Write a recursive method for Quicksort in Java (sort integers in an array). Assume that you have the following methods: (1) pickPivot(int[] array) that returns the array index of a pivot, (2) pivotArray(int[] array int pivotIndex) that places all values in the array less than or equal to the value of the pivot to the left of the pivot and all values greater than the value of the pivot to the right of the pivot. Explain the worst-case scenario in Quicksort. Why is the worst case is O(N^2). Explain the worst-case scenario in Mergesort. Why is Mergesort O(NlogN)? Provide one of the three solution provided in class (in pseudo code) for finding the convex hull for a given set of 2d points. Start from getting the integer input for the x-axis and y-axis values. Write a Java method that accepts the x-axis and the y-axis integer values of a query point as parameters and returns true if the query point is inside the convex hull and false if a point is outside the convex hull. The convex hull is provided as a circular doubly linked list of nodes where each node corresponds to a point that makes up the convex hull. There is a global reference for a node in the circular doubly linked list (Node start). The following methods are available to you: getRight(): returns the node to the right of the current node. getLeft (). returns the node to the left of the current node. whatTurn(Node a, Node b, int x, int y): returns I if left, 0 if collinear, and -1 if right, int x and int y are the x-axis and y-axis values of the query point. Node a and Node b indicates direction (moving from a to b. towards the query point). Write a method in Java for deleting a Node with value v from a BST. The BST property must be maintained after the deletion. Assume that you have a findValue(int v) that returns the Node containing value v. A Node has a value (int v) and both left and right child pointers (Node left, Node right), with the appropriate accessors and mutators for v, left, and right. Write a method in Java for printing the contents of a BST in order. A BST is comprised of Nodes that have a value (int v) and both left and right child pointers (Node left. Node right), with accessors for v, left, and right. There is also a global reference to the root node