Discrete Structure problem:

(a) An Eulerian cycle in an undirected graph G (V,E) is a cycle that goes over each edge of E exactly once, although it may go through vertices multiple times. Show that G has an Eulerian cycle if an only if it is connected and all vertices have even degree. (b) Describe, analyze, and implement (in whatever programming language you like) a depth-first search algorithm that finds an Eulerian cycle in a graph, if one exists, or reports that there is none (together with the evidence of non-existence that is, disconnected vertices or a vertex with odd degree). Your algorithm must work in O(V+El) time