Problem $3(20$ pts$)$ Given an connected edge weighted graph $G=(V,E,w)$ and a minimum spanning tree of $T$ of $G,$ Develop a deterministic algorithm that, in $O(n)$ time, updates the minimum spanning tree $T$ to reflect the reduced weight of the edge in $G,$ if such an update is necessary. The updated tree should remain a valid minimum spanning tree for the modified graph.