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
Varun Kumar V: 2011-07-06 03:41:42

use long long ints for output

Jay Pandya: 2011-06-29 05:37:47

no problem in dealing with negative numbers... and i think test cases may be 500 in a file..

Noszály Csaba: 2011-06-25 10:48:08

:D said: "Both bounds are specified properly."
I don not think so, because according to the specification it is not clear if we have to use bignum or not (no lower bound is given for costs).

EDIT: oh my eyes! "The square of..."
:D has right. :)

Last edit: 2011-06-25 17:44:38
cegprakash: 2011-04-08 03:46:18

testcases are awesome!!
got AC after 20 WA :P

BaLraM MaUryA: 2011-03-31 17:42:24

finaly got acc...

Last edit: 2011-04-17 04:23:47
:D: 2011-03-31 17:42:24

"The square of each cost value is less than 1,000,000". Both bounds are specified properly.

Nikhil Garg: 2011-03-31 17:42:24

Its weird but there are negative numbers in input. Not that its a problem, just that lower bound of vertex costs is not specified.

.::Manish Kumar::.: 2011-03-31 17:42:24

what would be answer for
2
-1 -1 -1
-1 -1 -1

it is -3.

Last edit: 2010-12-19 13:37:34
ymGXX: 2011-03-31 17:42:24

Be careful that there is a space between k and n in the output.


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