Write a java program.

 Extend the class BinarySearchTree by adding a public method displayItemsInRange (l, w) that outputs in ascending order of node value, all the nodes in a BST whose values, v lie in the range l < v < w . Use recursion and avoid entering any subtrees that can't contain any elements in the desired range. You must also write a test program that builds a BST and tests your method (see below).

Extend the class BinarySearchTree by adding a method split(theKey, lessThan,  greaterThan) that splits the binary search tree this into two binary search trees -- lessThan contains all of the elements of this whose keys are less than theKey , and  greaterThan contains all of the elements of this whose keys are greater than theKey. If the binary search tree this has an element whose key equals theKey, this element is returned as the value of the method invocation; otherwise, null is returned. Following the operation, this (the original BST) is an empty binary search tree.

 You must also include the main() method that tests your code. Also your BST must have no less than 10 nodes, but it cannot be a full binary tree, e.g., n < 2h-1