Eulierian cycle

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    An Eulierian cycle in a graph is a cycle (not necessarily simple) that uses every edge in the graph exactly one.
    Show that a graph has an Eulerian cycle if and only if every vertex has even degree and all of the vertices with nonzero degree belong to the same connected component.
    Design a linear-time algorithm to determine whether a graph has an Eulerian cycle, and if so, find one.

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