SAMER08A  Almost Shortest Path
Finding the shortest path that goes from a starting point to a destination point given a set of points and route lengths connecting them is an already well known problem, and it's even part of our daily lives, as shortest path programs are widely available nowadays.
Most people usually like very much these applications as they make their lives easier. Well, maybe not that much easier.
Now that almost everyone can have access to GPS navigation devices able to calculate shortest paths, most routes that form the shortest path are getting slower because of heavy traffic. As most people try to follow the same path, it's not worth it anymore to follow these directions.
With this in his mind, your boss asks you to develop a new application that only he will have access to, thus saving him time whenever he has a meeting or any urgent event. He asks you that the program must answer not the shortest path, but the almost shortest path. He defines the almost shortest path as the shortest path that goes from a starting point to a destination point such that no route between two consecutive points belongs to any shortest path from the starting point to the destination.
For example, suppose the figure below represents the map given, with circles representing location points, and lines representing direct, oneway routes with lengths indicated. The starting point is marked as S and the destination point is marked as D. The bold lines belong to a shortest path (in this case there are two shortest paths, each with total length 4). Thus, the almost shortest path would be the one indicated by dashed lines (total length 5), as no route between two consecutive points belongs to any shortest path. Notice that there could exist more than one possible answer, for instance if the route with length 3 had length 1. There could exist no possible answer as well.
Input
The input contains several test cases. The first line of a test case contains two integers N (2 ≤ N ≤ 500) and M (1 ≤ M ≤ 10^{4}), separated by a single space, indicating respectively the number of points in the map and the number of existing oneway routes connecting two points directly. Each point is identified by an integer between 0 and N 1. The second line contains two integers S and D, separated by a single space, indicating respectively the starting and the destination points (S ≠ D; 0 ≤ S, D < N).
Each one of the following M lines contains three integers U, V and P (U ≠ V; 0 ≤ U, V < N; 1 ≤ P ≤ 10^{3}), separated by single spaces, indicating the existence of a oneway route from U to V with distance P. There is at most one route from a given point U to a given point V, but notice that the existence of a route from U to V does not imply there is a route from V to U, and, if such road exists, it can have a different length. The end of input is indicated by a line containing only two zeros separated by a single space.
Output
For each test case in the input, your program must print a single line, containing 1 if it is not possible to match the requirements, or an integer representing the length of the almost shortest path found.
Example
Input: 7 9 0 6 0 1 1 0 2 1 0 3 2 0 4 3 1 5 2 2 6 4 3 6 2 4 6 4 5 6 1 4 6 0 2 0 1 1 1 2 1 1 3 1 3 2 1 2 0 3 3 0 2 6 8 0 1 0 1 1 0 2 2 0 3 3 2 5 3 3 4 2 4 1 1 5 1 1 3 0 1 0 0 Output: 5 1 6
hide comments
vicky_1998:
20171203 11:44:26
Wasted hours because of one line misplaces!!!!really frustrating


sam128:
20170814 12:28:25
AC in one go..Best problem so far on dkshtra....Try using maps to store the nodes and then delete it,,,if u are unable to delete it from vector 

dop1943:
20170721 12:32:59
best classical disjkstra's problem Last edit: 20170721 12:33:17 

code_aim:
20170609 17:11:46
One of the best questions of dijkstra's. 

himmi97:
20170524 17:24:45
@baqir00 you should use greater in priority_queue..I did the same mistake.


Siddharth:
20170423 20:14:28
Please don't use spojtoolkit for this because some tests are wrong. Btw very nice problem. Last edit: 20170423 20:14:58 

gboduljak:
20170408 12:36:40
fastio required 

flyingduchman_:
20170102 17:23:35
Find and store all shortest paths by running Dijkstra’s algorithm only once.


kr_abhinav:
20161222 18:34:56
Excellent problem!


levim:
20161003 19:14:33
Nice problem! 
Added by:  Diego Satoba 
Date:  20081123 
Time limit:  0.199s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  C CPP JAVA PASGPC PASFPC 
Resource:  South American Regional Contests 2008 