$q,$

Exercise $6$:

$[5$pts$]$ Compute the expected search costs for the following binary search trees for a set of $7$ keys with the following probabilities and give the optimal BST$.$

$\backslash$table$[[i,0,1,2,3,4,5,6,7],[p_i,,0\mathrm{.}04,0\mathrm{.}06,0\mathrm{.}08,0\mathrm{.}02,0\mathrm{.}10,0\mathrm{.}12,0\mathrm{.}14],[q_i,0\mathrm{.}06,0\mathrm{.}06,0\mathrm{.}06,0\mathrm{.}06,0\mathrm{.}05,0\mathrm{.}05,0\mathrm{.}05,0\mathrm{.}05]]$