Say you have k sorted lists, each with n/k elements. Show how to use a heap to merge all of these lists into a single sorted list in O(n log k) time. (11 points correct algorithm, 7 points for proof of correctness, 7 points for time analysis and efficiency.) The following statements may or may not be correct. In each case, either prove it (if it is correct) or give a counterexample (if it is not correct). Always assume that the graph G (V, E) is undirected, connected and the edge weights are positive. (5 points each)