depth-first-search

Why are the running times of BFS and DFS O(V+E), especially when there is a node that has a directed edge to a node that can be reached from the vertex, like in this example in the following site http://www.personal.kent.edu/~rmuhamma/Algorithms/MyAlgorithms/GraphAlgor/depthSearch.htm E is the set of all edges in the graph, as G={V,E}. So, |E| is count of all edges in the graph. This alone should be enough to convince you that the overall complexity can't be |V| times |E|, since we are not iterating over all the edges in the graph for each vertex. In the adjacency list representation, for each

Wikipedia about Depth First Search: Depth-first search (DFS) is an algorithm for traversing or searching a tree, tree structure, or graph. One starts at the root (selecting some node as the root in the graph case) and explores as far as possible along each branch before backtracking. So what is Breadth First Search? "an algorithm that choose a starting node, checks all nodes backtracks , chooses the shortest path, chose neighbour nodes backtracks , chose the shortest path, finally finds the optimal path because of traversing each path due to continuous backtracking. Regex find 's pruning --

I am bit confused after reading examples at DFS where output is printed in different fashion for both DFS approaches though both are said to be DFS. In fact DFS recursion approach print the output just in same fashion as BFS . Then what's the difference ? Is recursion approach given here not an example of DFS ? Using Stack // Iterative DFS using stack public void dfsUsingStack(Node node) { Stack<Node> stack=new Stack<Node>(); stack.add(node); node.visited=true; while (!stack.isEmpty()) { Node element=stack.pop(); System.out.print(element.data + " "); List<Node> neighbours=element.getNeighbours

I have a symmetrical graph and created a tree with all shortest path from a random vertex to any other vertex. Can I use the tree to construct a Minimum Spanning Tree(MST)? My algorithm is similar to depth-first algorithm. In the worst case, a shortest path tree does not help in finding a minimum spanning tree. Consider a graph where we want to find the MST. Add a source vertex with edges of an identical large length to each other vertex. The shortest path tree from that source consists of the very long edges, which we knew a priori, hence the shortest path tree is not useful in this case. 来源：

I was trying to use the code from this thread: Boost DFS back_edge , to record the cycles in an undirected graph. To do this I need to store the predecessors for each dfs tree when it finds a back_edge. Since this is an undirected graph I think we can not use directly on_back_edge() from EventVisitor Concept . So I was thinking to record the predecessors in the void back_edge() method of below code. But I am not sure how to do this and return the cycle vertices. Here is the code and the part I added for recording predecessors: #include <boost/config.hpp> #include <boost/graph/adjacency_list

I'm trying to solve the knight's tour problem using backtracking. I think the algorithm I have should work. I've tried but I can't figure out why it isn't working. It results in an infinite loop. However if I comment out the line that back track solutionBoard[dst.x][dst.y]=-1; it works! I just don't understand why! Any help would be appreciated. private int solutionBoard[][] = new int [8][8]; // The eight possible moves a knight can make from any given position private static final Point[] MOVES = new Point[] { new Point(-2, -1), new Point(-2, 1), new Point(2, -1), new Point(2, 1), new Point(

I have a nice graph (a list) containing 81 vertices (each vertex is an instance of a Vertex class). Each vertex has 20 neighbors. Each vertex has a number of possible values (ranging from 1 to 9) which, given some initial constraints to the problem will be on average 4 or 5. I implemented a simple DFS on this graph, that takes the node with less possible values, foreach value builds another "deepcopied" graph having only one of the possible value, and finally passes the "deepcopied" graph again into the DFS recursively. The issue is about speed; cProfiling my code I found out that 635 of the