# Write an algorithm for breadth first search and depth first search

This article will help any beginner to get some basic understanding about what graphs are, how they are represented, graph traversals using BFS and DFS. For each vertex u, define u. It then goes to the child on the right and finds the next left-most node in the tree to visit.

This should be an easy exercise for the reader. Note that 4 is in the stack twice this is okay, since we are maintaining a set of visited vertices. Start at a vertex. So, I decided to write an article for graph.

In addition, the content of this post will be very similar to our primer on treesso the familiar reader may benefit from reading that post as well. A more interesting question would be how they impact the cache and working set, but I think that will depend on the morphology of the tree.

While subsequently iterating over the adjacent Nodes we check to make sure the Node has not been visited before recursing.

At this point the state of the algorithm can be displayed like this: Better to offer ways to iterate through all neighbours and to fetch a specific neighbour. It would be better to implement an Iterator so that the caller can decide what to do with each node. Once the traversal is done, just discard the set.

Loop until the queue is empty. As an example, we can represent the edges for the above graph using the following adjacency matrix. Since Python passes these sets by reference, changes made to visitedNodes deep in the recursion persist after the recursive call ends.

What is a Graph? That is, the neighbors of more recently visited vertices vertex 2 have a preference in being processed over the remaining neighbors of earlier ones vertex 1.

Of course, in order to find paths with certain properties one must first be able to search through graphs in a structured way. A search-problem abstracts out the problem specific requirements from the actual search algorithm. We will often draw pictures of graphs instead of explicitly specifying their adjacency functions: When search is performed to a limited depth, the time is still linear in terms of the number of expanded vertices and edges although this number is not the same as the size of the entire graph because some vertices may be searched more than once and others not at all but the space complexity of this variant of DFS is only proportional to the depth limit, and as a result, is much smaller than the space needed for searching to the same depth using breadth-first search.

The vertex class is called Node, and it will contain as its data a value of arbitrary type and a list of neighboring vertices. Note that the word state is usually interchangeable with the word node or vertex.

Place the starting node s on the queue. Let us reexamine the example we used in the depth-first search to see this change in action. Second, this algorithm is not crystal clear on how the return values operate. Redundancy of information, i.

An example map of Germany with some connections between cities The breadth-first tree obtained when running BFS on the given map and starting in Frankfurt Time and space complexity[ edit ] The time complexity can be expressed as O.

Based upon the above steps, the following Java code shows the implementation of the BFS algorithm: The Basic Graph Data Structure We present the basic data structure in both mathematical terms and explicitly in Python. The updated code is straightforward: Depth-First Search For the remainder of this section, the goal is to determine if there is a vertex in the graph with the associated value being the integer 6.

Push the root first node to be visited onto S. Say that we have some data structure that has three operations:Graph traversal Algorithms Breadth first search in java Depth first search in java In DFS, You start with an un-visited node and start picking an adjacent node, until you have no choice, then you backtrack until you have another choice to pick a node, if not, you select another un-visited node.

Breadth First Vs Depth First. Ask Question. Breadth-First Search: The breadth-first search algorithm likes to stay as close as possible to the starting point.

I think it would be interesting to write both of them in a way that only by switching some lines of code would give you one algorithm or the other, so that you will see that your.

Breadth First Search is only every optimal if for instance you happen to be in a scenario where all actions have the same cost. Breadth First graph traversal algorithms also happen to be very computationally demanding in the way that they calculate the shortest path.

Take for instance if we have a binary tree of depth Depth First Search. Breadth First Traversal (or Search) Applications of Depth First Search; Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.