ACPC10D  Tri graphs
Here’s a simple graph problem: Find the shortest path from the topmiddle vertex to the bottommiddle vertex in a given trigraph. A trigraph is an acyclic graph of (N ≥ 2) rows and exactly 3 columns. Unlike regular graphs, the costs in a trigraph 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.
Input
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 ≤ N ≤ 100, 000) denoting the number of rows in the graph. N lines follow, each specifying three integers representing the cost of the vertices on the ith row from left to right. The square of each cost value is less than 1,000,000.
The last case is followed by a line with a single zero.
Output
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 topmiddle vertex to the bottommiddle vertex.
Example
Input:
4
13 7 5
7 13 6
14 3 12
15 6 16
0
Output:
1. 22
hide comments
Rafail Loizou:
20210205 20:52:38
Negative vertices... "The square of each cost value is less than 1,000,000."


s_tank00_:
20200731 13:05:03
my 100th submission 

horro:
20200722 23:47:37
Can be done using DP on TREE (hint : maximum sum of node problem ) 

robosapien:
20200709 00:45:06
Lesson learnt. Think simple. 

mokipooji:
20200627 08:48:32
can someone tell some corner cases also working for negative numbers checked with


deerawat:
20200624 13:32:41
changing long long int to double resulted in AC.


mayank_4321:
20200510 16:24:50
showing WA in java Last edit: 20200510 16:29:21 

mrdevesh_00:
20200427 11:36:07
AC in one go!!!!! 

aryan__0406:
20200424 12:51:36
This is a simple problem. Just think a little bit and try to analyze top to bottom. 

mrmajumder:
20200417 09:19:25
Check the line "The square of each cost value is less than 1,000,000", which clearly hints for negative numbers 
Added by:  Omar ElAzazy 
Date:  20101130 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  ACPC 2010 