编程介的小学生 2017-04-24 12:36 采纳率: 20.5%
浏览 753
已采纳

Fold-up Patterns

Fold-up patterns for solids like cubes or octahedrons can be found in many books on geometry, but without actually folding them it is hard to tell whether the constructions really work. In this problem, we will consider a special class of such patterns.

Given a fold-up pattern built from unit squares in the plane, together with a description along what edges it should be folded in what direction, decide whether it will result in a closed surface of a solid in three dimensions. If it does, find the volume of the solid.

More precisely, the pattern consists of a connected set of unit squares in the plane. For any edge between connected sides you are told whether to fold forward, backward (always at a right angle), or not at all along that edge. If an edge between two adjacent squares in the pattern is not mentioned in the input, you may assume that the squares are not connected and can be ripped apart when folding. However, connected edges must always be folded according to the description.

For our purposes a closed surface is one where every square in the pattern separates the inside from the outside. When folded, the squares of the pattern lie on a rectangular, 3-dimensional grid, and each separates a cell (cubes of side length one unit) on the inside from one on the outside. For every cell it must be clear whether it is inside or outside. The following sketch illustrates this rule in two dimensions.

Note that even the second pattern above satisfies our definition of a closed surface, but the interior is not connected.

Two different squares may not occupy exactly the same position in space, though they may (and will for a closed surface) touch at edges and vertices. Make sure that the pattern does not interpenetrate itself through connected edges. Apart from that, do not worry about the process of folding, e.g. what edges are folded first or whether part of the structure is in the way for the rest.

Input

The input file consists of several test cases.

For each test case, the first line contains two integers n and e. These are the number n (1 <= n <= 200) of squares in the pattern and the number e (0 <= e <= 300) of edges. Squares are labelled by the integers 0 to n - 1. The following e lines describe one edge each using the four numbers s1; s2; p; f :

The two numbers s1 and s2 (with 0 <= s1 < s2 < n) of the squares that are joined by the edge.

The position p of the square s2 with respect to the square s1 in the pattern. Here p = 0;1;2;3 mean above, to the left, below, or to the right of s1, respectively (see sketch below).

The number f =0;1;2 tells you to fold along the edge either not at all, forward, or back, respectively (see sketch).

You can also assume that the pattern is connected and can be drawn in the plane without overlapping.

At the end of the input file, there will be a line containing two zeros (instead of n and e). Do not process that line.

Output

For each scenario print ��Test case #k:��, where k is the number of the test case (starting from 1).

Then, on the same line, print either ��not a closed surface�� if the pattern does not form a closed surface or ��closed surface, volume=�� and the volume as an integer if it does.

Sample Input

6 5
0 2 2 1
1 2 3 1
2 3 3 1
2 4 2 1
4 5 2 1
5 4
0 2 2 1
1 2 3 1
2 3 3 1
2 4 2 1
0 0

Sample Output

Test case #1: closed surface, volume=1
Test case #2: not a closed surface

  • 写回答

1条回答 默认 最新

  • threenewbee 2017-05-09 15:56
    关注
    本回答被题主选为最佳回答 , 对您是否有帮助呢?
    评论

报告相同问题?

悬赏问题

  • ¥15 求差集那个函数有问题,有无佬可以解决
  • ¥15 【提问】基于Invest的水源涵养
  • ¥20 微信网友居然可以通过vx号找到我绑的手机号
  • ¥15 寻一个支付宝扫码远程授权登录的软件助手app
  • ¥15 解riccati方程组
  • ¥15 display:none;样式在嵌套结构中的已设置了display样式的元素上不起作用?
  • ¥15 使用rabbitMQ 消息队列作为url源进行多线程爬取时,总有几个url没有处理的问题。
  • ¥15 Ubuntu在安装序列比对软件STAR时出现报错如何解决
  • ¥50 树莓派安卓APK系统签名
  • ¥65 汇编语言除法溢出问题