TRAFFICN - Traffic Network

The city traffic network consists of n nodes numbered from 1 to n and m one-way roads connecting pairs of nodes. In order to reduce the length of the shortest path between two different critical nodes s and t, a list of k two-way roads are proposed as candidates to be constructed. Your task is to write a program to choose one two-way road from the proposed list in order to minimize the resulting shortest path between s and t.


The input file consists of several data sets. The first line of the input file contains the number of data sets which is a positive integer and is not bigger than 20. The following lines describe the data sets.

For each data set, the first line contains five positive integers n (n ≤ 10 000), m (m ≤ 100 000), k (k < 300), s (1 ≤ s ≤ n), t (1 ≤ t ≤ n) separated by space. The ith line of the following m lines contains three integers di, ci, li separated by space, representing the length li ( 0< li ≤ 1000) of the ith one-way road connecting node di to ci. The jth line of the next k lines contains three positive integers uj, vj and qj (qj ≤ 1000) separated by space, representing the jth proposed two-way road of length qj connecting node uj to vj.


For each data set, write on one line the smallest possible length of the shortest path after building the chosen one two-way road from the proposed list. In case, there does not exist a path from s to t, write -1.


Sample Input
4 5 3 1 4
1 2 13
2 3 19
3 1 25
3 4 17
4 1 18
1 3 23
2 3 5
2 4 25	

Sample Output

hide comments
ankur2409: 2019-03-28 15:52:55

Very nice problem.Only check out for -1 condition.Costed me many WA

piyushchavan88: 2019-03-26 19:22:22

Very amazing concept...and for c++ users don't use LONG_LONG_MAX as it will flow out of bound so I'd recommend use 10^12 or 10^13.

architkl: 2018-12-21 16:40:51

Most people are getting WA with INT_MAX because when you add one of those k roads to check for min path it causes an overflow.

mittalprateek: 2018-10-17 08:09:46

be careful you are adding an extra undirected (bidirected) edge to the graph ....use fast io...

junior97: 2018-08-21 15:04:41

copy the graph and connect the k roads between them, run dijk just once .

s_a_k_s_h_a_m: 2018-07-08 18:48:10

a good problem
you need to apply dijkstra two times - a single source dijkstra for 's' (d1) and a single sink dijkstra for 't' (d2)
now check d1[uj]+d2[vj]+qj,d1[vj]+d2[uj]+qj for minimum

be1035016: 2018-07-01 12:58:26

nice problem

Bác Ba Phì: 2018-06-30 05:57:33

2000 AC submissions, and only 5 of them are in Java. I think the time limit is way too strict for Java.

shahi9935: 2018-06-09 04:11:18

Thanku @ansh_gupta788 and @sherlock11 for your thoughts

sherlock11: 2018-04-13 18:48:37

the problem states that " use at most one road and not exactly one road"........this costed me 3 WA...
this is very nice problem on diJkstra...HAPPY CODING!!!!!!

Last edit: 2018-04-14 11:09:51

Added by:Duc
Time limit:0.140s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM Regional, Ho Chi Minh City 2008