2. Consider the following recursive algorithm implemented as a Java method: public static boolean isPalindrome (String s) { if (s.length() == return true; 0) { } else if (s.length() return true; == } 1) { } else if (s.charAt(0) != s.charAt(s.length()-1)) { return false; } else { return isPalindrome (s.substring(1, s.length()-2)); Assuming that the recursive call takes 15 basic operations, a return statement takes 3 basic operations and that any of the if statements takes 7 basic operations, give a recurrence describing the worst-case running time for this algorithm.

Consider the following recursive method in Java that determines ifa 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;elsereturn ( 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 operationsrequired 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.

The following recursive method called z is created. This method accepts two parameters: A string s, and an integer index  The code in the method is:      if (index == s.length())        return "";          <------ base case     if(index % 2 == 0)        return ""+ s.charAt(index) + z(s,index+1);           <---- recursive call     else        return z(s,index+1);             <----- recursive call   What would be the output with the call:   z("javajavajava",0);

Consider a recursive method below. static void mysteryRecursion (String x) { if (x.length() < 1) { System.out.println(x); } else { System.out.println (x.charAt (0) + " " + x.charAt (x.length () - 1)) ; mysteryRecursion (x.substring (1, x.length () - 1)); What gets printed if I make the method call mysteryRecursion("helloworld");