You should perform the actions below on the original tree and show the final tree (each action is independent). Also, indicate which turns are needed in each case.

a) Enter the 'J' key with priority 2.

b) Delete the 'T' key from the tree.

c) Split the tree into two trees for the key value 'K'.

3.1.1 Definitions A treap is a binary tree in which every node has both a search key and a priority, where the inorder sequence of search keys is sorted and each node's priority is smaller than the priorities of its children.1 In other words, a treap is simultaneously a binary search tree for the search keys and a (min-)heap for the priorities. In our examples, we will use letters for the search keys and numbers for the priorities. M, 4 A treap. Letters are search keys; numbers are priorities