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Animated example of a breadth-first search. Black: explored, grey: queued to be explored later on BFS on Maze-solving algorithm Top part of Tic-tac-toe game tree. Breadth-first search (BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property.
A more sophisticated analysis of running time can be given via infinite ordinal numbers; for example, the breadth-first search of the depth 2 tree above will take ω·2 steps: ω for the first level, and then another ω for the second level.
The algorithm is called lexicographic breadth-first search because the order it produces is an ordering that could also have been produced by a breadth-first search, and because if the ordering is used to index the rows and columns of an adjacency matrix of a graph then the algorithm sorts the rows and columns into lexicographical order.
Dijkstra's algorithm starts with infinite distances and tries to improve them step by step: Create a set of all unvisited nodes: the unvisited set. Assign to every node a distance from start value: for the starting node, it is zero, and for all other nodes, it is infinity, since initially no path is known to these nodes.
Pseudocode is commonly used in textbooks and scientific publications related to computer science and numerical computation to describe algorithms in a way that is accessible to programmers regardless of their familiarity with specific programming languages.
The following example shows the first steps of Ford–Fulkerson in a flow network with 4 nodes, source and sink . This example shows the worst-case behaviour of the algorithm. In each step, only a flow of is sent across the network. If breadth-first-search were used instead, only two steps would be needed.
The breadth-first-search algorithm is a way to explore the vertices of a graph layer by layer. It is a basic algorithm in graph theory which can be used as a part of other graph algorithms. For instance, BFS is used by Dinic's algorithm to find maximum flow in a graph.
Some hobbyists have developed computer programs that will solve Sudoku puzzles using a backtracking algorithm, which is a type of brute force search. [3] Backtracking is a depth-first search (in contrast to a breadth-first search), because it will completely explore one branch to a possible solution before moving to another branch.