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.


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.


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.


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.


13 7 5
7 13 6
14 3 12
15 6 16

1. 22

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

CAUTION: -ve nodes ahead!

Last edit: 2020-02-17 20:04:06
ak8325: 2020-01-01 23:16:21

If you are getting WA.. ask yourself
1. Are you considering examples with negative weight ?
2. Should topmost left node be considered while calculating any path? ans is NO because path must start from top middle and there is no path from top middle to top left.

akash619j: 2019-08-17 21:11:37

Can cost be negative? I think its not clearly mentioned in the problem statement...

anand_undavia: 2019-06-23 09:31:56

Java: br.readLine().split("\\s+"); Gave me TLE :P
br.readLine().split(" ") => AC

cenation007: 2019-06-20 09:00:37

easy peasy lemon squeezy
AC in one go :)

aryan29: 2019-06-08 15:22:43

DP is amazing my 2nd DP problem AC in 1 go but overcomplicate it

sahilsinghss: 2019-03-26 10:49:33

Wohoo 100 done

bloodgreed99: 2019-01-27 15:03:15

DP introductory question

gaurav1614: 2018-12-26 21:34:06

very easy problem.think in terms of reachable and unreachable nodes.

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

simple dp with a small corner case

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