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Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking.
It also maintains a value v.lowlink that represents the smallest index of any node on the stack known to be reachable from v through v's DFS subtree, including v itself. Therefore v must be left on the stack if v.lowlink < v.index, whereas v must be removed as the root of a strongly connected component if v.lowlink == v.index.
The "non-recursive implementation of DFS" given in this Wiki entry is "fake DFS" or "pseudo-DFS". It is not a true DFS. The posted pseudo-DFS algorithm produces the DFS-like vertex discovery sequence, but that where its similarity with DFS ends. In canonical DFS algorithm stack depth is limited to the length of the longest DFS path in the graph.
A simple alternative to the above algorithm uses chain decompositions, which are special ear decompositions depending on DFS-trees. [3] Chain decompositions can be computed in linear time by this traversing rule. Let C be a chain decomposition of G. Then G is 2-vertex-connected if and only if G has minimum degree 2 and C 1 is the only cycle in C.
According to the above definition, deterministic finite automata are always complete: they define from each state a transition for each input symbol. While this is the most common definition, some authors use the term deterministic finite automaton for a slightly different notion: an automaton that defines at most one transition for each state ...
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The definition of a generator appears identical to that of a function, except the keyword yield is used in place of return. However, a generator is an object with persistent state, which can repeatedly enter and leave the same scope. A generator call can then be used in place of a list, or other structure whose elements will be iterated over.
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