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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] Another possible ...
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.
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):
In any graph, directed or undirected, there is a straightforward algorithm for finding a widest path once the weight of its minimum-weight edge is known: simply delete all smaller edges and search for any path among the remaining edges using breadth-first search or depth-first search.
Breadth-first search: traverses a graph level by level; Brute-force search: an exhaustive and reliable search method, but computationally inefficient in many applications; D*: an incremental heuristic search algorithm; Depth-first search: traverses a graph branch by branch; Dijkstra's algorithm: a special case of A* for which no heuristic ...
In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points ), together with a set of unordered pairs of these ...
The underlying issue is that 2 occurs in two places in the graph, as a child of 1 and as a child of 3, and the place where it's discovered first is later in the depth-first order. For breadth-first search it doesn't affect the correctness of the algorithm whether you do the check before enqueueing or after dequeueing. But for depth-first search ...
In the hypothetical situation where Nodes A, B, and C form a connected undirected graph with edges AB = 3, AC = 4, and BC = −2, the optimal path from A to C costs 1, and the optimal path from A to B costs 2. Dijkstra's Algorithm starting from A will first examine B, as that is the closest.