# Breadth First Search And Depth First Search Algorithm Pdf

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- Breadth-First Search Algorithm [BFS] with Example
- Breadth First Search (BFS) Algorithm with EXAMPLE
- Breadth first search
- Depth-first search

## Breadth-First Search Algorithm [BFS] with Example

Depth-first search DFS is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node selecting some arbitrary node as the root node in the case of a graph and explores as far as possible along each branch before backtracking. The time and space analysis of DFS differs according to its application area. Thus, in this setting, the time and space bounds are the same as for breadth-first search and the choice of which of these two algorithms to use depends less on their complexity and more on the different properties of the vertex orderings the two algorithms produce.

For applications of DFS in relation to specific domains, such as searching for solutions in artificial intelligence or web-crawling, the graph to be traversed is often either too large to visit in its entirety or infinite DFS may suffer from non-termination. In such cases, search is only performed to a limited depth ; due to limited resources, such as memory or disk space, one typically does not use data structures to keep track of the set of all previously visited vertices.

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.

For such applications, DFS also lends itself much better to heuristic methods for choosing a likely-looking branch. When an appropriate depth limit is not known a priori, iterative deepening depth-first search applies DFS repeatedly with a sequence of increasing limits. In the artificial intelligence mode of analysis, with a branching factor greater than one, iterative deepening increases the running time by only a constant factor over the case in which the correct depth limit is known due to the geometric growth of the number of nodes per level.

DFS may also be used to collect a sample of graph nodes. Iterative deepening is one technique to avoid this infinite loop and would reach all nodes.

A convenient description of a depth-first search of a graph is in terms of a spanning tree of the vertices reached during the search. Based on this spanning tree, the edges of the original graph can be divided into three classes: forward edges , which point from a node of the tree to one of its descendants, back edges , which point from a node to one of its ancestors, and cross edges , which do neither.

Sometimes tree edges , edges which belong to the spanning tree itself, are classified separately from forward edges. If the original graph is undirected then all of its edges are tree edges or back edges. An enumeration of the vertices of a graph is said to be a DFS ordering if it is the possible output of the application of DFS to this graph.

It is also possible to use depth-first search to linearly order the vertices of a graph or tree. There are four possible ways of doing this:. Note that repeat visits in the form of backtracking to a node, to check if it has still unvisited neighbors, are included here even if it is found to have none.

Reverse postordering produces a topological sorting of any directed acyclic graph. This ordering is also useful in control flow analysis as it often represents a natural linearization of the control flows. A recursive implementation of DFS: [5].

The order in which the vertices are discovered by this algorithm is called the lexicographic order. These two variations of DFS visit the neighbors of each vertex in the opposite order from each other: the first neighbor of v visited by the recursive variation is the first one in the list of adjacent edges, while in the iterative variation the first visited neighbor is the last one in the list of adjacent edges.

The non-recursive implementation is similar to breadth-first search but differs from it in two ways:. If G is a tree , replacing the queue of the breadth-first search algorithm with a stack will yield a depth-first search algorithm.

For general graphs, replacing the stack of the iterative depth-first search implementation with a queue would also produce a breadth-first search algorithm, although a somewhat nonstandard one. Another possible implementation of iterative depth-first search uses a stack of iterators of the list of neighbors of a node, instead of a stack of nodes.

This yields the same traversal as recursive DFS. This ordering is called the lexicographic depth-first search ordering. John Reif considered the complexity of computing the lexicographic depth-first search ordering, given a graph and a source. A decision version of the problem testing whether some vertex u occurs before some vertex v in this order is P -complete , [11] meaning that it is "a nightmare for parallel processing ".

A depth-first search ordering not necessarily the lexicographic one , can be computed by a randomized parallel algorithm in the complexity class RNC. From Wikipedia, the free encyclopedia. Search algorithm. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources.

Unsourced material may be challenged and removed. Play media. Leiserson, and Ronald L. Retrieved Algorithms in Java. Information Processing Letters. Thomas H. Cormen , Charles E. Leiserson , Ronald L. Rivest , and Clifford Stein. Introduction to Algorithms , Second Edition. Section Goodrich, Michael T. Data structures and algorithms. Categories : Graph algorithms Search algorithms. Hidden categories: Articles with short description Short description matches Wikidata Articles needing additional references from July All articles needing additional references All articles with unsourced statements Articles with unsourced statements from June Commons category link is on Wikidata Articles with example pseudocode Articles containing video clips.

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## Breadth First Search (BFS) Algorithm with EXAMPLE

In this tutorial, you will learn about breadth first search algorithm. Traversal means visiting all the nodes of a graph. Breadth First Traversal or Breadth First Search is a recursive algorithm for searching all the vertices of a graph or tree data structure. The graph might have two different disconnected parts so to make sure that we cover every vertex, we can also run the BFS algorithm on every node. Let's see how the Breadth First Search algorithm works with an example. We use an undirected graph with 5 vertices. We start from vertex 0, the BFS algorithm starts by putting it in the Visited list and putting all its adjacent vertices in the stack.

Artificial Intelligence is the study of building agents that act rationally. Most of the time, these agents perform some kind of search algorithm in the background in order to achieve their tasks. There are far too many powerful search algorithms out there to fit in a single article. Instead, this article will discuss six of the fundamental search algorithms, divided into two categories, as shown below. Note that there is much more to search algorithms that the chart I have provided above. However, this article will mostly stick to the above chart, exploring the algorithms given there. The search algorithms in this section have no additional information on the goal node other than the one provided in the problem definition.

Graph nodes are labelled from 1 to n, and m edges connect pairs of nodes. These edges can either be unidirectional or bidirectional. Graph algorithms have formulated and solved a lot of problems such as shortest path, network flow problems, graph colouring problems, and much more. Some particular popular types of graphs are:. The graph is traversed using two popular traversal algorithms Depth-first search and the Breadth-first search algorithm.

Depth-First and Breadth-First. Search. CS Program Design Paradigms which we search doesn't matter we have to search algorithm finds the nodes.

## Breadth first search

After a DFS traversal of any graph G, all its edges can be put in one of the following 4 classes-. Watch this Video Lecture. Next Article- Breadth First Search. Get more notes and other study material of Design and Analysis of Algorithms. It is used for traversing or searching a graph in a systematic fashion.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs and how to get involved. Subjects: Data Structures and Algorithms cs. DS Cite as: arXiv

### Depth-first search

To browse Academia. Skip to main content. By using our site, you agree to our collection of information through the use of cookies. To learn more, view our Privacy Policy. Log In Sign Up. Download Free PDF. A appraisal paper on Breadth-first search, Depth-first search and Red black tree.

Breadth-first search BFS is an algorithm that is used to graph data or searching tree or traversing structures. The full form of BFS is the Breadth-first search. The algorithm efficiently visits and marks all the key nodes in a graph in an accurate breadthwise fashion. This algorithm selects a single node initial or source point in a graph and then visits all the nodes adjacent to the selected node. Remember, BFS accesses these nodes one by one. Once the algorithm visits and marks the starting node, then it moves towards the nearest unvisited nodes and analyses them.

Depth-first search DFS is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node selecting some arbitrary node as the root node in the case of a graph and explores as far as possible along each branch before backtracking. The time and space analysis of DFS differs according to its application area. Thus, in this setting, the time and space bounds are the same as for breadth-first search and the choice of which of these two algorithms to use depends less on their complexity and more on the different properties of the vertex orderings the two algorithms produce. For applications of DFS in relation to specific domains, such as searching for solutions in artificial intelligence or web-crawling, the graph to be traversed is often either too large to visit in its entirety or infinite DFS may suffer from non-termination. In such cases, search is only performed to a limited depth ; due to limited resources, such as memory or disk space, one typically does not use data structures to keep track of the set of all previously visited vertices. 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.

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PDF | The depth-first search is an organized graph traversal that recursively SEARCH The breadth-first search is a graph traversal algorithm.

Adrian Sampson shows how to develop depth-first search dfs and breadth-first search bfs.

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