$1.$ Give the name of the algorithm that results from each of the following special cases:

a$.$ Local beam search with k$=1.$

a$.$ Hill Climbing

b$.$ Local beam search with one initial state and no limit on the number of states retained.

a$.$ BFS

c$.$ Simulated annealing with T$=0$ at all times $($and omitting the termination test$).$

a$.$ Hill Climbing

d$.$ Simulated annealing with T$=\backslash$infty at all times.

a$.$ DFS

e$.$ Genetic algorithm with population size N $=1$

a$.$ Hill Climbing