This is for an Introduction to Algorithms course, so no specific programming language should be used.

Please write the algorithm in general pseudocode and provide Proof of Correctness and Runtime Analysis.

Please show your work, and DO NOT use any pre-existing solutions to this question on Chegg Study, if any exist.

You are given a 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 0(m) to test if T still remains the minimum spanning tree of the graph. You may assume that all edge weights are distinct both before and after the update. HINT: If e ET, consider the cut obtained by deleting e from T. If e & T, consider the cycle formed by adding e to T. You are given a 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 0(m) to test if T still remains the minimum spanning tree of the graph. You may assume that all edge weights are distinct both before and after the update. HINT: If e ET, consider the cut obtained by deleting e from T. If e & T, consider the cycle formed by adding e to T