Depth first search and breadth first searching
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1. Depth first search is an algorithm for traversing tree and graph data structures where one starts at the root node and explores as deep as possible along each branch before backtracking. 2. It can be implemented using a stack and explores edges out of the most recently discovered vertex before backtracking to explore other paths. 3. Breadth first search begins at a root node and inspects all neighboring nodes before exploring nodes further away, implementing it using a queue.
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The document discusses depth first search (DFS), an algorithm for traversing or searching trees or graphs. It begins with an introduction to DFS, explaining that it explores edges out of the most recently discovered vertex as deep as possible before backtracking. It then provides pseudocode for the DFS algorithm and explains that it has a time complexity of O(V+E), where V is the number of vertices and E is the number of edges. Finally, it lists some applications of DFS such as cycle detection, solving mazes, and analyzing networks.
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This document discusses different search algorithms for traversing tree structures:
- Depth-first search (DFS) explores the deepest paths first, using a stack data structure. It is complete but not optimal.
- Breadth-first search (BFS) explores all nodes at each depth level first, before deeper levels, using a queue. It finds the minimum depth goal node.
- Uniform cost search prioritizes exploring the lowest cost path first, using a priority queue ordered by path cost. It is optimal, finding the least cost goal node.
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Two main types of search methods are uninformed and informed searches. Uninformed searches like breadth-first, depth-first, and uniform-cost searches use only the problem definition, while informed searches like A* use a heuristic function to estimate solution costs. Breadth-first search expands the shallowest nodes first, while depth-first search expands the deepest nodes first. Both are complete for finite search spaces but breadth-first uses more memory and depth-first may explore inefficient paths first.
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Abstract: This PDSG workship introduces basic concepts on Tree and Graph Theory. It covers topics for level-first search (BFS), inorder, preorder and postorder depth first search (DFS), depth limited search (DLS), iterative depth search (IDS), as well as tri-coding to prevent revisiting nodes in a cyclic paths in a graph. Examples are given pictorially, pseudo code and in Python.
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This document discusses graph representation and traversal techniques. It begins by defining graph terminology like vertices, edges, adjacency, and paths. It then covers different ways to represent graphs, including adjacency lists and matrices. It describes the pros and cons of each representation. The document also explains depth-first search and breadth-first search traversal algorithms in detail, including pseudocode. It analyzes the time complexity of these algorithms. Finally, it briefly discusses other graph topics like strongly connected components and biconnected components.
Final slide4 (bsc csit) chapter 4
The document describes various search algorithms used to solve pathfinding problems represented as graphs. It discusses uninformed searches like breadth-first search (BFS) and depth-first search (DFS) as well as methods for evaluating search performance in terms of completeness, time complexity, space complexity, and optimality. BFS uses a queue to expand shallow nodes first, guaranteeing an optimal solution but with exponential time and space costs. DFS uses a stack to expand deep nodes first, providing better space efficiency but not guaranteeing an optimal solution.
Algorithm presentation (1)
The document presents an overview of depth-first search (DFS) algorithms and applications. It discusses DFS traversal of trees and graphs, cycle detection in directed and undirected graphs, strongly connected components, and topological sorting. Examples are provided for tree traversals, cycle finding, and Kosaraju's algorithm for strongly connected components. Complexities of O(V+E) are noted for cycle detection and topological sorting. Key concepts and algorithms for graph search and analysis using DFS are summarized.
Data structure
Breadth First Search (BFS) and Depth First Search (DFS) are two graph traversal algorithms. BFS uses a queue to visit all neighbor nodes at the present depth prior to moving to the next depth level, while DFS uses a stack to explore as far as possible along each branch before backtracking. The document provides pseudocode for BFS and DFS algorithms and explains their process through examples of traversing graphs from a starting node.
searching technique
This document discusses and compares different search algorithms:
1) Depth-first search explores paths in a depth-first manner, pursuing each path to completion before backtracking. It is appropriate when space is limited or many solutions exist with long paths.
2) Breadth-first search explores paths by number of arcs, prioritizing shorter paths. It is useful when space is not limited or few short solutions exist.
3) Depth-limited search limits depth-first search's depth to avoid infinite paths, but may miss deep goals. Its time complexity is linear in branch factor and limit, space linear in branch factor and limit for the iterative version.
kumattt).pptx
This document provides an overview of depth-first search (DFS) and breadth-first search (BFS) algorithms. It introduces the presenter, Kumar Ayush Singh Deo, and their subject on analyzing and digitizing algorithms. Key topics covered include definitions of graphs, how DFS and BFS work by exploring adjacent vertices, analysis of time complexity when using adjacency lists or matrices, examples of DFS on directed and undirected graphs illustrated with pseudocode, and applications of DFS and BFS.
RPT_AI_03_PartB_UNINFORMED_FINAL.pptx
Iterative deepening search is an uninformed search strategy that combines the benefits of depth-first and breadth-first search. It gradually increases the depth limit in iterations, starting from 0, until a goal is found. This occurs when the depth limit reaches the depth of the shallowest goal node. Iterative deepening search is optimal, complete, and has reasonable time and space complexities. It is suitable for problems with large search spaces where the solution depth is unknown.
Bfs and dfs
The document discusses Breadth First Search (BFS) and Depth First Search (DFS) graph traversal algorithms. BFS uses a queue data structure and explores neighbor nodes level-wise, starting from a source node. Its time and space complexity is O(V+E) and O(V) respectively. DFS uses a stack and explores nodes by going deeper first until reaching a dead end, then backtracks. Its complexity is O(V+E) for adjacency lists and O(V^2) for adjacency matrices. Both algorithms are used for path finding, cycle detection and other graph applications.
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Depth first search and breadth first searching
- 1. CSE-134 Submitted by Mohammad Kawsar Hamid Submitted to Kawser Wajed Nafi ID:131-15-2223 Daffodil International University
- 2. 1.Depth first search was first investigated by French Mathematician Charles Pierre tremaux. 2.It is an algorithm for traversing tree or graph data structures. 3.One starts at the root and explores as deep as possible along each branch before backtracking. 4.It can be implemented using stack.
- 3. Depth-first searching A depth-first search (DFS) explores a path all the way to a leaf before backtracking and exploring another path. For example, after searching A, then B, then D, the search backtracks and tries another path from B. Node are explored in the order A B D E H L M N I O P C F G J K Q. N will be found before J.L M N O P G Q H JI K FED B C A
- 4. 1.In Depth first search edges are explored out of the most recently dis-covered vertex. Only edges to unexplored vertices are explored. 2.When all of vertices edges have been explored, the search “back-tracks” to explore edges leaving the vertex from which vertex was discovered. 3.The process continues until we have discovered all the vertices that are reachable from the original source vertex. 4.If any undiscovered vertices remain, then one of them is selected as a new source vertex. 5.This process if repeated until all vertices are discovered. Idea of The Depth First Search Algorithm
- 5. 1.The Breadth first search begins at a root node and inspects all the neighboring nodes. 2.Then for each of those neighbor nodes in turn, it inspects their neighbor nodes which were unvisited, and so on. 3.It can be implemented using queue.
- 6. Breadth First Searching A breadth-first search (BFS) explores nodes nearest the root before exploring nodes further away. For example, after searching A, then B, then C, the search proceeds with D, E, F, G. Node are explored in the order A B C D E F G H I J K L M N O P Q. J will be found before N. L M N O P G Q H JI K FED B C A
- 7. Enqueue the root node Dequeue a node and examine it If the element sought is found in this node, quit the search and return a result. Otherwise enqueue any successors (the direct child nodes) that have not yet been discovered. If the queue is empty, every node on the graph has been examined – quit the search and return "not found". If the queue is not empty, repeat from Step 2. Idea of Breadth First Search