As a caveat, remember that there can be exponentially many shortest paths between two nodes in a graph. Any algorithm for this will potentially take exponential time. That said, there are a few relatively straightforward algorithms that can find all the paths. Here’s two. BFS + Reverse DFS When running a breadth-first search over a … Read more
(I’m assuming that this is just some kind of thought exercise, or even a trick homework/interview question, but I suppose I could imagine some bizarre scenario where you’re not allowed any heap space for some reason [some really bad custom memory manager? some bizarre runtime/OS issues?] while you still have access to the stack…) Breadth-first … Read more
To do so, you need to store a map:V->V (from vertices to vertices), which will map from each node v, the vertex u that “discovered” v. You will populate this map during the iterations of BFS. Later – you can reconstruct the path by simply going from the target node (in the map) up until … Read more
You should have look at http://en.wikipedia.org/wiki/Breadth-first_search first. Below is a quick implementation, in which I used a list of list to represent the queue of paths. # graph is in adjacent list representation graph = { ‘1’: [‘2’, ‘3’, ‘4’], ‘2’: [‘5’, ‘6’], ‘5’: [‘9′, ’10’], ‘4’: [‘7’, ‘8’], ‘7’: [’11’, ’12’] } def bfs(graph, … Read more
These two terms differentiate between two different ways of walking a tree. It is probably easiest just to exhibit the difference. Consider the tree: A / \ B C / / \ D E F A depth first traversal would visit the nodes in this order A, B, D, C, E, F Notice that you … Read more
Finding all possible paths is a hard problem, since there are exponential number of simple paths. Even finding the kth shortest path [or longest path] are NP-Hard. One possible solution to find all paths [or all paths up to a certain length] from s to t is BFS, without keeping a visited set, or for … Read more