(Cycle cover 2-page limit your solutions should fit on two sides of 1 page)

Your task is to give an algorithm which finds a cycle cover for a given graph or correctly reports that no cycle cover exists. An analysis of correctness along with the time and space complexity should also be included in your solution. You should base your algorithm on a reduction to bipartite matching. ( A cycle cover of a given directed graph G = (V, E) is a set of vertex-disjoint cycles that cover all the vertices. )

Solution guidelines For problems that require you to provide an algorithm, you must give the following:

1. a precise description of the algorithm in English and, if helpful, pseudocode,

2. a proof of correctness,

3. an analysis of running time and space.