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For example, given a binary tree of infinite depth, a depth-first search will go down one side (by convention the left side) of the tree, never visiting the rest, and indeed an in-order or post-order traversal will never visit any nodes, as it has not reached a leaf (and in fact never will). By contrast, a breadth-first (level-order) traversal ...
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.
This is a retouched picture, which means that it has been digitally altered from its original version.Modifications: added dotted-line arrow showing order of breadth-first traversal.
Binary trees can also be stored in breadth-first order as an implicit data structure in arrays, and if the tree is a complete binary tree, this method wastes no space.
Notably, given an infinite tree, [d] the corecursive breadth-first traversal will traverse all nodes, just as for a finite tree, while the recursive depth-first traversal will go down one branch and not traverse all nodes, and indeed if traversing post-order, as in this example (or in-order), it will visit no nodes at all, because it never ...
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.
Every tree with only countably many vertices is a planar graph. Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G. More specific types spanning trees, existing in every connected finite graph, include depth-first search trees and breadth-first search trees.