Rohan is playing a game in his class in which he takes heights of two persons and then find the greatest common divisor of those heights. You have to help rohan by writing c code using recursion
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Rohan is playing a game in his class in which he takes heights of two persons and then find the greatest common divisor of those heights. You have to help rohan by writing c code using recursion
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- The word ladder game was invented by Lewis Carroll in 1877. The idea is to begin with a start word and then change one letter at a time until you arrive at an end word. Each word along the way must be an English word. For example, starting from FISH, you can arrive at MAST through the following word ladder:FISH, WISH, WASH, MASH, MAST Write a program that uses recursion to find the word ladder given a start word and an end word, or that determines no word ladder exists. Use the file words.txt that is available online with the source code for the book as your dictionary of valid words. This file contains 87,314 words. Your program does not need to find the shortest word ladder between words; any word ladder will do if one exists. list aalii aardvark aardvarks aardwolf aba abaca abaci abacist aback abacus abacuses abaft abalone abalones abamp abampere abandon abandoned abandonee abandoner abandonersDetermine whether a string is a palindromeA palindrome is a string of characters that reads the same from right to left as it does from left to right, regardless of punctuation and spaces.The specifications for this assignment are: •Write and test a non-recursive solution in Java that determines whether a string is a palindrome •Your program should consist of at least two methods: (1) the main method (2) the method which performs the task of determining whether the specified string is a palindrome. You should name this method isPalindrome. You should name the class that contains your “main” method and the isPalindrome method FindPalindrome. •You must use a Stack and a Queue in your solution: Write your own Stack and Queue based on the Vector in the Java API and use those in your solution. You should name those classes StackVector and QueueVector respectively. You already have access to the relevant exception classes and interfaces for the above ADTs. •All of your belong to a Java…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 n! where the number of terms in the sequence is sufficient to generate the required precision in decimal places. 1+ 2! + ... 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…
- In what instances do you think it’s impractical to use recursion over loops?Write a recursive function for int powerOfTwo (int k). The function determines the value of 2k. (Note: k is a positive integer). Example, when k=0 the function returns 1 and when k-3 the function returns 8. To show that your code is correct, give the recursive trace for powerOfTwo (2) that returns 4.Pascal's triangle is a useful recursive definition that tells us the coefficients in the expansion of the polynomial (x + a)^n. Each element in the triangle has a coordinate, given by the row it is on and its position in the row (which you could call a column). Every number in Pascals triangle is defined as the sum of the item above it and the item above it and to the left. If there is a position that does not have an entry, we treat it as if we had a 0 there. *picture of the pascals triangle* Given the following recursive function signature, write the recursive function that takes a row and a column and finds the value at that position in the triangle. Assume that the triangle starts at row 0 and column 0. Examples: pascal(2, 1) -> 2, pascal(1, 2) -> 0 public int pascal(int row, int column) { }
- This section is divided into two subsections. Each subsection contains a problem to be solved using both recursive and non-recursive approaches. You need to implement the solution in one of your preferred languages ( C++, or JAVA). In addition, you need to provide the order growth analysis and plot the input size vs. run-time graph for both approaches. The n th Triangle Problem Write a code for finding the n th triangle number of triangle sequences: 1, 3, 6, 10, ..., n. That is, your code should accept an integer number, which indicates the triangle levels, and returns how many dots we need to form a triangle with respect to the given level. For example, consider the Fig 1. For n = 3 (can be also written as T3), your code should returns 6. Provide a single program consists of the following: • Write a function called TriangularRecursive for the recursive version that takes number of level as an int argument. Hints: 1) Identify the base case for the TriangularRecursive function. 2) Let…Can you please help me with this coding problem WITHOUT USING RECURSION?Suppose you are working in the pizza company named Dominoes. Dominoes provides the best in class pizza in the world so While dealing with the coustomer you got a number on every billed amount. SO here your task is to identifiy that the billing amount is a magic number or not. A number is said to be a magic number, if the sum of its digits are calculated till a single digit recursively by adding the sum of the digits after every addition. If the single digit comes out to be 1,then the number is a magic number. Input : 1234Output : Yes it is Input : 12345Output : No it is not
- Ex. 01 : Recursion About So far, we have learned that we can perform repetitive tasks using loops. However, another way is by creating methods that call themselves. This programming technique is called recursion and, a method that calls itself within it's own body is called a recursive method. One use of recursion is to perform repetitive tasks instead of using loops, since some problems seem to be solved more naturally with recursion than with loops. To solve a problem using recursion, it is broken down into sub-problems. Each sub-problem is similar to the original problem, but smaller in size. You can apply the same approach to each sub-problem to solve it recursively. All recursive methods use conditional tests to either 1. stop or 2. continue the recursion. Each recursive method has the following characteristics: 1. end/terminating case: One or more end cases to stop the recursion. 2. recursive case: reduces the problem in to smaller sub-problems, until it reaches (becomes) the end…9. Ackermann's Function Ackermann's function is a recursive mathematical algorithm that can be used to test how well a computer performs recursion. Write a method ackermann (m, n), which solves Ackermann's function. Use the following logic in your method: If m = 0 then return n + 1 If n = 0 then return ackermann (m Otherwise, return ackermann(m 1, 1) 1, ackermann (m, n - 1))Write a recursive function (Java) called Fac which takes one positive integer argument (n) and returns n! You may not use a built-in factorial method or function.