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
ashish jaiswal:
20150830 22:04:50
piece of cake 

/* EDWARD KENWAY */:
20150825 09:26:10
simple DP but don't forget to consider negative values. 

kimo:
20150820 07:55:44
There is negative input, beware of it!! 

Diksha Jaiswal:
20150720 12:55:18
1 WA cos of wrong output format :D 

Sulabh Kumar:
20150708 09:03:36
Dp works but bellman ford gives TLE. 

SangKuan:
20150621 11:09:13
thanks @Haijun Deng 

TP:
20150527 13:06:36
Got it!!! Last edit: 20150529 11:06:07 

scyth3r:
20150510 01:48:38
2 WA...replaced i by j once :<:( 

Abhilash:
20150418 15:53:15
Do bottom up. topdown might get RTE 

vikikrishna:
20150401 00:57:56
Nyc DP

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 