given a network with n stations. assuming the shortest between s,t was found using dijkstra's algorithm. let that path be denoted as $(a_1,a_2,...,a_k)$
assume that between the nodes s and t, there's an at least additional path with the same weight, but with different edges(meaning both paths have different edges, nothing in common). how can we find that additional path?
My attempt: let's create an array that holds the parent. that array will be separate, so the value of $parent[v_i]$ for some vertex $v_i \in V$ stores the parent of $v_i$ in the array, in the shortest path tree that is formed by the algorithm. now, we'll initiate the first element, meaning the parent of the root to be -1, and if we find shorter path through some vertex u, we can make u the parent of the current vertex. but i am not sure it solves the problem unfortunately.
would really appreciate if you could explain what you do so i can understand it.
tried to do a research on the site, but couldn't find a similar problem with no same edges and i don't know how to solve it, so i am asking for help here
thank you very much