[USACO11FEB] Cow Line

Posted 2020-10-04 日拱一卒 功不唐捐

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);
        }
    }
}