In this problem, we are investigating the vector X which is used in functional link

neural networks. X must be efficiently generated from the feature vector x$.$

$($a$)$ Give an efficient algorithm for generating X for the second degree case. The

elements do not have to be in any particular order.

$($b$)$ Give an efficient algorithm for generating X for the third degree case. $($Hint; use

three nested loops$)$

$($c$)$ Find an expression for K$($n$,$N$).$