I’m looking for an algorithm to find an Euler path in a graph. I’ve seen a good one a couple of weeks ago but I can’t find it now, I remember there was tagging edges, something with even/odd connections… Do you know a similar, simple and straightforward algorithm?
The Wikipedia Example Looks like the diameter is 3 to me by definition. The longest shortest paths have length of 3 edges, e.g. between 6-1 and 6-2. The Mesh Example Here’s your second definition, with some typographical correction so that it makes sense: Diameter D of a network is defined as the longest path of the shortest paths between any … Read more
Use Prim’s algorithm when you have a graph with lots of edges. For a graph with V vertices E edges, Kruskal’s algorithm runs in O(E log V) time and Prim’s algorithm can run in O(E + V log V) amortized time, if you use a Fibonacci Heap. Prim’s algorithm is significantly faster in the limit when you’ve got a really dense graph with many … Read more
If the input matrix is guaranteed to describe transitive connectivity, it has a peculiar form that allows for an algorithm probing only a subset of the matrix elements. Here is an example implementation in Python: An optimized version of the same algorithm (less readable, but faster and more easily translatable into other languages) is the following:
Your sum can be rewritten as and the first group is O(N) while the other is O(E).
That heavily depends on the structure of the search tree and the number and location of solutions (aka searched-for items). If you know a solution is not far from the root of the tree, a breadth first search (BFS) might be better. If the tree is very deep and solutions are rare, depth first search … Read more