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
s_tank00_: 2020-07-31 13:05:03

my 100th submission

horro: 2020-07-22 23:47:37

Can be done using DP on TREE (hint : maximum sum of node problem )

robosapien: 2020-07-09 00:45:06

Lesson learnt. Think simple.

mokipooji: 2020-06-27 08:48:32

can someone tell some corner cases also working for negative numbers checked with
3
-1 -1 -1
-1 -2 -1
-1 -1 -1
-6
2
-1 -1 -1
-1 -2 -1
-4

deerawat: 2020-06-24 13:32:41

changing long long int to double resulted in AC.
Don't know why??
any answers!!

mayank_4321: 2020-05-10 16:24:50

showing WA in java

Last edit: 2020-05-10 16:29:21
mrdevesh_00: 2020-04-27 11:36:07

AC in one go!!!!!

aryan__0406: 2020-04-24 12:51:36

This is a simple problem. Just think a little bit and try to analyze top to bottom.

mrmajumder: 2020-04-17 09:19:25

Check the line "The square of each cost value is less than 1,000,000", which clearly hints for negative numbers

shikhar_may7: 2020-02-17 20:03:49

CAUTION: -ve nodes ahead!

Last edit: 2020-02-17 20:04:06

Added by:Omar ElAzazy
Date:2010-11-30
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:ACPC 2010