SP7975 ACPC10D - Tri graphs

Here’s a simple graph problem: Find the shortest path from the top-middle vertex to the bottom-middle vertex in a given tri-graph. A tri-graph is an acyclic graph of (N >= 2) rows and exactly 3 columns. Unlike regular graphs, the costs in a tri-graph are associated with the vertices rather than the edges.  So, considering the example with N = 4, the cost of going straight down from the top to bottom along the middle vertices is 7 + 13 + 3 + 6 = 29. The layout of the directional edges in the graph are always the same as illustrated in the figure.

Your program will be tested on one or more test cases. Each test case is specified using N + 1 lines where the first line specifies a single integer (2 The last case is followed by a line with a single zero.

For each test case, print the following line: k. n Where k is the test case number (starting at one,) and n is the least cost to go from the top-middle vertex to the bottom-middle vertex.