Task 1 Count the number of vowels in a phrase using recursion only. You can think of this problem as "I can count the number of vowels in this phrase by counting the number of vowels in the first character, then counting the number of vowels in the rest of the phrase." We define a vowel as being A, E, I, O or U. This is one of those problems that can just as easily be solved with traditional programming structures such as a loop - but we're asking you to use recursion for the exercise. Consider: what replaces the loop structure? When will we stop recursion? Task 2 The constant e (Euler's number) is approximated by the following sequence: 1₁ 1+ + 1 1! 2! + ... + n! where the number of terms in the sequence is sufficient to generate the required precision in decimal places. We say that there is some value epsilon (e) such that, when the change in the approximation from one term to the next is less than said epsilon, we have reached sufficient precision. That is, when the term you're proposing to add is less than epsilon, you don't add it - you're already there. Write a recursive program to computer Euler's Number to an epsilon of 0.0000001 Check your results using an online tool like Wolfram Alpha. You will also need a helper method to compute the factorial of a number - this should also be done recursively.

For this exercise, you are going to write a recursive function that counts down to a Blastoff! Your recursive function will not actually print. It will return a String that can be printed from the main function. Each recursive call will add on to that string. In your main function, prompt the user for a starting value, then print the results. Sample Output Please enter a number to start: 5 5 4 3 2 1 Blastoff!     import java.util.Scanner; public class Countdown{public static void main(String[] args){// Start here}public static String countdown(int number){// Base case - return Blastoff!// Recursive call}}

The triangle.cpp ProgramDoes recursion actually work? If you run the triangle.cpp program, you’ll see that itdoes. The program uses recursion to calculate triangular numbers. Enter a value for the term number, n, and the program will display the value of the corresponding triangular number.  show the triangle.cpp program

Personal project Q5. This question is concerned with the design and analysis of recursive algorithms. You are given a problem statement as shown below. This problem is concerned with performing calculations on a sequence ? of real numbers. Whilst this could be done using a conventional loop-based approach, your answer must be developed using a recursive algorithm. No marks will be given if your answer uses loops. FindAverageAndProduct(a1, ...., an) such that n > 1 Input: A sequence of real values A = (a1, ..., an) Output:, A 2-tuple (average, product) containing the average (average) of all the values and the product (product) of all the values of the elements in A. Your recursive algorithm should use a single recursive structure to find the average and product values, and should not use two separate instances of a recursive design. You should not employ any global variables. (a) Produce a pseudo code design for a recursive algorithm to solve this problem.   (b) Draw a call-stack…

def height(words, word): The length of a word is easy enough to define by tallying up its characters. Taking the road less traveled, we define the height of the given word with a recursive rule for the height of the given word to follow from the heights of two words whose concatenation it is. First, any character string that is not one of the actual words automatically has zero height. Second, an actual word that cannot be broken into a concatenation of two nonempty actual words has the height of one. Otherwise, the height of an actual word equals one plus the larger of the heights of the two actual words whose combined concatenation it can be expressed as. To make these heights unambiguous for words that can be split into two non-empty subwords in multiple ways, this splitting is done the best way that produces the tallest final height. Since the list of words is known to be sorted, you can use binary search (available as the function bisect_left in the bisect module) to quickly…

ANSWER SHOULD BE WRITTEN IN JAVA CODE USING RECURSION Problem Statement Given a string as input return true or false depending on whether it satisfies these rules: 1) The string begins with an 'x' 2) Each 'x' is followed by nothing, 'x' or 'yy' 3) Each 'yy' is followed by nothing or 'x'

Written explaination required

in kotlin Write two versions of a recursive palindrome check function.  One version should have a block body, and the other should have an expression body.  Review the lecture slide about the substring function first.  Use this algorithm: if the length of the string is less than 2, return true else if the first and last characters are not equal (!=) return false else return the result of a recursive call with the substring from the second character (the one at index 1) to the second to last character. Use a main that uses a loop to test the palindrome function using this list of strings:     val ss = listOf("", "A", "AA", "AB", "AAA", "ABA", "ABB", "AAAA", "AABA", "ABBA", "ABCBA", "ABCAB")

The Eight Queen Problem is to find a solution to place a queen in each row on a chessboard such that no queens can attack each other. write a program to solve the eight queen problem using the recursion and display the result. Program in java

python 3 Write a program that lists all ways people can line up for a photo (all permutations of a list of strings). The program will read a list of one word names, then use a recursive method to create and output all possible orderings of those names, one ordering per line. When the input is: Julia Lucas Mia then the output is (must match the below ordering): Julia Lucas Mia Julia Mia Lucas Lucas Julia Mia Lucas Mia Julia Mia Julia Lucas Mia Lucas Julia question: is it any way that i can use ('if' statement as base case, and 'else' statement as recursive case) in the code below? thanks. code: def all_permutations(permList, nameList):# TODO: Implement method to create and output all permutations of the list of names.def createPermutationsList(nameList):f = len(nameList) if f == 0:return [] if f == 1:return [nameList] permList = [] for i in range(f):newList = nameList[i]remaining = nameList[:i] + nameList[i+1:]for p in createPermutationsList(remaining):permList.append([newList] + p)…