P3014 [USACO11FEB]牛线Cow Line

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    • 660提交
  • 题目提供者 FarmerJohn2
  • 评测方式 云端评测
  • 标签 动态规划,动规,dp 枚举,暴力 贪心 USACO 2011
  • 难度 普及+/提高
  • 时空限制 1000ms / 128MB

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    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.

    N(1<=N<=20)头牛,编号为1...N,正在与FJ玩一个疯狂的游戏。奶牛会排成一行(牛线),问FJ此时的行号是多少。之后,FJ会给牛一个行号,牛必须按照新行号排列成线。

    行号是通过以字典序对行的所有排列进行编号来分配的。比如说:FJ有5头牛,让他们排为行号3,排列顺序为:

    1:1 2 3 4 5

    2:1 2 3 5 4

    3:1 2 4 3 5

    因此,牛将在牛线1 2 4 3 5中。

    之后,奶牛排列为“1 2 5 3 4”,并向FJ问他们的行号。继续列表:

    4:1 2 4 5 3

    5:1 2 5 3 4

    FJ可以看到这里的答案是5。

    FJ和奶牛希望你的帮助玩他们的游戏。他们需要K(1<=K<=10000)组查询,查询有两个部分:C_i将是“P”或“Q”的命令。

    如果C_i是'P',则查询的第二部分将是一个整数A_i(1 <= A_i <= N!),它是行号。此时,你需要回答正确的牛线。

    如果C_i是“Q”,则查询的第二部分将是N个不同的整数B_ij(1 <= B_ij <= N)。这将表示一条牛线,此时你需要输出正确的行号。

    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: 复制
    5 2 
    P 
    3 
    Q 
    1 2 5 3 4 
    
    输出样例#1: 复制
    1 2 4 3 5 
    5 
    

    说明

    感谢@prcups 提供翻译

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