Disjoint Set Explain! Given the following disjoint$-$set what would be the result of the following calls on union if we add the "union$-$by$-$rank" optimization. Draw the forest at each stage with correspondingA. Consider the following disjoint$-$set. What would be the result of the following calls

on union if we add the union$-$by$-$size and path compression optimizations? Show the

forest in each case. $($i$)$ union$(3,14),($ii$)$ union$(5,13),($iii$)$ union $(3,9)$

B$.$ Explain with a relevant example how you can solve dynamic connectivity problem

using union$-$find ADT. ranks for each tree. union $\backslash ((2,13)\backslash )$ union $\backslash ((4,12)\backslash )$ union $\backslash ((2,8)\backslash )$Given the following disjoint$-$set what would be the result of the following calls on union if we add the "union$-$by$-$rank" optimization. Draw the forest at each stage with corresponding ranks for each tree. union $\backslash ((5,8)\backslash )$ union $\backslash ((1,2)\backslash )$ union $\backslash ((7,3)\backslash )$