$3.$ a$.$

Implementthebacktrackingalgorithmforthen$-$queensprobleminthelan$-$ guage of your choice. Run your program for a sample of n values to get the numbers of nodes in the algorithm$$s state$-$space trees. Compare these num$-$ bers with the numbers of candidate solutions generated by the exhaustive$-$ search algorithm for this problem $($see Problem $9$ in Exercises $3\mathrm{.}4).$

b$.$ For each value of n for which you run your program in part $($a$),$ estimate the size of the state$-$space tree by the method described in Section $12\mathrm{.}1$ and compare the estimate with the actual number of nodes you obtained.