Classical eulerian cycle algorithm: Difference between revisions
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== Induction step == | == Induction step == | ||
If the start node has | |||
== Complexity == | |||
Both for directed andundirected graphs, the asymtptotic complexity is <math>\mathcal{O}(n+m)</math>, where <math>n</mah> is he number of nodes and <math>m</math> the number of edges/ars. | |||
== Remark == | |||
Of course, the edges/arcs need not be removed permanently. However, when an edge/arc is processed, it mus be hidden from the algorithm up to its termination to meet the linear complexity. | |||
Revision as of 09:04, 12 October 2014
General information
Algorithmic problem: Eulerian cycle
Type of algorithm: recursion with an arbitrarily chosen start node as an additional input.
Induction basis
Abstract view: The output sequence [math]\displaystyle{ S }[/math] of nodes and arcs is initialized so as to contain the start node [math]\displaystyle{ s }[/math] and nothing else.
Induction step
If the start node has
Complexity
Both for directed andundirected graphs, the asymtptotic complexity is [math]\displaystyle{ \mathcal{O}(n+m) }[/math], where [math]\displaystyle{ n\lt /mah\gt is he number of nodes and \lt math\gt m }[/math] the number of edges/ars.
Remark
Of course, the edges/arcs need not be removed permanently. However, when an edge/arc is processed, it mus be hidden from the algorithm up to its termination to meet the linear complexity.