$1.$ Write the time and space complexity of depth$-$first search in terms of its branching $2$ factor $\backslash ($ b $\backslash ),$ and search depth d $.$ Is this algorithm optimal? Why$/$why not?

$2.$ Use the following tree to indicate the order that nodes are expanded, for Depth$-$

first search, Iterative deepening depth$-$first search, Breadth$-$first search, and Uniform cost search. Assume that G $($double box$)$ is the only goal node. Here, path costs are shown to the right of each path. For each search strategy, write down the order of node exnansion sten by step to reach the goal node $\backslash ($ G $\backslash ).$