
ZOJ Problem Set  1185
In order to build a ship to travel to Eindhoven, The Netherlands, various sheet metal parts have to be cut from rectangular pieces of sheet metal. Each part is a convex polygon with at most 8 vertices. Each rectangular piece of sheet metal has width n and height m, so that the four corners of the sheet can be specified by the Cartesian coordinates (0, 0), (0, m), (n, m) and (n, 0) in clockwise order. The cutting machine available can make only straightline cuts completely through the metal. That is, it cannot cut halfway through the sheet, turn, and then cut some more. You are asked to write a program to determine the minimum total length of cuts this machine has to make in order to cut out the polygon. The cuts must be along the edges of the poligon. For example, if n = m = 100, and the polygon has vertices (80, 80), (70, 30), (20, 20) and (20, 80), the following diagram shows the optimal cut (the thick lines). The numbers show the order in which the cuts are made. This problem contains multiple test cases! The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks. The output format consists of N output blocks. There is a blank line between output blocks.
1 100 100
Source: East Central North America 1998 