Please solve the graph question in detail and clear.

Question 1: Shortest Cycle Involving a Given Node. You are given a directed graph G :(V, E) using an adjacency list representation and a vertex (node) u of the graph. Write an algorithm to perform the following tasks: 1(A) Write an algorithm that decides (true/false) whether the vertex u belongs to a cycle. What is the complexity for your algorithm in terms of the number of vertices IV and the number of edges |E|? Note: Throughout this assignment you may describe your algorithms using words and definitely use algorithms that you have already learned in class. A brief description will do. YOUR ANSWER HERE 1(B) Write an algorithm which prints the smallest length cycle involving the vertex u. What is the complexity for your algorithm in terms of the number of vertices IV and the number of edges |E|? YOUR ANSWER HERE