dating app dansk Morsø - Define single source shortest path problem
This is done using relaxation by keeping track of a previous-vertex pointer p[v] for each vertex, so that the shortest path is found by following all the previous-vertex pointers and reversing the sequence.
We have already seen how to solve this problem in the case where all the edges have the the relaxation criteria gives equalities.
Additionally, the path to any reachable vertex can be found by starting at the vertex and following the π's back to the source.
(As a side effect, we might like to find the actual shortest path, but usually this can be done easily while we are computing the distances.) There are many algorithms for solving this problem, but most are based on the same technique, known as The reason for relaxing a problem is that we can start off with very high upper bounds and lower them incrementally until they settle on the correct answer.
For shortest paths this is done by setting d(s,t) initially to zero when t=s and +∞ when t≠s (this choice doesn't require looking at the graph).
MST solves the problem of finding a minimum total weight subset of edges that spans all the vertices.