write, in Java, a method which runs in O(N²logN) time complexity.

Show a definition for a recursive Java method long powerOf2(int n) that returns the value of 2" (assume n is non-negative).

Design and implement a program that implements Euclid’s algorithm for finding the greatest common divisor of two positive integers. The greatest common divisor is the largest integer that divides both values without producing a remainder. In a class called DivisorCalc, define a static method called gcd that accepts two integers, num1 and num2. Create a driver to test your implementation. The recursive algorithm is defined as follows:gcd (num1, num2) is num2 if num2 <= num1 and num2evenly divides num1gcd (num1, num2) is gcd(num2, num1) if num1 < num2gcd (num1, num2) is gcd(num2, num1%num2) otherwise

JAVA: Write a recursive method named threeSum that accepts a list of integers and prints all combinations of three integers in the list that sum to 0. For example, if given the list [-1, 0, 1, 2, -1, -4], print the following lines of output: [-1, 0, 1] [-1, 2, -1] [0, 1, -1] You may print the lines of output in any order. The elements in each three-element sublist should appear in the same relative order that they appeared in the original list. Do not print duplicate lists; if the same exact sublist can be made in multiple ways, print it only once. If there are no combinations of three elements that sum to 0, print no output. The list passed to your method must be back to its original state at the end of the call. Either do not modify it, or if you modify it, fully undo your modifications before the method returns. Constraints: Do not declare any global variables. You can use any data structures you like, and your code can contain loops, but the overall algorithm must be recursive and…

Consider the following implementation of binarySearch: public static bool binarySearch(int[] a, int item) { int first = 0; int last = a.length - 1; while( first <= last) { int mid = (first + last)/2; if(a[mid] item) return true; else if (a[mid] < item) first = mid + 1; else last = mid - 1; } return false; == } how many times is the line of code int mid = (first + last)/2; executed when it is called with a = {2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37} and item = 2?

Write a Java program that expands a given binomial (x + y)^n, where integer n is user input. To do the work of the binomial expression, first create a method that accepts n as a parameter and then returns an array holding the coefficients needed for the binomial expansion using the Pascal’s Triangle method. Create a 2nd method which takes the array holding the coefficients as a parameter and prints the appropriate binomial expansion. For example, if n = 5 is entered by the user, the method calculating the coefficients should return {1,5,10,10,5,1} and the method that prints the expansion should print the following: (x + y)^5 = x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5 Your main method should use an appropriate loop for repeated inputs and automatically call the methods to calculate the coefficients and print the binomial expansion. There isn’t a need for a menu although you should ask the user if they want to quit or continue after their binomial expansion is printed each time.…