Consider the following recursive method in Java that determines if a string is a palindrome (i.e., reads the same forward or backwards) or not: Public boolean isPalindrome ( String str ){ If( str.length() ≤ 1 ) return true; else return ( str.charAt (0) == str.charAt( str.length() – 1 ) && isPalindrome( str.substring(1..str.length() - 1))); } // end of isPalindrome a. Explain convincingly why the recurrence below for f(n), where n is the length of the string parameter str, is a correct expression for the number of primitive operations required by a call isPalindrome. t(0) = Θ(1) t(1) = Θ(1) t(?) = t(? − 2) + Θ(1) b. Show that t(n) = Θ(n), solves the recurrence for t(n) in (a) above.

Write a static recursive method in Java called mRecursion that displays all of the permutations of the charactersin a string passed to the method as its argument. For example, the character sequence abc has thefollowing permutations: acb, bac, bca, cab, cba. Then Write a static method called getInput that get aninput string from the user and passed it to the mRecursion method written above in a method call.Please does so using what I already had   //Get input from in to call recursive method        //to display those char permutations        public static String getInput ( ) {            Scanner in = new Scanner(System.in);            String combination = in.nextLine();            System.out.println("Enter string:);             return stringComb; //Method to show permutations of a desired string// This only return 3 string combination for some reason        static void myRecursion(String aString) {            //isEmpty check            if ( aString.length() == 0){…

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.

public class Main {      static int findPosSum(int A[], int N)  {  if (N <= 0)    return 0;       {      if(A[N-1]>0)      return (findPosSum(A, N - 1) + A[N - 1]);      else      return findPosSum(A, N - 1);     }   } public static void main(String[] args)  {    int demo[] = { 11, -22, 33, -4, 25,12 };  System.out.println(findPosSum(demo, demo.length));  } }  Consider the recursive function you wrote in the previous problem. Suppose the initial call to the function has an array of N elements, how many recursive calls will be made? How many statements are executed in each call? What is the total number of statements executed for all recursive calls? What is the big O for this function?