DFS can be used because the graph is directed and all of the edge weights are positive.
What is Algorithms?
An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms function as a detailed sequence of instructions that carry out predetermined operations sequentially. All aspects of IT employ algorithms extensively.
Steps can be taken. There may be a path from v to z* but not from z* to v or different from each with different weights, so we just need to apply DFS, dijkstras twice, starting with vertex v, to find the path length until z*. Then we need to add the path weights.
The problem is clear in that we need to find path weight from v to z* and z* to v. There may be more than one path that leads from v to z*, thus we must locate them all and store some of them because each loop will require a time complexity of O(V+E).
where, in the given graph, E stands for edges and V for vertex. When a graph is complete, meaning there is a path connecting every vertex to every other vertex, we must execute this technique V times to determine the total number of paths. As a result, the time complexity is O(V(V+E)).
Then we must repeat the process from z* to v, but this time we must choose every path whose weights satisfy the specified condition. In the worst case, we must repeat this process (V-1) times, thus the time complexity will be the same as before. As a result, our time complexity will be O(V(V+E)) overall.
Since the graph is directed and every edge weight is positive, DFS may be used.
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