In computer science, breadth-first search (BFS) is a tree search algorithm used for traversing or searching a tree, tree structure, or graph. Intuitively, you start at the root node and explore all the neighboring nodes. Then for each of those nearest nodes, explore their unexplored neighbor nodes, and so on until it finds the goal.

Formally, BFS is an uninformed search method that aims to expand and examine all nodes of a tree systematically in search of a solution. In other words, it exhaustively searches the entire tree without considering the goal until it finds it. It does not use a heuristic.

From the standpoint of the algorithm, all child nodes obtained by expanding a node are added to a FIFO queue. In typical implementations, nodes that have not yet been examined for their neighbors are placed in some container (such as a queue or linked list) called "open" and then once examined are placed in the container "closed".

When searching in an unweighted cyclic graph (one that is not a tree) for a shortest path, BFS may be adapted by keeping a bit on each node to indicate that it has already been visited.

• BFS is complete - it finds a goal-state if one exists. (That is, it reaches every node on the tree.)
• BFS is optimal - it finds the smallest number of steps to reach the goal.
• BFS has space complexity linear in the size(edges plus vertices) of the tree/graph searched as it needs to store all expanded nodes in memory.
• BFS has time complexity linear in the size(edges plus vertices) of the graph or tree searched.

For the following graph:

a breadth-first search starting at A, and assuming that the left edges in the shown graph are chosen before right edges, will result in the search visiting the nodes in the following order: A, B, C, E, D, F, G. Compare with depth-first search.

Pseudocode

 function BFS (Start, Goal) { 
     push(Queue,Start)
     while notEmpty(Queue)) {
         Node := pop(Queue)
         if Node = Goal {
             return Node
         }
         for each Child in Expand(Node) {
           push(Queue, Child)
         }
     }
 }

See also

• depth-first search
• iterative deepening depth-first search
• best-first search

External links

• Dictionary of Algorithms and Data Structures: breadth-first search
• C++ Boost Graph Library: Breadth-First Search