Input: A directed graph G with n vertices. Task: If one can add at most one directed edge to G such that every vertex can reach all other vertices, then print 'Yes'. Otherwise, print 'Unsatisfiable'. Give an efficient algorithm (to the best of your knowledge) and a formal proof of correctness for your algorithm. An answer without any formal proof will be considered incomplete. Analyze the running time of the algorithm. You must write down your algorithm as pseudocode

in java replit code please

agents: An agent is trying to eat all the food in a maze that contains obstacles, but he now has the help of his friends! An agent  cannot occupy  a  square that has an obstacle. There are initially k pieces of food (represented by dots), at positions (f1,...,fk). There are also n agents at positions (p1,...,pn). Initially, all agents start at random locations in the maze. Consider a search problem in which all agents move simultaneously ;that is, in each step each agent moves into some adjacent position (N, S, E, or W, or STOP). Note that any number of agents may occupy the same position.           Figure 1: A maze with 3 agents For each of the following heuristics, indicate (yes/no) whether or not it is h1: The number of dots (representing food) remaining. [ True, False ]. h2(s)=0, where s is a state node. [ True, False ]. h3(s)=1, where s is a state node. [ True, False ].

= Trace the Winnow algorithm with 3: 1 for the following input. Suppose the domain is vectors of length n = 6 over {V1, V2, V3, V4, V5, V6} and the actual labels are with respect to formula v₁/v3/v6; for example, the true label of (1, 0, 1, 0, 1, 1) is '1' and that of 1, 1, 1, 1, 1,0 is '0'. The input vectors are: x1 = (1, 0, 1, 1, 0, 1) x2 = (1,0,1,1,0,0) x3 = x4= X5 x6 x7 x8 = = = = x9 = (0, 1, 0, 1, 0, 1) 1, 1, 1, 0, 0, 1) (1, (0, 1, 1, 1, 1,0) (1, 1, 1, 1, 1, 1) (0, 1, 0, 1, 1, 1) (1, 1, 0, 1, 1, 1) (1, 0, 1, 0, 0, 1) You need to follow the same assumptions as in the example in Slide 4 of Module 11. Show your work and specify whether it is possible that the algorithm makes more mistakes after processing the above vectors; justify your answer.