Problem 4: You are given an undirected graph G with n vertices and m edges, and a minimum spanning tree T of the graph. Suppose one of the edge weights w(e) of the graph is updated. Give an algorithm that runs in time O(m) to test if T stl remains the minimum spanning tree of the graph. You may assume that all edge weights are distinct both before and after the update (Hint: IfeE T, consider the cut obtained by deleting e from T. If T, consider the cycle formed by adding e to T.) Problem 4: You are given an undirected graph G with n vertices and m edges, and a minimum spanning tree T of the graph. Suppose one of the edge weights w(e) of the graph is updated. Give an algorithm that runs in time O(m) to test if T stl remains the minimum spanning tree of the graph. You may assume that all edge weights are distinct both before and after the update (Hint: IfeE T, consider the cut obtained by deleting e from T. If T, consider the cycle formed by adding e to T.)