(Sum series) Write a recursive method to compute the following series:
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- Exercise 1: (Design of algorithm to find greatest common divisor) In mathematics, the greatest common divisor (gcd) of two or more integers is the largest positive integer that divides each of the integers. For example, the gcd of 8 and 12 is 4. Why? Divisors of 8 are 1, 2, 4, 8. Divisors of 12 are 1, 2, 4, 6, 12 Thus, the common divisors of 8 and 12 are 1, 2, 4. Out of these common divisors, the greatest one is 4. Therefore, the greatest common divisor (gcd) of 8 and 12 is 4. Write a programming code for a function FindGCD(m,n) that find the greatest common divisor. You can use any language of Java/C++/Python/Octave. Find GCD Algorithm: Step 1 Make an array to store common divisors of two integers m, n. Step 2 Check all the integers from 1 to minimun(m,n) whether they divide both m, n. If yes, add it to the array. Step 3 Return the maximum number in the array.arrow_forward12 - question The following method is a recursive pow method to compute exponents, there is a logical error in this code. Please choose the line which has the error. 1. public static int pow (int x, int y) { 2. if (y>1) 3. return x * pow (x, y - 1); 4. else 5. return y; 6. } a. Line 2 b. Line 3 C. Line 4 d. Line 5arrow_forward(Mathematical Analysis of Recursive Algorithms) 9. Consider the following recursive algorithm for computing the sum of the first n cube: S(n) = 1³ +23³ +3³ +...+n³. Algorithm S(n) //Input: A positive integer n //Output: The sum of the first n cubes if n = 1 return 1 else return S(n − 1) +n*n*n a) Set up and solve a recurrence relation for the number of times the algorithm's basic operation is executed. b) How does this algorithm compare with the straightforward non-recursive algorithm for computing this function?arrow_forward
- Recursive Power MethodWrite a method called powCal that uses recursion to raise a number to a power. The method should accept two arguments: The first argument is the exponent and the second argument is the number to be raised (example” powCal(10,2) means 210). Assume that the exponent is a nonnegative integer. Demonstrate the method in a program called Recursive (This means that you need to write a program that has at least two methods: main and 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 powCal method work).arrow_forward4. CodeW. X b For fun X Solved x b Answer x+ Ohttps://codeworko... CodeWorkout X264: Recursion Programming Exercise: Multiply For function multiply,write the missing base case condition and action. This function will multiply two numbers x and y.You can assume that both x and y are positive. Examples: multiply(2, 3) -> 6 Your Answer: 1 public int multiply(int x, int y) { 2. if > { > } else { return multiply(x 1, y) + y; 3. 5. { 7. 1:08 AM 50°F Clear 日arrow_forwardJava 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)=1arrow_forward
- Which of the following statements are correct? Iteration is always worse than recursion. Recursion uses more memory than an iterative approach. Recursion uses less memory than an iterative approach. O Iterative function is always easier to write than recursion.arrow_forward2. Sum: a recursive function that computes the sum of integers 1, 2, 3, …., n for a given number n. So Sum(6) should return 1 + 2 + 3 + 4 + 5 + 6 , i.e. 21.sum(n) = n + sum(n-1)arrow_forwarda. Prompt the user to type a word on console and save the input into variable b. Implement recursive method(s) isPalindrome() to check if the given word is a palindrome and call it from the main(). c. Implement recursive method(s) theLength() to calculate the length of the given word (its number of characters) d. Display your results on console in the following format: "You word palindrome." consists of_ characters, this a e. Explain in comments the algorithms you use (how the recursion works, where is the base case, there is the recursive call(s), how you reduce the problem complexity).arrow_forward
- 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;}If the base case is replaced with “if(x = = 1) return 1;” the method will still compute the same thing.arrow_forwardExponent y Catherine Arellano mplement a recursive function that returns he exponent given the base and the result. for example, if the base is 2 and the result is 3, then the output should be 3 because the exponent needed for 2 to become 8 is 3 (i.e. 23 = 8) nstructions: 1. In the code editor, you are provided with a main() function that asks the user for two integer inputs: 1. The first integer is the base 2. The second integer is the result 2. Furthermore, you are provided with the getExponent() function. The details of this function are the following: 1. Return type - int 2. Name - getExponent 3. Parameters 1. int - base 2. int - result 4. Description - this recursive function returns the exponent 5. Your task is to add the base case and the general case so it will work Score: 0/5 Overview 1080 main.c exponent.h 1 #include 2 #include "exponent.h" 3 int main(void) { 4 int base, result; 5 6 printf("Enter the base: "); scanf("%d", &base); 7 8 9 printf("Enter the result: ");…arrow_forward7. Recursive Power Method In Python, design a function that uses recursion to raise a number to a power. The function should accept two arguments: the number to be raised, and the exponent. Assume the exponent is a nonnegative integer.arrow_forward
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