Problem 5: Let T be a binary search tree with n elements. Write an O(n)-time algorithm that builds a skip list S from T such that, in the worst-case, the time complexity of the search operation in S is O(log n). Hint: construct a deterministic skip list.

a.Given the steps of Kruskal’s algorithm, analyze each loop and find its running time cost in terms of V and E.   MST-KRUSKAL(G,w) A ←  for each vertex v  V MAKE-SET(v) sort E into non-decreasing order by w for each (u, v) taken from the sorted list if FIND-SET(u)  FIND-SET(v) then A ← A  {(u, v)} UNION(u, v) return A b. What is the total asymptotic running time of Kruskal’s algorithm

In the worst-case scenario, binary tree sort employing a self-balancing binary search tree requires O(n log n) time, which is slower than merge sort.

In the worst-case situation, binary tree sort using a self-balancing binary search tree requires O(n log n) time, which is slower than merge sort.