TRAFFICN  Traffic Network
English  Vietnamese 
The city traffic network consists of n nodes numbered from 1 to n and m oneway 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 twoway roads are proposed as candidates to be constructed. Your task is to write a program to choose one twoway road from the proposed list in order to minimize the resulting shortest path between s and t.
Input
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 oneway 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 twoway road of length qj connecting node uj to vj.
Output
For each data set, write on one line the smallest possible length of the shortest path after building the chosen one twoway road from the proposed list. In case, there does not exist a path from s to t, write 1.
Example
Sample Input 1 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 35
hide comments
peeyush taneja:
20150726 22:01:44
Finally AC 

Dhruv Mullick:
20150529 16:40:52
The question should rather read "write a program to choose at most one twoway road". 

KESHAV BANSAL:
20150131 07:58:17
tle while using scanf


AlcatraZ:
20150122 20:42:18
For my algo, INT_MAX is working fine ..But if you are adding anything to INT_MAX you will get an integer overflow.. Last edit: 20150125 22:14:55 

Pranav Vaish:
20141210 23:54:03
Very tight time constraints. Had to optimize a lot!. Please increase the time to 2 seconds at least. 

ABHISHEK004:
20141024 18:47:33
@Archit Jain


___Durgesh___:
20140924 12:29:01
whts wrong wid cin & cout getting tle &


N0VICE:
20140812 19:52:59
finally accepted after tonnes of WAs


Dario Sindicic:
20140802 15:16:15
200th learn new dijkstra 

Archit Jain:
20140721 22:38:43
assign INF as 1061109567 then AC

Added by:  Duc 
Date:  20090104 
Time limit:  0.140s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  ACM Regional, Ho Chi Minh City 2008 