s task is also more difficult than it might seem, because the order in which you call the methods in the previous three exercises is important.Write a method isBST() that takes a Node as argument and returns true if the argument node is the root of a binary search tree, false otherwise. Hint : This task is also more difficult than it might seem, because th

A palindrome is a string that reads the same forward and backward. For example,“deed” and “level” are palindromes. Write an algorithm in pseudocode that testswhether a string is a palindrome. Implement your algorithm as a static method inJava. The method should call itself recursively and determine if the string is apalindrome.Write a main method that reads a string from the user as input and pass it to thestatic method. You need to validate the string and make sure it contains only letters(no digits or special characters are allowed). The main method should displaywhether the string is a palindrome or not. a)  Read the string from the user and validate it.b)  Create a method that calls itself recursively and returns whether thestring is a palindrome or not.c)  Include a test table with at least the following test cases:1. Invalid input. For example, string contains a number or specialcharacter.2. A valid string that is a palindrome.3. A valid string that is not a palindrome.

We were given the following code to solve a Pentomino puzzle, several methods might need to be added or editted to solve the problem. The program should take in an input of 3 4 5 6 for 3x20 4x15 5x12 6x10 grids. Then output the number of correct solutions for them (respectively its 2, 368, 1010, and 2339) import java.util.ArrayList;import java.util.LinkedList;import java.util.List; public class DLX {    class DataNode {        DataNode L, R, U, D;        ColumnNode C;                public DataNode() {            L = R = U = D = this;        }         public DataNode(ColumnNode c) {            this();            C = c;        }        DataNode linkDown(DataNode node) {            node.D = this.D;            node.D.U = node;            node.U = this;            this.D = node;            return node;        }        DataNode linkRight(DataNode node) {            node.R = this.R;            node.R.L = node;            node.L = this;            this.R = node;            return node;…

For JAVA.