Based on the following state space graph,

a$.$ Construct the corresponding search tree with the indication of the path length to each node. In the state space graph, each number annotates the associated link length, though some are bi$-$directional and some uni$-$directional.

b$.$ For each of the following graph search strategies, work out the order in which states are expanded, as well as the path returned by graph search. In all cases, assume ties resolve in a way that states with earlier alphabetical order are expanded first. Remember that in graph search, search a state is expanded only once. Your answers are required to include both result and operation process for full credit.

i$.$ Depth$-$first search

ii$.$ Breadth$-$first search

iii. Uniform cost search