We know that the decision version of the Traveling Salesman Problem $($TSP$)$ is an NP$-$complete problem. Which of the following statements are true? Justify each answer.

a$)$ There is no algorithm that finds the optimal solution for arbitrary instances of TSP$.$

b$)$ There is no polynomial algorithm that finds the optimal solution for arbitrary instances of TSP$.$

c$)$ If an algorithm finds the optimal solution for any instance of TSP$,$ then that algorithm has exponential complexity.

d$)$ It cannot happen that TSP $\backslash$in P if P

e NP$.$

e$)$ The only alternative to solve TSP in practice is to implement a heuristic.