#P1118. [USACO06FEB] Backward Digit Sums G/S

    ID: 701 远端评测题 1000ms 125MiB 尝试: 0 已通过: 0 难度: (无) 上传者: 标签>搜索枚举暴力深度优先搜索DFSUSACO2006

[USACO06FEB] Backward Digit Sums G/S

题目描述

FJ and his cows enjoy playing a mental game. They write down the numbers from 11 toN(1N10) N(1 \le N \le 10) in a certain order and then sum adjacent numbers to produce a new list with one fewer number. They repeat this until only a single number is left. For example, one instance of the game (when N=4N=4) might go like this:

    3   1   2   4
      4   3   6
        7   9
         16

Behind FJ's back, the cows have started playing a more difficult game, in which they try to determine the starting sequence from only the final total and the number NN. Unfortunately, the game is a bit above FJ's mental arithmetic capabilities.

Write a program to help FJ play the game and keep up with the cows.

有这么一个游戏:

写出一个11NN的排列aia_i,然后每次将相邻两个数相加,构成新的序列,再对新序列进行这样的操作,显然每次构成的序列都比上一次的序列长度少11,直到只剩下一个数字位置。下面是一个例子:

3,1,2,43,1,2,4

4,3,64,3,6

7,97,9

1616

最后得到1616这样一个数字。

现在想要倒着玩这样一个游戏,如果知道NN,知道最后得到的数字的大小sumsum,请你求出最初序列aia_i,为11NN的一个排列。若答案有多种可能,则输出字典序最小的那一个。

管理员注:本题描述有误,这里字典序指的是1,2,3,4,5,6,7,8,9,10,11,121,2,3,4,5,6,7,8,9,10,11,12

而不是1,10,11,12,2,3,4,5,6,7,8,91,10,11,12,2,3,4,5,6,7,8,9

输入格式

两个正整数n,sumn,sum

输出格式

输出包括11行,为字典序最小的那个答案。

当无解的时候,请什么也不输出。(好奇葩啊)

4 16
3 1 2 4

提示

对于40%40\%的数据,n7n≤7

对于80%80\%的数据,n10n≤10

对于100%100\%的数据,n12,sum12345n≤12,sum≤12345