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Breadth-first search (BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property. It starts at the tree root and explores all nodes at the present depth prior to moving on to the nodes at the next depth level.
By contrast, a breadth-first search will never reach the grandchildren, as it seeks to exhaust the children first. 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 ...
The recursive implementation will visit the nodes from the example graph in the following order: A, B, D, F, E, C, G. The non-recursive implementation will visit the nodes as: A, E, F, B, D, C, G. The non-recursive implementation is similar to breadth-first search but differs from it in two ways: it uses a stack instead of a queue, and
The basic idea of the algorithm is this: a depth-first search (DFS) begins from an arbitrary start node (and subsequent depth-first searches are conducted on any nodes that have not yet been found). As usual with depth-first search, the search visits every node of the graph exactly once, refusing to revisit any node that has already been visited.
A level-order walk effectively performs a breadth-first search over the entirety of a tree; nodes are traversed level by level, where the root node is visited first, followed by its direct child nodes and their siblings, followed by its grandchild nodes and their siblings, etc., until all nodes in the tree have been traversed.
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.
IDDFS achieves breadth-first search's completeness (when the branching factor is finite) using depth-first search's space-efficiency. If a solution exists, it will find a solution path with the fewest arcs. [2] Iterative deepening visits states multiple times, and it may seem wasteful.
We should either have only a pseudocode implementation, or maybe Python or some other reads-mostly-like-pseudocode language if it can be made sufficiently close to pseudocode. The fact that java.util.LinkedList is in the example suggests to me that the example says more about Java than about BFS. —Ben FrantzDale 12:53, 11 May 2010 (UTC)