$4.$ Given a graph $\backslash ($ G$($V$,$ E$)\backslash )$ and its MST$,$ consider there are changes to edges of the graph. In such occasion you must update the MST without rebuilding it$.$ There are certain edges which are in MST and others which might not be in MST$.$ Determine how you must update your MST in no more than $\backslash (\backslash$mathrm$\{$O$\}(\backslash$mathrm$\{$V$\}+\backslash$mathrm$\{$E$\})\backslash )$ time if:

a$.$ Weight of an edge which is in MST decreases

b$.$ Weight of an edge which is in MST increases

c$.$ Weight of an edge which is NOT in MST decreases

d$.$ Weight of an edge which is NOT in MST increases

e$.$ How would you convert the Minimal Spanning tree to Maximum Spanning tree $($build tree from scratch$).$ You can call Prim's or Kruskal's algorithm without making any change to the algorithm.