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

5 2

P

3

Q

1 2 5 3 4

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[];

bool v[];

int p[];

int main()

{

    int n,q,cnt,now,sum;

    long long x,tot;

    char c[];

    scanf("%d%d",&n,&q);

    jc[]=;

    for(int i=;i<=n;i++) jc[i]=jc[i-]*i;

    while(q--)

    {

        scanf("%s",c);

        if(c[]=='P')

        {

            scanf("%lld",&x);

            memset(v,,sizeof(v));

            for(int i=;i<n;i++)

            {

                cnt=now=;

                while(x>jc[n-i]) x-=jc[n-i],cnt++;

                for(int i=;i<=;i++)

                    if(!v[i])

                    {

                        now++;

                        if(now==cnt+)

                        {

                            printf("%d ",i);

                            v[i]=true;

                            continue;

                        }

                    }

            }

            for(int i=;i<=;i++)

                if(!v[i])

                {

                    printf("%d\n",i);

                    break;

                }

        }

        else

        {

            tot=,sum;

            for(int i=;i<=n;i++) scanf("%d",&p[i]);

            memset(v,,sizeof(v));

            for(int i=;i<n;i++)

            {

                sum=;

                for(now=;now<=n;now++)

                    if(!v[now] && now<p[i]) sum++;

                v[p[i]]=true;

                tot+=sum*jc[n-i];

            }

            printf("%lld\n",tot+);

        }

    }

}