1 2 4 3 5 5 题意：询问这是第几个全排列，询问第k个全排列是什么
#include<cstdio>
#include<cstring>
using namespace std;
long long jc[21];
bool v[21];
int p[21];
int main()
{
jc[1]=1;
for(int i=2;i<=20;i++) jc[i]=jc[i-1]*i;
int n,q,cnt,now;
long long x,tot;
char c[5];
scanf("%d%d",&n,&q);
while(q--)
{
scanf("%s",c);
if(c[0]==‘P‘)
{
scanf("%lld",&x);
memset(v,0,sizeof(v));
for(int i=1;i<n;i++)
{
cnt=now=0;
while(x>jc[n-i]) x-=jc[n-i],cnt++;
for(int i=1;i<=20;i++)
if(!v[i])
{
now++;
if(now==cnt+1)
{
printf("%d",i);
continue;
}
}
}
for(int i=1;i<=20;i++)
if(!v[i])
{
printf("%d\n",i);
break;
}
}
else
{
tot=0,sum;
for(int i=1;i<=n;i++) scanf("%d",&p[i]);
memset(v,0,sizeof(v));
for(int i=1;i<=n;i++)
{
sum=0;
for(now=1;now<=n;now++)
if(!v[now]) break;
else sum++;
v[now]=true;
now-=sum;
tot+=(now-1)*jc[n-i];
}
printf("lld\n",tot);
}
}
}