What is a recursive method? What is an infinite recursion? Explain and demonstrate with examples. Implement the search (element) in a list using recursion. Explain it with at least 3 different java examples

Complete the following recursive function that returns the sum of all the numbers in a list that are positive and even numbers. Replace the bold text with the correct expression. #lang racket (define (positiveEvenNums 1st) (if (null? 1st) (if (THE CAR OF THE LIST IS POSITIVE AND EVEN) (+ (car 1st) (positiveEvenNums (cdr 1st))) (positiveEvenNums (cdr 1st))))) (positiveEvenNums '(-3 8 4 3 -2 0 5))

Consider a grid of size (x, y) where x and y are positive integers. The following figure shows an example grid of size (2,3) and two points p1 and p2 in the grid. Assume that x and y of p2 is greater than x and y of p1. p2(2,2) ectangular Snip p1(0,0) Write a recursive method named countPaths that returns the number of distinct shortest paths from p1 to p2. The method takes 4 ints as the parameters – i.e., x and y values of the two points: x1, y1, x2, and y2. Note that you do not need to print the paths. Count only. To be shortest, a path will only consist of only upward and rightward movements where each movement increases x- or y-coordinate value by 1. In the figure above, |(right, up, right, up) or (right, right, up, up) are both shortest paths from p1 to p2. For example, countPaths (0, 0, 2, 2) returns 6 countPaths (0, 0, 1, 1) returns 2 countPaths (2, 1, 2, 2) returns 1

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Keeping in mind data structures, recursion, and using Java What is the value returned from the following method when it is called with the value 5?   int mystery(int x, int y)    {       if (y == 0)          return 1;       if (y == 1)          return x;       return x * mystery(x, y-1);    }

Write and test a Java/Python recursive method for finding the minimum element in an array, A, of n elements. What the running time? Hint: an array of size 1 would be the stop condition. The implementation is similar to linearSum method in lecture 5 examples. You can use the Math.min method for finding the minimum of two numbers.

Implement the logarithmBase22 method which, given a long integer number, returns the result of Logz2(number), rounded down to the nearest floor integer. Design and implement this as a recursive method. Read the test cases in the JUnit tester file for more detailed specification.

Write code in Java: -Must be recursive import java.util.*; import java.lang.*; import java.io.*; //*Analysis goes here*   //*Design goes here* class AllPermutation { public static void displayPermutation(String s) { //*Code goes here* } public static void displayPermutation(String s1, String s2) { //*Code goes here* } } //*Driver class should not be changed* class DriverMain { public static void main(String args[]) { Scanner input = new Scanner(System.in); AllPermutation.displayPermutation(input.nextLine()); } }

Answer the given question with a proper explanation and step-by-step solution. 3. Draw the recursion tree when n = 8, where n represents the length of the array, for the following recursive method:int sum(int[] array, int first, int last) {if (first == last)return array[first];int mid = (first + last) / 2;return sum(array, first, mid) + sum(array, mid + 1, last);} Determine a formula that counts the numbers of nodes in the recursion tree. What is the Big- for execution time? Determine a formula that expresses the height of the tree. What is the Big- for memory? Write an iterative solution for this same problem and compare its efficiency with this recursive solution. 4. Using the recursive method in problem 3 and assuming n is the length of the array. Modify the recursion tree from the previous problem to show the amount of work on each activation and the row sums. Determine the initial conditions and recurrence equation. Determine the critical exponent. Apply the Little…

Write java program recursive method to display all odd numbers from the given number to 1 .