For each of the following problems, decide if the provided answer correctly solves the problem. If it does then analyse the running-time of the algorithm. If it does not, give an example demonstrating why not. (a) Problem: In a weighted directed graph, find the longest simple (i.e. no repeated vertices) path between two vertices s and t. Solution: Multiply all edges by -1 and, using the Bellman-Ford algo- rithm, find the shortest path between s and t in the new graph. This will be the longest path in the original graph. (b) Problem: In a connected weighted graph with distinct edge weights, find the spanning tree with maximum weight. Solution: Order the edges by weight from smallest to largest. Remove edges following this order, as long as removing an edge does not dis- connect the graph. When all edges have been processed, the remaining edges form the maximum spanning tree c) Problem: Given an array A of n non-negative integers and a positive inte- ger k, find the smallest value of maxij