Weighted shortest path (3) P25235


Statement
 

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Write a program that, given a directed graph with positive costs at the arcs, and two vertices x and y, computes the minimum cost to go from x to y, and the minimum number of steps of all the paths that go from x to y with such minimum cost.

Input

Input consists of several cases. Every case begins with the number of vertices n and the number of arcs m. Follow m triples u, v, c, indicating that there is an arc u → v of cost c, where u ≠ v and 1 ≤ c ≤ 104. Finally, we have x and y. Assume 1 ≤ n ≤ 104, 0 ≤ m ≤ 5n, and that for every pair of vertices u and v there is at most one arc of the kind u → v. All numbers are integers. Vertices are numbered from 0 to n−1.

The condition for c was previously c ≤ 1000. It was updated to create new test cases.

Output

For every case, print the minimum cost to go from x to y, and the minimum number of steps to achieve this cost. If there is no path from x to y, state so.

Public test cases

  • Input

    6 10
1 0 6
1 5 15
3 4 3
3 1 8
4 0 20
0 5 5
0 2 1
5 1 10
4 1 2
2 3 4
3 5

2 1
0 1 1000
1 0

3 3
0 2 100
0 1 40
1 2 60
0 2

    Output

    cost 16, 4 step(s)
no path from 1 to 0
cost 100, 1 step(s)
    • Information
    Author
    Salvador Roura
    Language
    English
    Official solutions
    C++ Python
    User solutions
    C++ Python