Please how your work not the code, and espically for c$)$ show a sketch and and for D$)$ prove and show answer please:

$1.$ Regarding the $5-$Queens problem $(n-$Queen problem with $n=5),$ answer

following questions:

a$)$ Complete state space tree is a state space built by DFS without calling

any nodes as non$-$promising so that no pruning of tree branches occurs. Suppose

you solve a $5-$Queens problem with DFS without pruning to construct the

complete state space tree. How many nodes are there in this tree?

b$)$ How many potential solutions $($including wrong ones$)$ are there by using

the strategy in $($a$)$ where DFS is used without pruning?

c$)$ Now let's attempt to solve the $5-$Queens problem by using the

backtracking algorithm with DFS and treating any nodes as non$-$promising if it is

along any column or diagonal of previously placed queens. Suppose we visit

children of a node in left$-$to$-$right order. Show a sketch of the portion of the

pruned state space tree that would lead to the first solution.

d$)$ Display the first solution found by $($c$)$ and answer how many nodes you

visited to reach this solution from the root node in the pruned state space tree.