Write a recursive Java method that calculates the sum of n positive integer numbers. The math function is: f(n) = 1 + 2 + 3 + … + n.
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- Write a recursive Java method that calculates the sum of n positive integer numbers. The math function is: f(n) = 1 + 2 + 3 + … + n.
Code:
public static int Func(int n)
{
if (n <= 1)
return n;
return n + Func(n - 1);
}
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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…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)=1Do not use static variables to implement recursive methods. USING JAVA USING: // P5 public static long computePay(int day) { } You have been offered a job that pays as follows: On the first day, you are paid 1 cent, on the second day, 2 cents, on the third day, 4 cents and so on. In other words, your pay doubles every day. Write a recursive method computePay that for a given day number computes the pay in cents. Assume that you accumulate all the money that you are paid. Write a recursive method computeSavings that computes the sum that you have accumulated on a given day. Show the output of computePay and computeSavings for day number 39.
- T/F 6. Consider the following recursive sum method:public int sum(int x){if (x == 0) return 0;else return sum(x - 1) + 1;}Write a recursive method that takes two integers n and m as parameters, where m is one digit number. The method should output odd digits in n that are greater then m. For example: If n =374, m=5, the method should output 7 If n =5239, m=2, the method should output 9 3 5 The method prototype: public static void printDigits(int n, int m)1. Write a recursive method expFive(n) to compute y=5^n. For instance, if n is 0, y is 1. If n is 3, then y is 125. If n is 4, then y is 625. The recursive method cannot have loops. Then write a testing program to call the recursive method. If you run your program, the results should look like this: > run RecExpTest Enter a number: 3 125 >run RecExpTest Enter a number: 3125 2. For two integers m and n, their GCD(Greatest Common Divisor) can be computed by a recursive function. Write a recursive method gcd(m,n) to find their Greatest Common Divisor. Once m is 0, the function returns n. Once n is 0, the function returns m. If neither is 0, the function can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n. Although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit. Meaning your code needs to follow the given algorithm. Then…
- java Write a recursive method largestDigitthat accepts an integer parameter and returns the largest digit value that appears in that integer. Your method should work for both positive and negative numbers. If a number contains only a single digit, that digit's value is by definition the largest. The following table shows several example calls: Call Value Returned largestDigit(14263203) 6 largestDigit(845) 8 largestDigit(52649) 9 largestDigit(3) 3 largestDigit(0) 0 largestDigit(-573026) 7 largestDigit(-2) 2 Obey the following restrictions in your solution: You may not use a String, Scanner, array, or any data structure (list, stack, map, etc.). Your method must be recursive and not use any loops (for, while, etc.). Your solution should run in no worse than O(N) time, where N is the number of digits in the number.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(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…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…
- Using JAVA Recursive Power Method Write a method called powCalthat uses recursion to raise a number to a power. The method should accept two arguments: The first argument is the exponentand the second argument is the number to be raised(example”powCal(10,2)means2^10). Assume that the exponent is anonnegative integer. Demonstrate the method in a program called Recursive (This means that you need to write a program that has at least two methods: mainand powCal. The powCal method is where you implement the requirements above and the main method is where you make a method call to demonstrate how your powCalmethod work).Java - How many recursive calls will be made if the following method is called with 6? void greeting(int n) { system.out.println(“Hello!”); greeting(n-1); }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,…