Consider the following recursive method. public static int rec(int x){ if (x < 3) { return 0; if (x <20) { return 1 + rec (x-10) +rec (x-5); } return x + rec (x-10); How many times is the method rec () called then initially called as rec (21)? Include the initial call.
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- 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…Note: Java Consider the following recursive method: public static int Fun(int x) { if(x == 0) //line 1 return 0 //line 2 else if( x == 1) //line 3 return 1; //line 4 else //line 5 return (x*Fun(x-1)); //line 5 } a) Is Fun(4) a valid call? If so, what is the value? If not, explain why? Answer: b) Is Fun(-4) is a valid call? If so, what is the value? If not, explain why? Answer: (c) Consider the following method. public static int res(int[] list, int first, int last) { if (first == last) return list[first]; else return list[first] + res(list, first + 1, last); } Given the declaration int[] A = {2, 4, 6, 8, 10}; What is the output of the following statement? out.println(res(A, 0, 2)); out.println(res(A, 0,…Consider the following recursive method: public static int Fun(int x){ if(x == 0) //line 1 return 0 //line 2 else if( x == 1) //line 3 return 1; //line 4 else //line 5 return (x*Fun(x-1)); //line 5 } 1) Is Fun(4) a valid call? If so, what is the value? If not, explain why? 2) Is Fun(-4) is a valid call? If so, what is the value? If not, explain why?
- import java.util.Scanner; public class LabProgram { // Recursive method to draw the triangle public static void drawTriangle(int baseLength, int currentLength) { if (currentLength <= 0) { return; // Base case: stop when currentLength is 0 or negative } // Calculate the number of spaces needed for formatting int spaces = (baseLength - currentLength) / 2; if (currentLength == baseLength) { // If it's the first line, don't output spaces before the first '*' System.out.println(" ".repeat(spaces) + "*".repeat(currentLength)); } else { // Output spaces and asterisks System.out.println(" ".repeat(spaces) + "*".repeat(currentLength)); } // Recursively call drawTriangle with the reduced currentLength drawTriangle(baseLength, currentLength - 2); } public static void drawTriangle(int baseLength) { drawTriangle(baseLength, baseLength); } public…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)=1import java.util.Scanner; public class LabProgram { // Recursive method to draw the triangle public static void drawTriangle(int baseLength, int currentLength) { if (currentLength <= 0) { return; // Base case: stop when currentLength is 0 or negative } // Calculate the number of spaces needed for formatting int spaces = (baseLength - currentLength) / 2; if (currentLength == baseLength) { // If it's the first line, don't output spaces before the first '*' System.out.println("*".repeat(currentLength) + " "); } else { // Output spaces and asterisks System.out.println(" ".repeat(spaces) + "*".repeat(currentLength) + " "); } // Recursively call drawTriangle with the reduced currentLength drawTriangle(baseLength, currentLength - 2); } public static void drawTriangle(int baseLength) { drawTriangle(baseLength, baseLength); } public static…
- Question 4 Consider the following recursive method. public static void mystery(int x) { if(x % 5 >= 2) { mystery(x + 1); } if(x % 5 1) { mystery(x - 1); } 11 System.out.print(x + "); } What is output by mystery (18) ? 19 20 20 19 == 20 19 18 17 20 19 18 20 1 ptsGiven the following recursive method:public static int think(int x) {if(x<10)if(x%2!=0)return x;elsereturn 0;elseif(x%2!=0)return x%10 + think(x/10);elsereturn think(x/10);}Trace (in details) the calling of the above method with any input from your choice such that thereturned value will be 19T/F 6. Consider the following recursive sum method:public int sum(int x){if (x == 0) return 0;else return sum(x - 1) + 1;}
- Public class Utilities { getDigits Method: public static java.lang.String getDigits(java.lang.String str) Returns a string with the digits (if any) present in the str parameter. You can assume str will never be null. You can use Character.isDigit() to determine whether a character is a digit. You may not use an auxiliary method in order to implement this method. Your implementation must be recursive and you may not use any loop construct. From the String class, the only methods you can use are length(), isEmpty(), charAt() and substring. Do not use ++ or -- in any recursive call argument. It may lead to an infinite recursion. For example, use index + 1, instead of index++. Parameters: str - Returns: String with digits or empty stringConsider the following recursive method.int recursum(int a, int b){if (a%b == 0)return b;elsereturn recursum (b, a%b);}a. What is the output given by recursum (48, 18)?b. What is the output given by recursum (85, 25) ?Write a recursive method to determine whether a String contains a 'q' not immediately followed by a 'u' (ignoring capitalization). In other words: • the word does contain at least one 'q' • and that q is followed by anything except a 'u' Carefully review the provided driver program to see example test cases. The method header is: public static boolean qNotFollowedByU(String word)