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- If your first name starts with a letter from A-J inclusively: Create a recursive algorithm to compute the product of two positive integers, m and n, using only addition and subtraction. Implement the Java or Python code. Hint: You need subtraction to count down from m or n and addition to do the arithmetic needed to get the right answer. Check linearSum method from Week 5 examples. If your first name starts with a letter from K-Z inclusively: Write a recursive method to produce the following pattern: * ** *** **** *** ** * Test the method by asking the user to enter the number of asterisks of the maximum line (for example, the user should enter 4 in this case).Which one is correct for the following snippet of code? def factorial1(x): if x== 0: return 1 return x *factorial1(x-1) def factorial2 (x,y=1): if x== 0: return y return factorial2 (x-1,x*y) Group of answer choices a) Both factorial1() and factorial2() aren’t tail recursive. b) Both factorial1() and factorial2() are tail recursive. c) factorial1() is tail recursive but factorial2() isn’t. d) factorial2() is tail recursive but factorial1() isn’t.Course: Algorithm Project: We will use the defintion of of n-Queens Problem from the chapter Backtracking. In this project you need to describe Problem and Algorithm and Indicate input and output clearly. Analyze and prove the time complexity of your algorithm. Implement the algorithm using backtracking(including writing testing case).illustrate key functions with comments indicating: What it does, what each parameter is used for, how it handles errors etc. Indicate the testing scenarios and testing the results in a clear way. Make sure source is commented appropriately and structured well.
- Find the complexity of the following blocks of code or algorithm’s description.[Note: your answer must show the steps that lead to your final answer] 1) The algorithm solves the problem ofsize n by recursively solving subproblems of size n – 1, and thencombining the solutions in constanttime.2) The algorithm solves the problemby breaking it into 16 subproblems of 1/4 the scale,recursively solving each submaze, and then combining thesolutions in linear time3) The algorithm solves the problem ofsize n by dividing it into 32 subproblems of size n/2, recursivelysolving each sub-problem, and thencombining the solutions in O(n5)timeDetermine how many times the innermost loop will be iterated when the following algorithm segment is implemented and run. (Assume that m, n, and p are positive integers.) for i:=1 to m for j :=1 to n for k = 1 to p [Statements in body of inner loop. None contain branching statements that lead outside the loop.] next k next j next iInstructions : Complete the tasks listed below. ask Lists Complete the body for the recursive method fac(n) which computes n! (n factorial) for n >= 0. Note: n! = n(n - 1) (n - 2) (n - 2)… (2) (1), where n > 0 and zero factorial, 0! = 1. Complete the body for the recursive method sum(n) to compute the sum of the first n positive integers. Complete the body for the recursive method pow(x,n) for computing xn, for a positive integer n, and real number x. Complete the body for the recursive method isPalindrome(str) to determine if a string of text is a palindrome. This method accepts a String and returns true if the string reads the same forwards as backwards. The string is trivially true for empty or one(1) letter strings. Hint: You should make use of the subtring and charAt methods of the String. Run the Viewer of the Sierpinski Triangles and give a description of what you observed as it relates to recursion. Write a short summary (2-3 sentences is enough) of your…
- # Exercise 1. Implement the algorithm covered in lectures that determines if an integer n is prime. Your function should return True, if n is prime, and False otherwise. Your algorithm has to be effective for n ~ 1,000,000,000,000.def isPrime(n):Algorithm problem w/ recurrence: Frying pancakes: a small pan can only hold two pancakes at a time. Each pancake needs to be fried on both sides. Frying one side takes 1 minute, no matter how many pancakes are on the pan. Consider this recursive algorithm: If n <= 2, fry the pancakes or the two pancakes together on each side. If n > 2, fry any two pancakes together on each side and then apply the same process recursively to the remaining n-2 pancakes. a. Set up and solve the recurrence for the amount of time this algorithm needs to fry n pancakes. b. Explain why this algorithm does not fry the pancakes in the minimum time for all n > 0. c. Give a correct recursive algorithm that executes the task in the minimum amount of time. > I was not sure how to start this. I have had trouble with recurrence in the past. Also from the work that I did do, I didn't know how there could be a better algorithm. Thanks in advanceFor the following problem please write an algorithm in plain English .i.e give details as to how you will solve the problem.A deck of 52 playing cards (as used for playing bridge) has to be sorted. At the end of the attempt, the sorted deck of cards should be on the table with the backside up.The order within a suite is Ace - King - Queen - Jack- 10 -9 - 8 - 7- 6- 5- 4- 3- 2. The very first card in the sorted deck is the Ace of Clubs, the next ones are the King of Clubs, the Queen of Clubs, the Jack of Clubs, the 10 of Clubs ... down to the 2 of Clubs. The next card is Ace of Spades, followed by the King of Spades etc. The hearts and diamonds cards follow in the same order.The deck of cards must be well-shuffled immediately prior to the challenge.Please write the algorithm in steps like you write a recipe for a dish.If any steps need to be repeated try to use a loop.Please try to not use any programming language.(IT's one question just with a lot of instructions to be understood well)
- Nuts and bolts You are given a collection of n bolts of different widths and n corresponding nuts. You are allowed to try a nut and bolt together, from which you can determine whether the nut is larger than the bolt, smaller than the bolt, or matches the bolt exactly. However, there is no way to compare two nuts together or two bolts together. The problem is to match each bolt to its nut. Design an algorithm for this problem with average-case efficiency in (n log n).Determine how many times the innermost loop will be iterated when the following algorithm segment is implemented and run. for i:= 8 to 60 for j = 10 to 30 [Statements in body of inner loop. None contain branching statements that lead outside the loop.] next j next i# Put the code below # consider using np.where() method to preprocess "Sex" column. # replace F in "Sex" F" with 1 and replace "M" with 0 # consider using the following condition: df['Sex'].values == 'F' # if this condition is met, put 1 otherwise 0. # Update the "Sex" column import numpy as np df['Sex'] = np.where() #complete this line of code by putting the appropriate code inside () df