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To traverse arbitrary trees (not necessarily binary trees) with depth-first search, perform the following operations at each node: If the current node is empty then return. Visit the current node for pre-order traversal. For each i from 1 to the current node's number of subtrees − 1, or from the latter to the former for reverse traversal, do:
Reverse-search algorithms are a class of algorithms for generating all objects of a given size, from certain classes of combinatorial objects. In many cases, these methods allow the objects to be generated in polynomial time per object, using only enough memory to store a constant number of objects ( polynomial space ).
For binary trees there is additionally in-ordering and reverse in-ordering. For example, when searching the directed graph below beginning at node A, the sequence of traversals is either A B D B A C A or A C D C A B A (choosing to first visit B or C from A is up to the algorithm).
Patricia trees are a particular implementation of the compressed binary trie that uses the binary encoding of the string keys in its representation. [23] [15]: 140 Every node in a Patricia tree contains an index, known as a "skip number", that stores the node's branching index to avoid empty subtrees during traversal.
Search trees store data in a way that makes an efficient search algorithm possible via tree traversal. A binary search tree is a type of binary tree; Representing sorted lists of data; Computer-generated imagery: Space partitioning, including binary space partitioning; Digital compositing; Storing Barnes–Hut trees used to simulate galaxies ...
A universal traversal sequence is a sequence of instructions comprising a graph traversal for any regular graph with a set number of vertices and for any starting vertex. A probabilistic proof was used by Aleliunas et al. to show that there exists a universal traversal sequence with number of instructions proportional to O ( n 5 ) for any ...
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):
The reverse-delete algorithm is an algorithm in graph theory used to obtain a minimum spanning tree from a given connected, edge-weighted graph. It first appeared in Kruskal (1956) , but it should not be confused with Kruskal's algorithm which appears in the same paper.