Trace Recursive algorithms when it is given m = 7,n = 10 and b = 2 as input. That is show all the steps Algorithm uses to find 210mod 7. Trace Recursive Algorithms when it finds gcd (126,660). That is show all the steps used by algorithm to find gcd (126,660). Trace Recursive Algorithm when it is given n = 7 as input. That is show all steps used by algorithm to find 7!.
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- Assume that for each number I n is not 2. How could the algorithm be modified to handle the situation where n is odd? I have two approaches: one that directly adjusts the recursive method and the other that mixes the iterative and recursive approaches. Just one of the two tasks must be completed (as long as it works and does not increase the BigOh of the running time.)Suppose a recursive algorithm performs 2 recursive calls. Assume the first recursive call isof size at most 70% the original input size, and the second call is of size at most 25% of theoriginal input size. In addition, the algorithm performs O(n) additional work after makingthese recursive calls. What is the big-Oh run time of this algorithm?Let n be a positive integer and let MaxCrossing(n) be a function that returns the maximum number of line crossings that you can create by drawing n straight lines. Write down a recursive formula for MaxCrossing(n) and analyze the time complexity of the corresponding recursive algorithm. You must write a formal recursive formula including the base case and general recursive step.
- 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)Q10. Consider the following algorithm: g1 = 7 g2 = 6 For k starting at 3 and ending with 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?Exercise 2. Give a recursive definition for the factorial operation k! n! for n ≥ 1. (remember that 1! = 0! = 1) Provide an algorithm in pseudo code to evaluate k! n! as one function Provide an algorithm in pseudo code to evaluate k! n! as three functions Evaluate the complexity of the algorithm at point 2 Evaluate the complexity of the algorithm at point 3
- Question 2 Consider the following algorithm: g1 = 7 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? Your Answer: Question 2 options: Answersuppose that n is not 2i for any integer i. How would we change the algorithm so that it handles the case when n is odd? I have two solutions: one that modifies the recursive algorithm directly, and one that combines the iterative algorithm and the recursive algorithm. You only need to do one of the two (as long as it works and does not increase the BigOh of the running time.)A game is played by moving a marker ahead either 2 or 3 steps on a linear path. Let cn be the number of different ways a path of length n can be covered. Given, Cn =Cn-2 + Cn-3, Ci=0, c2=1, c3=1 Write a recursive algorithm to compute Cn.
- In a Collatz sequence, all of its terms are positive integers which satisfy the following recursive formula an=0.5an−1 if an−1 is even an=3an−1+1 if an−1 is odd Directions: Given an initial term implement a Collatz sequence, and find its length.Input: a1Output: the length of the Collatz sequence Don't use some sort of menu loop to get user inputUse recursion tree to guess a bound, then proof it using induction. Finally, use master theorem (if applicable) to directly get the bound. Try to make your bounds as tight as possible. T(n) = 2T(n/2) + n T(n) = 2T(n-2) + nTiling: The precondition to the problem is that you are given threeintegers n, i, j, where i and j are in the range 1 to 2n. You have a 2n by 2n squareboard of squares. You have a sufficient number of tiles each with the shape . Your goalis to place nonoverlapping tiles on the board to cover each of the 2n × 2n tiles except forthe single square at location i, j. Give a recursive algorithm for this problem in whichyou place one tile yourself and then have four friends help you. What is your base case?