Develop an algorithm to compute the second-best spanning tree. Use the MST property effectively to develop the algorithm and prove its correctness. What is its running time?

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Solving idea: we first run the MST algorithm from class. Let’s say we can eventually store the edges that are in MST and those which are not. For each of the latter, we try to add it to the MST. A cycle will be obtained due to MST property. Therefore, we identify the edge having the biggest weight from the cycle, but which is different than the edge we have added. We keep track of the difference occurred in the weight of the spanning tree and chose in the end the edge for which the difference is minimized (compared to weight of the MST)....

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