# Breadth First Search And Depth First Search Algorithm Pdf

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## A appraisal paper on Breadth-first search, Depth-first search and Red black tree

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 ".

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.

Namespaces Article Talk. Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version. Wikimedia Commons Wikibooks. Order in which the nodes are visited. Graph algorithms Search algorithms List of graph algorithms. Dynamic programming Graph traversal Tree traversal Search games. Wikimedia Commons has media related to Depth-first search.

## Breadth First Search (BFS) Algorithm 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.

Adrian Sampson shows how to develop depth-first search dfs and breadth-first search bfs. Both algorithms are used to traverse a graph, "visiting" each of its nodes in an orderly fashion. He assumes you are familiar with the idea. He also figures out the time complexity of these algorithms. Finally, he shows you how to implement a DFS walk of a graph. In this 2.

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.

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.

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.

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.

### Depth-first search

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Никому не позволено действовать в обход фильтров. - Ошибаешься, - возразила.  - Я только что говорила с Джаббой. Он сказал, что в прошлом году сам установил переключатель. Личный помощник директора отказывался верить ее словам.

Сначала она едва заметно вздрогнула, словно от озноба, и тут же ее захлестнула волна отчаяния. Приоткрыв дрожащие губы, она попыталась что-то сказать, но слов не последовало. Не спуская со Стратмора ледяного взгляда, Сьюзан сделала шаг вперед и протянула к нему руку с зажатым в ней предметом. Стратмор был почти уверен, что в руке Сьюзан сжимала беретту, нацеленную ему в живот, но пистолет лежал на полу, стиснутый в пальцах Хейла. Предмет, который она держала, был гораздо меньшего размера. Стратмор опустил глаза и тут же все понял.

- Это невозможно. Он перезагрузил монитор, надеясь, что все дело в каком-то мелком сбое. Но, ожив, монитор вновь показал то же. Чатрукьяну вдруг стало холодно. У сотрудников лаборатории систем безопасности была единственная обязанность - поддерживать ТРАНСТЕКСТ в чистоте, следить, чтобы в него не проникли вирусы.

Убедительно.  - Сьюзан нахмурилась.  - Итак, вы полагаете, что Северная Дакота - реальное лицо. - Боюсь, что. И мы должны его найти.

Фонтейн давно всем доказал, что близко к сердцу принимает интересы сотрудников. Если, помогая ему, нужно закрыть на что-то глаза, то так тому и. Увы, Мидж платили за то, чтобы она задавала вопросы, и Бринкерхофф опасался, что именно с этой целью она отправится прямо в шифровалку.

Далекий голос… - Дэвид. Он почувствовал болезненное жжение в боку. Мое тело мне больше не принадлежит. И все же он слышал чей-то голос, зовущий. Тихий, едва различимый.

Единственная спиральная лестница упиралась в каменную камеру квадратной формы, в стенах были проделаны узкие прорези для обозрения, но, разумеется, никакого выхода он не. Дэвид Беккер поднялся на последнюю крутую ступеньку и, едва держась на ногах, шагнул в крошечную каменную клетку. Со всех сторон его окружали высокие стены с узкими прорезями по всему периметру.

Сьюзан Флетчер, - ответил Бринкерхофф. Человек-гигант удивленно поднял брови. Даже перепачканная сажей и промокшая, Сьюзан Флетчер производила более сильное впечатление, чем он мог предположить.

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