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If G is a tree, replacing the queue of the 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. [7]
A depth-first search (DFS) is an algorithm for traversing a finite graph. DFS visits the child vertices before visiting the sibling vertices; that is, it traverses the depth of any particular path before exploring its breadth. A stack (often the program's call stack via recursion) is generally used when implementing the algorithm.
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.
An alternative algorithm for topological sorting is based on depth-first search.The algorithm loops through each node of the graph, in an arbitrary order, initiating a depth-first search that terminates when it hits any node that has already been visited since the beginning of the topological sort or the node has no outgoing edges (i.e., a leaf node):
A stack (LIFO queue) will yield a depth-first algorithm. A best-first branch and bound algorithm can be obtained by using a priority queue that sorts nodes on their lower bound. [3] Examples of best-first search algorithms with this premise are Dijkstra's algorithm and its descendant A* search. The depth-first variant is recommended when no ...
Conversely, a beam width of 1 corresponds to a hill-climbing algorithm. [3] The beam width bounds the memory required to perform the search. Since a goal state could potentially be pruned, beam search sacrifices completeness (the guarantee that an algorithm will terminate with a solution, if one exists).
3D version of Prim's algorithm. Vertical layers are labeled 1 through 4 from bottom to top. Stairs up are indicated with "/"; stairs down with "\", and stairs up-and-down with "x". Source code is included with the image description. Other algorithms exist that require only enough memory to store one line of a 2D maze or one plane of a 3D maze.
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]