UVA Bandwidth

题目例如以下：

Bandwidth 

Given a graph (V,E) where V is a set of nodes and E is a set of arcsin VxV, and an ordering on the elements in V, then the bandwidth of a node v is defined as the maximum distance in theordering between v and any node to which it is connected in thegraph. The bandwidth of the ordering is then defined as the maximum ofthe individual bandwidths. For example, consider the following graph:

This can be ordered in many ways, two of which are illustrated below:

For these orderings, the bandwidths of the nodes (in order) are 6, 6,1, 4, 1, 1, 6, 6 giving an ordering bandwidth of 6, and 5, 3, 1, 4, 3,5, 1, 4 giving an ordering bandwidth of 5.

Write a program that will find the ordering of a graph that minimisesthe bandwidth.

Input

Input will consist of a series of graphs. Each graph will appear on aline by itself. The entire file will be terminated by a lineconsisting of a single #. For each graph, the input will consist ofa series of records separated by `;'. Each record will consist of anode name (a single upper case character in the the range `A' to `Z'),followed by a `:' and at least one of its neighbours. The graph willcontain no more than 8 nodes.

Output

Output will consist of one line for each graph, listing the orderingof the nodes followed by an arrow (->) and the bandwidth for thatordering. All items must be separated from their neighbours by exactlyone space. If more than one ordering produces the same bandwidth, thenchoose the smallest in lexicographic ordering, that is the one thatwould appear first in an alphabetic listing.

Sample input

A:FB;B:GC;D:GC;F:AGH;E:HD
#

Sample output

A B C F G D H E -> 3

给一个图，求出使图的带宽为最小值的节点的排列，带宽指每一个节点的与相邻节点在排列中距离的最大值。图的带宽是节点带宽的最大值。因为节点最多仅仅有八个，直接枚举全排列就可以。假设节点数较多应该剪枝，但本题显然不须要。

AC的代码例如以下：