Here we will combine the familiar task of constructing arrays with the new ideas of functions and conditional statements.

Write a function named array$\_$builder that takes two inputs, positive integers i and $n,$ and outputs a vector $v.$ The output $v$ should depend on i and $n$ as follows:

If $i=1,$ return a vector $v=[1,2,3,$dots,$n]$

If $i=2,$ return a vector $v=[n,n-1,n-2,$dots,$1]$

If $i=3,$ return a vector $v=[1,-1,1,-1,$dots$]$$ $($total length $n).$

If $i=4,$ return a vector $v=[1^2,3^2,5^2,$dots,$(2n+1{)}^2]$

If $i=5,$ return a vector $v=[n,n-1,$dots,$1,0,1,$dots,$n-1,n]$

If $i=6,$ return a vector $v=[2,11,101,1001,10001,$dots$]($total length $n)$

If $i=7,$ return a vector $v=[2,7,12,17,$dots$]($last value not exceeding $n).$

If $i=8,$ return a vector $v=[1,-5,9,-13,17,-21,25,$dots$]($total length $n)$

If $i=9,$ return a vector $v=[0,0,1,0,0,1,$dots,$0,0,1]($total length $3n)$

You can assume that $i$ is one of these values.

Function