Sub$-$Algorithm: Find$\_$Square$($n$,$m$)$

Requires: positive intergers $($n$,$m$)$

Returns: square root of a perfect square number without using the square root function

if m$*$m $==$ n

Return m

Elseif m$*$m $>$ n

Return $-1$

Else

Return Find$\_$Square$($n$,$m $+1)$

Algorithm: NoSquarelist$($n$)$

Requires: a positive interger $($n$)$

Returns: a list consisting of all integers less than n that are not perfect squares

Let n$=$ createlist$\_$i$-$j$(1,$ n$)$

Return NoSquarelisthelper$($list$)$

Sub$-$Algorithm: createlist$\_$i$-$j$($i$,$ j$)$

Requires: positive intergers

Returns: a list from i to j

If i$>$j

Return x

Else

Return cons$($i$,($tail$($createlist$\_$i$-$j$($i$+1,$j$)$

Let X$=$ cons$($list$)$

Sub$-$Algorithm: NoSquarelisthelper$($list$)$

Requires: non empty list

Returns: a list consisting of all integers that are not perfect squares

If isEmpty$($list$)$

Return nil

Let x $=$ Find$\_$Square$($value$($list$),1)$

If x $!=-1$ && x $*$ x $==$ value$($list$)//$Perfect square case

Return NoSquarelisthelper$($delNth$(1,$ list$))//$Skip the element

Else $//$Not a perfect square

Return cons$($value$($list$),$ NoSquarelisthelper$($nil$)//$Retain the element

Value$($List$)$ returns the first element of a list

delNth$($n$,$ list$)$ returns a list with the nth element deleted