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- use JAVA to write the code. : Euclid’s algorithm for finding the greatest common divisor (gdc) of two numbers The algorithm: given two numbers, n1 and n2: Divide n1 by n2 and let r be the remainder. If the remainder r is 0, the algorithm is finished and the answer is n2. (If the remainder is 1, the numbers are mutually prime and we are done-see below.) Set n1 to the value of n2, set n2 to the value of r, and go back to step 1. Entering 0 for one of the values is bad. It should work for the other value, but you have to figure out which is OK and which is bad. Catch this problem as it happens and make the user enter another value until they enter an acceptable one. Give an appropriate error message if this happens.Which one is correct for the following snippet of code? def factorial1(x): if x== 0: return 1 return x *factorial1(x-1) def factorial2 (x,y=1): if x== 0: return y return factorial2 (x-1,x*y) Group of answer choices a) Both factorial1() and factorial2() aren’t tail recursive. b) Both factorial1() and factorial2() are tail recursive. c) factorial1() is tail recursive but factorial2() isn’t. d) factorial2() is tail recursive but factorial1() isn’t.Given code: int s=0; for ( int i=1; i<5; i++ ){ s = s + i ; } Which one is correct, after running the code. Group of answer choices s=1 s=15 s=10 s=5
- - Use java RECURSION to print out this shape. - You need to call the method 2 times - use 2 or 3 for loops hints: - for (int i = 0; i < ?????; i++) sout(" ") - for (int i = 0; i < ?????; i++) sout(symbol) - put different if statements when you call yourself, one gets activated when you go up, one gets activated when you go down. - This method should be used; public static void printShape4(int row, char symbol, int currentRow) { } !!! do not use other methods, everything should be inside this methodPLEASE answer ASAP I will give upvotes if you answer as soon as possible This is Iterative ImprovementIf your first name starts with a letter from A-J inclusively: Write a recursive method that takes a string as argument and determines if the string has more vowels than consonants. Test the method by asking the user to enter a string. Hint: Write your recursive method to first count vowels and consonants.
- JAVA Question 2: For two integers m and n, their GCD (Greatest Common Divisor) can be computed by a recursive method. Write a recursive method gcd(m,n) to find their Greatest Common Divisor. Method body: If m is 0, the method returns n. If n is 0, the method returns m. If neither is 0, the method can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n (or m % n). The recursive method cannot have loops. Note: although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit. main method: Prompt and read in two numbers to find the greatest common divisor. Call the gcd method with the two numbers as its argument. Print the result to the monitor. Example program run: Enter m: 12 Enter n: 28 GCD(12,28) = 4 And here is what I have so far, package CSCI1302;import java.util.*;public class RecursionDemo { public static void…5. Palindrome Detector A palindrome is any word, phrase, or sentence that reads the same forward and backward. Here are some well-known palindromes: Able was I, ere I saw Elba A man, a plan, a canal, Panama Desserts, I stressed Kayak Write a boolean method that uses recursion to determine whether a string argument is a palindrome. The method should return true if the argument reads the same forward and backward. Demonstrate the method in a program.Please complete the following Java program using the math.random function. USE THE Math.random() class. DO NOT use arrays, the Random function. (i.e keep the program simple using while loops, if/else, for loops, etc)
- Java Program: Recursive Method There are n people in a room where n is an integer greater then or equal to 2. Each person shakes hands once with every other person. What is the total number of handshakes in the room? Write a recursive method to solve this problem with the following header:public static int handshake(int n)where handshake(n) returns the total number of handshakes for n people in the room. To get you started if there are only one or two people in the room, then:handshake(1)=0handshake(2)=1Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. anglers have recently gotten back from a fishing excursion. The I-th angler has gotten a fish of weight man-made intelligence. Anglers will flaunt the fish they got to one another. To do as such, they initially pick a request where they show their fish (every angler shows his fish precisely once, in this way, officially, the request for showing fish is a stage of integers from 1 to n). Then, at that point, they show the fish they discovered by the picked request. At the point when an angler shows his fish, he may either become glad, become dismal, or stay content. Assume an angler shows a fish of weight x, and the most extreme load of a formerly shown fish is y (y=0 if that angler is quick to show his fish). Then, at that point: in the event that x≥2y, the angler becomes cheerful; in the event that 2x≤y, the angler becomes miserable; in the event that none of these two…Exercise III: Catalan numbers For n e N, denote by c, to be the number of ways to form a "mountain range" with n upstrokes (U) and n downstrokes (D) that all stay above a horizontal line. For instance: for n = 1, only UD is allowed, so c = 1; • for n = 2, only UUDD and UDUD are allowed, so c2 = 2. 1. Check that c3 = 5 by writing down or drawing all possible options. 2. Consider the power series +00 g(x) = 2 n=0 (by definition co = 1) called the generating function of the sequence (en). Justify that cn < 4" for each n, and deduce that the radius of convergence of g is at least 1/4. 3. It can be show that for r E (-1/4, 1/4), g(x) = 1+ xg(r)? and therefore 1- VI 4.x g(x) = 2.x Use this formula and the known power series of V1+ x to write the first terms of the power series expansion of g, in the form g(x) = co + c1x + c2x2 + C3x + c4x* + ·.. Show how you obtain a few terms, but you do not need to show all computations and you can use a calculator for fractions. Check that you recover co,…
