Suppose that all edge weights in graph G are distinct. Let T be the set

of all spanning trees of G$,$ and let T be a minimum spanning tree of G$.$ We define second$-$best

minimum spanning tree as a spanning tree T $$ such that

w$($T $)=$ min$\{$w$($T $)$ : T $$ in T $\{$T $\}\},$

where w is the weight function of G$.$

Design an efficient algorithm to find the second$-$best minimum spanning tree of G$.$ Justify the

correctness of your algorithm and provide an analysis of its time complexity.