1. How many recursive calls the Recursive Memoization Version of the Fibonacchi Recursion will take to calculate F (6)? 8 9.
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A: Question :- find gcd of two number taken from user in recursive manner
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- Recursion can be direct or indirect. It is direct when a function calls itself and it is indirect recursion when a function calls another function that then calls the first function. To illustrate solving a problem using recursion, consider the Fibonacci series: - 1,1,2,3,5,8,13,21,34...The way to solve this problem is to examine the series carefully. The first two numbers are 1. Each subsequent number is the sum of the previous two numbers. Thus, the seventh number is the sum of the sixth and fifth numbers. More generally, the nth number is the sum of n - 2 and n - 1, as long as n > 2.Recursive functions need a stop condition. Something must happen to cause the program to stop recursing, or it will never end. In the Fibonacci series, n < 3 is a stop condition. The algorithm to use is this: 1. Ask the user for a position in the series.2. Call the fib () function with that position, passing in the value the user entered.3. The fib () function examines the argument (n). If n < 3…Suppose you are given two integer values x and y. Construct a recursive algo-rithm that uses any combination of the following operations: addition, subtraction, comparison. Calculate the remainder of x divided by y. Specify a set ofexample values for x and y which will result in at least 3 or more recursive calls,and draw the recursion trace diagram for your example.The Tower of Hanoi is a puzzle where n disks of different sizes arestacked in ascending order on one rod and there are two other rods with nodisks on them. The objective is to move all disks from the first rod to thethird, such that:- only one disk is moved at a time- a larger disk can never be placed on top of a smaller oneWrite a recursive function that outputs the sequence of steps needed tosolve the puzzle with n disks.Write a test program in C++ that allows the user to input number of disks andthen uses your function to output the steps needed to solve the puzzle.Hint: If you could move up n−1 of the disks from the first post to thethird post using the second post as a spare, the last disk could be moved fromthe first post to the second post. Then by using the same technique you canmove the n−1 disks from the third post to the second post, using the firstdisk as a spare. There! You have the puzzle solved. You only have to decidewhat the nonrecursive case is, what the recursive…
- using recursion please8. Give a recursive definition of the sequence {an}, n =1, 2, 3, ... ifa) an = 4n − 2. b) an = 1 + (−1)n.c) an = n(n + 1). d) an = n2.Question) What are the rules for writing a recursive algorithm? a) Base case needs to be tested first b) Reduction should solve a problem with smaller size. c) We should always attempt reducing the problem to a smaller problem. d) The problem should be divided into two equal parts, otherwise recursion will not work. a) only a) and b) a), b), and c) a), b), c), and d)
- g1 = 5 g2 = 6 for k in range(3,8): gk = (k-1)·gk-1 + gk-2 What is the last term, g8, of the recursive sequence generated as a result of executing this algorithm?The first examples of recursion are the mathematical functions factorial and fibonacci. These functions are defined for non-negative integers using the following recursive formulas:factorial(0) = 1factorial(N) = N*factorial(N-1) for N > 0fibonacci(0) = 1fibonacci(1) = 1fibonacci(N) = fibonacci(N-1) + fibonacci(N-2) for N > 1Write recursive functions to compute factorial(N) and fibonacci(N) for a given non-negative integer N, and write a main() routine to test your functions.(In fact, factorial and fibonacci are really not very good examples of recursion, since the most natural way to compute them is to use simple for loops. Furthermore, fibonacci is a particularly bad example, since the natural recursive approach to computing this function is extremely inefficient.)Everyday we experience some variety of recursion in our lives. Please give an example with (pusedo code) on how paying your monthly bills can be coded into a recursion algorithm.
- Which recursive sequence would produce the sequence 6,−9,21,...6,−9,21,...?The recursive Fibonacci function is inefficient becausea) it does many repeated computationsb) recursion is inherently inefficient compared to iterationc) calculating Fibonacci numbers is intractabled) fibbing is morally wrongA recursive sequence is defined by - d k = 6 d k − 1 + 3 , for all integers k ≥ 2 and d1 = 2 Use iteration to guess an explicit formula for the above sequence.