For Problems 3 and 4, the Node class is declared as: class Node { int value; Node next; // constructors } Implement the method int numberPositive(Node head) that counts the numbe positive integers in a linked list of integers recursively. Assume the linked list is reference 3. head. Implement the method Node search (Node head, int key) that returns the reference to the node with the value key in a linked list of distinct integers recursively. 4. Assume the linked list is reference by head. The method returns null if the search fails.

Recursion Practice Welcome back! In this lab, we will be reviewing recursion by practicing with some basic recursion problems. Objectives Increase familiarity with recursive logic by working through several recursive problems. Taking into consideration a few corner cases through analyzing the test cases. Using a regex expression that will remove punctuation. Getting Started This lab includes the following .java file: L4/└── Recursion.java└── Main.java**Main.java is a read-only file used for testing. It is not included in the starter jar.Here is the starter jar if you would like to code in a different environment: L4.jar.   Please complete ALL functions. Make sure to read the description for each function carefully. Do not include any for or while loops in your methods. These can all be completed in a purely recursive style, so do it recursively! In the spirit of incremental development, implement each method one at a time, look at the test cases and take into consideration what is…

write a code in java (using recursion)

Fix the code below so that there is a function that calculate the height of the triangle.   package recursion; import javax.swing.*;import java.awt.*; /** * Draw a Sierpinski Triangle of a given order on a JPanel. *  *  */public class SierpinskiPanel extends JPanel {     private static final int WIDTH = 810;    private static final int HEIGHT = 830;        private int order;     /**     * Construct a new SierpinskiPanel.     */    public SierpinskiPanel(int order) {                this.order = order;                this.setMinimumSize(new Dimension(WIDTH, HEIGHT));        this.setMaximumSize(new Dimension(WIDTH, HEIGHT));        this.setPreferredSize(new Dimension(WIDTH, HEIGHT));    }        public static double height(double size) {        double h = (size * Math.sqrt(3)) / 2.0;        return h;    }    /**     * Draw an inverted triangle at the specified location on this JPanel.     *      * @param x the x coordinate of the upper left corner of the triangle     * @param y the y…