Could anyone help me with this question please? Thank you very much!

1. Suppose a given problem has a finite state space (assume a problem such as travelling from one city to another), but we allow negative step-costs (assume all step costs are integer values). All goal states are reachable from the start state. (a) If solutions are not allowed to contain cycles, how much of the state space must we explore before finding the optimal solution? Explain. (b) How is the optimal solution affected if solutions are allowed to contain cycles? Explain