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- Q12: Assume that each of the expressions below gives the processing time T(n) spent by an algorithm for solving a problem of size n. Select the dominant term(s) having the steepest increase in n and specify the lowest Big-Oh complexity of each algorithm. For example, the dominant term in 0.1n + 10m'is 10n and it is O(n). Expression Dominant term(s) 0(...) 5+ 0.001n + 0.025n 500n + 100n'5 + 50n logio n 0.3n + 5n + 2.5 · n75 n° log,n + n(log, n) n log;n+n log, n 100n + 0.01n 0.01n + 100n18. What is the running time of the following algorithm? Input: The number n is a power of 2. 1: i = n 2: while i 1 do 3: 4: 5: 6: 7: end while 8: i = [i/2] 9: end while j=1 while j1. A runner targets herself to improve her time on a certain course by 3 seconds a day. If onday 0 she runs the course in 3 minutes, how fast must she run it on day 14 to stay ontarget?2. A certain computer algorithm executes twice as many operations when it is run with aninput of size k as when it is run with an input of size k − 1 (where k is an integer that isgreater than 1). When the algorithm is run with an input of size 1, it executes sevenoperations. How many operations does it execute when it is run with an input of size 25?1. A certain computer algorithm executes four times as many operations when it is run with an input of size n as when it is run with an input of size n – 1. Here, n > 1 is an integer. When the algorithm is run with an input of size 1, it executes 12 operations. How many operations does the algorithm execute when it is run with an input of size 5? How many operations does the algorithm execute when it is run with an input of size n?# 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):CS211 Non-recursive solution for Towers of Hanoi Using the algorithm discussed in class, write an iterative program to solve the Towers of Hanoi problem. The problem: You are given three towers a, b, and c. We start with n rings on tower a and we need to transfer them to tower b subject to the following restrictions: 1. We can only move one ring at a time, and 2. We may never put a larger numbered ring on top of a smaller numbered one. There are always 3 towers. Your program will prompt the user for the number of rings. Here is the algorithm. Definition: A ring is "available" if it is on the top of one of the towers. Definition: The "candidate" is the smallest available ring that has not been moved on the most recent move. The first candidate is ring 1. The Algorithm: 1. Find the candidate. 2. Move the candidate (right or left, depending if the number of rings is odd or even) to the closest tower on which it can be placed. Move "around the circle" if necessary. 3. If not done, go back…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 advanceNuts 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).4. Consider the following recursive algorithm. ALGORITHM Q(n) //Input: A positive integer n if n = 1 return 1 else return Q(n – 1) + 2 * n – 1 a. Set up a recurrence relation for this function's values and solve it to deter- mine what this algorithm computes. b. Set up a recurrence relation for the number of multiplications made by this algorithm and solve it. c. Set up a recurrence relation for the number of additions/subtractions made by this algorithm and solve it.Please code in JAVA implement and test the GET-MEMORY algorithm This algorithm uses the Next-Fit(First-Fit-With-A-Roving-Pointer) technique. then implement and test the FREE-MEMORY algorithm. Implement the “GET_MEMORY” and “FREE_MEMORY” algorithms. Comprehensive testing must be done for each algorithm. Following are sample run results for each: GET_MEMORY IS RUNNING……… Initial FSB list FSB# Location Size 1 7 4 2 14 10 3 30 20 . . . . . . Rover is 14 ---------------------------------------------------------------------------- Allocation request for 5 words Allocation was successful Allocation was in location 14 FSB# Location Size…calculate number of operations in this algorithm void my_dgemv(int n, double* A, double* x, double* y) { double alpha=1.0, beta=1.0; int lda=n, incx=1, incy=1; cblas_dgemv(CblasRowMajor, CblasNoTrans, n, n, alpha, A, lda, x, incx, beta, y, incy); }For funX |C Solved xb Answer x+ CodeW X https://codeworko... 田) CodeWorkout X267: Recursion Programming Exercise: Cumulative Sum For function sumtok, write the missing recursive call. This function returns the sum of the values from1 to k. Examples: sumtok(5) -> 15 Your Answer: 1 public int sumtok(int k) { 2. } (0 => ) return 0; 3. } else { return > 6. { Check my answer! Reset Next exercise 1:09 AMSEE MORE QUESTIONS