Suppose you started with an empty binary search tree. We've seen previously that inserting the keys 1, 2, 3, 4, 5, 6, 7 (in that order) would lead to a binary search tree whose shape we called degenerate. Propose a second ordering of the same keys that would also lead to a degenerate-shaped binary search tree. If possible, propose a third ordering of the same keys that would also lead to a degenerate-shaped binary search tree. If there are no more orderings other than the one we provided and the second one you proposed, briefly explain why there are no more.

A Binary Search Tree (BST) can be used to efficiently implement a sorted set. It stores uniquevalues and offers an efficient membership method (contains).A binary search tree (BST) is a binary tree with the additional binary search tree property.The binary search tree property states that for every node n in the tree1. n.data is greater than the data value of all nodes in the sub-tree rooted with n.left.2. n.data is less than the data value of all nodes in the sub-tree rooted with n.right.As we are implementing a set, all data (strings) in the tree will be unique. Every node in the treewill have its own distinct string. Strings will be compared using the canonical way (as defined bythe compareTo() method in the String class).For example, the binary tree on the left (below) IS a binary search tree and the one on the rightis NOT.You will implement several methods in the BinaryTree and BST classes. The BST class mustextend the BinaryTree class. Methods that you must complete (implement or…

Create the Sample class, which has a constructor that accepts an array p[] of double values as an input and supports the following two operations: Return an index i with a probability of p[i]/T (where T is the total of the numbers in p[]) and alter(i, v) to change the value of p[i] to v. Use a full binary tree with an inferred weight of p[i] for each node. Keep the total weight of all the nodes in its subtree in each node. Pick a random number between 0 and T to obtain a random index and use the cumulative weights to select which branch of the subtree to examine. Change the weights of all nodes on the path from the root to i when updating p[i]. Avoid explicit pointers, as we do for heaps.