A hill$-$climbing algorithm that never visits states with lower value $($or higher cost$)$ is guaranteed to find the optimal solution if given enough time to find a solution.

Suppose the temperature schedule for simulated annealing is set to be constant up to time $N$ and zero thereafter. For any finite problem, we can set $N$ large enough so that the algorithm is returns an optimal solution with probability $1.$

For any local$-$search problem, hill$-$climbing will return a global optimum if the algorithm is run starting at any state that is a neighbor of a globally optimal state.

Stochastic hill climbing is guaranteed to arrive at a global optimum.

Part II: Long answer problems $(80$ points in total$)$