Eulerian cycle

Definition

A Eulerian cycle is a cycle in a directed or undirected graph that contains each edge/arc exactly once.

Redundant information for clarification: In the directed case, each arc must have forward orientatin on the cycle.

Input

A strongly connected directed or connected undirected graph.

Output

A Eulerian cycle as an alternating sequence of nodes and edges/arcs or, alternatively, the (correct) message that no such cycle exists.

Known algorithms

Classical eulerian cycle algorithm

Example

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  Final Step