Q$1$ An application requires storing and operating on several disjoint sets using

an array representation of disjoint$-$set forests.

$1.$ Assume the application requires a large number of Union operations

to be performed. In what scenario will such operations result in

unbalanced trees of high depths? $[1$ point$]$

$2.$ Of the functions Make$-$Set, Find$-$Set, and Union which one can

be modified to avoid the above scenario? Explain how you would

change that function.