ACPC10D - Tri graphs

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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.

a

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 top-middle vertex to the bottom-middle vertex.

Example

Input:
4
13 7 5
7 13 6
14 3 12
15 6 16
0

Output:
1. 22

hide comments
masterchef2209: 2018-10-11 23:29:50

simple dp with a small corner case

be1035016: 2018-06-19 12:39:46

define your own maxima if you are using it.dont rely on LONG_MAX in c++.

foool: 2018-06-17 00:54:12

top down AC....

ducky94tb: 2018-01-11 18:03:46

My careless, wasted too many time

Last edit: 2018-01-11 18:05:10
bani_raheja: 2018-01-02 20:14:10

easy af. Perfect example of "DP is nothing but brute force"

sdeven_0245: 2017-12-31 13:03:43

Easy one !!!!

dushyant7917: 2017-12-19 12:29:59

@karthik1997 why for testcase:
2
-1 -1 -1
-1 -1 -5
o/p: -3 shouldn't it be (-1-1=2)?

karthik1997: 2017-12-15 09:30:33

Note :
Negative nodes
output format : <testcase><dot><space><result><newline>
Try to use constant space . :P

jha_gaurav98: 2017-10-18 08:59:36

The cost of vertices can even be negative. Costed me 1 wa

gourav_123: 2017-10-17 23:47:30

after this solve http://www.spoj.com/problems/BYTESM2/


Added by:Omar ElAzazy
Date:2010-11-30
Time limit:0.262s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:ACPC 2010