The time complexity of the efficient algorithm for n Insert and Retrieve_Max operations on a set {} depends on the data structure used to implement the set.
If a balanced binary search tree, such as AVL Tree, Red-Black Tree or Splay Tree is used to implement the set, the time complexity of each operation would be O(log n). The Insert operation would take O(log n) time to find the correct position to insert the new element, and Retrieve_Max operation would take O(log n) time to traverse the rightmost path in the tree to find the maximum element.
Therefore, the time complexity of n Insert and Retrieve_Max operations on a set implemented using a balanced binary search tree would be O(n log n).
If a heap is used to implement the set, the Insert operation would take O(log n) time to maintain the heap property after inserting the new element. The Retrieve_Max operation would take O(1) time to return the maximum element, which is the root of the heap.
Therefore, the time complexity of n Insert and Retrieve_Max operations on a set implemented using a heap would be O(n log n) for Insert operations and O(n) for Retrieve_Max operations, resulting in a total time complexity of O(n log n).
