Consider a directed graph on n vertices, where each vertex has exactly one outgoing edge. This graph consists of a collection of cycles as well as additional vertices that have paths to the cycles, which we call the branches. Describe a linear time algorithm that identifies all of the cycles and computes the length of each cycle. You can assume that the input is given as an array A, where A[i] is the neighbor of i, so that the graph has the edge (i, A[i]). For clarity, make sure that you describe in English the main steps of your algorithm, and don't just provide code. Justify the correctness of your algorithm. Consider a directed graph on n vertices, where each vertex has exactly one outgoing edge. This graph consists of a collection of cycles as well as additional vertices that have paths to the cycles, which we call the branches. Describe a linear time algorithm that identifies all of the cycles and computes the length of each cycle. You can assume that the input is given as an array A, where A[i] is the neighbor of i, so that the graph has the edge (i, A[i]). For clarity, make sure that you describe in English the main steps of your algorithm, and don't just provide code. Justify the correctness of your algorithm