Let T be a binary search tree. Suppose we want to include a field v. size, the number of items stored in the subtree of v, at each node v. Given T, describe an algorithm that will populate all the size fields in T. What is the running time of your algorithm? Now suppose we make modifications to T by inserting or removing items. For each modification i.e., an insertion or a removal describe the modifications that have to be made to the size fields of the nodes in T. How much time will such modifications take? Using the binary search tree 011 Figure 3.4, insert an item with key equal to 52 and show the changes that have to be made on the size fields of the nodes in the tree. Now, remove the item with key equal to 75. Again, show the changes that have to be made 011 the size fields of the nodes in the tree