BFS ONE

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. Extra memory, usually a queue, is needed to keep track of the child nodes that were encountered but not yet explored. For example, in a chess endgame, a chess engine may build the game tree from the current position by applying all possible moves and use breadth-first search to find a win position for White. Implicit trees (such as game trees or other problem-solving trees) may be of infinite size; breadth-first search is guaranteed to find a solution node[1] if one exists. In contrast, (plain) depth-first search (DFS), which explores the node branch as far as possible before backtracking and expanding other nodes,[2] may get lost in an infinite branch and never make it to the solution node. Iterative deepening depth-first search avoids the latter drawback at the price of exploring the tree's top parts over and over again. On the other hand, both depth-first algorithms typically require far less extra memory than breadth-first search.[3] Breadth-first search can be generalized to both undirected graphs and directed graphs with a given start node (sometimes referred to as a 'search key').[4] In state space search in artificial intelligence, repeated searches of vertices are often allowed, while in theoretical analysis of algorithms based on breadth-first search, precautions are typically taken to prevent repetitions. BFS and its application in finding connected components of graphs were invented in 1945 by Konrad Zuse, in his (rejected) Ph.D. thesis on the Plankalkül programming language, but this was not published until 1972.[5] It was reinvented in 1959 by Edward F. Moore, who used it to find the shortest path out of a maze,[6][7] and later developed by C. Y. Lee into a wire routing algorithm (published in 1961).[8] Pseudocode Input: A graph G and a starting vertex root of G Output: Goal state. The parent links trace the shortest path back to root[9] 1 procedure BFS(G, root) is 2 let Q be a queue 3 label root as explored 4 Q.enqueue(root) 5 while Q is not empty do 6 v := Q.dequeue() 7 if v is the goal then 8 return v 9 for all edges from v to w in G.adjacentEdges(v) do 10 if w is not labeled as explored then 11 label w as explored 12 w.parent := v 13 Q.enqueue(w) More details This non-recursive implementation is similar to the non-recursive implementation of depth-first search, but differs from it in two ways: 1. it uses a queue (First In First Out) instead of a stack (Last In First Out) and 2. it checks whether a vertex has been explored before enqueueing the vertex rather than delaying this check until the vertex is dequeued from the queue. If G is a tree, replacing the queue of this 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.[10] The Q queue contains the frontier along which the algorithm is currently searching. Nodes can be labelled as explored by storing them in a set, or by an attribute on each node, depending on the implementation. Note that the word node is usually interchangeable with the word vertex. The parent attribute of each node is useful for accessing the nodes in a shortest path, for example by backtracking from the destination node up to the starting node, once the BFS has been run, and the predecessors nodes have been set. Breadth-first search produces a so-called breadth first tree. You can see how a breadth first tree looks in the following example.