Suppose that it takes 0.004 seconds to run a program on a test data set of size n = 200. Assume that the number of items in the actual data set is 4000. What would be the expected run time (show your work) if the program is applied to the actual data set and the underlying algorithm is: a) 0(n) b) 0(n2)
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- Suppose that it takes 0.004 seconds to run a program on a test data set of size n = 200. Assume that the number of items in the actual data set is 4000. What would be the expected run time (show your work) if the program is applied to the actual data set and the underlying
algorithm is:
a) 0(n)
b) 0(n2)
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- A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k – 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 26? For each integer n 2 1, let s, -1 be the number of operations the algorithm executes when it is run with an input of size n. Then s, = and s = for each integer k 2 1. Therefore, So, S1, S21 -Select--- with constant Select--- |, which is So, for every integer n 2 0, s, It follows that for an input of size 26, the number of ... is operations executed by the algorithm is s which equals ---Select--- v2) A computer science student designed two candidate algorithms for a problem while working on his part-time job The time complexity of these two algorithms are T1(n) = 3 n log n and T2(n) = nº/5 . a) Which algorithm is better? Why? b) If we run both algorithms at the same time with an input size of 105, which algorithm produces results faster than the other one? Why?A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k - 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 24? For each integernz 1, let s,-1 be the number of operations the algorithm executes when it is run with an input of size n. Then for each integer 2 1. Therefore, So, S3. Sz. is -Select- and s,= with constant Select- ,which is . So, for every integer n 2 0, s, = It follows that for an input of size 24, the number of operations executed by the algorithm is s -Select-v which equals Need Heln? Desd
- I. Compute for the running time for each algorithm 1. for i = 1 to n do Statement B 2. for(j=1; js n*n*n;j++) for (k=1; ksn) Statement f; for(m=1;mA computer science student designed two candidate algorithms for a problem while working on his part-time job The time complexity of these two algorithms are T,(n) = 3 n logn and T2(n) = n6/5 a) Which algorithm is better? Why? b) If we run both algorithms at the same time with an input size of 105, which algorithm produces results faster than the other one? Why?Design an algorithm to find the kth number such that the only prime factors are 3, 5, and 7. Note that 3, 5, and 7 do not have to be factors, but it should not have any other prime factors. For example, the first several multiples would be (in order) 1, 3, 5, 7, 9, 15, 21.Let A be an algorithm which has an execution time O (N5), where N is the size of the entry. Which of the following statements is NOT true about Algorithm A? Question 3 options: For any N, there may be entries for which the execution time is greater than N4 seconds. For any N, there may be entries for which the execution time is greater than N6 seconds. For any N, there may be entries for which the execution time is less than N4 seconds. For any N, there may be entries for which the execution time is less than N6 seconds. There are constants A and B such that for all N the execution time is less than A × N5 + B seconds.Q2. The following algorithm returns the product of two numbers, a and b. The parameters x and y are natural numbers. First, prove the correctness of the algorithm. Then, analyze the time complexity of the algorithm in the worst case scenario. function mult (a, b) if b = 0: return 0 else if b is odd: return (mult (2a, b/2 ) +a) else: return (mult (2a, b/2 ) )Theory Of Computation.. Write pseudocode for an algorithm relies on R to find the lowest cost ticket. You may assume that $0 is the lowest possible price.Consider the following pseudo-code algorithm: S := 0 for i := 1 to n for j := 1 to i s := s+j· (i – j+1) next j next i 1. Make a table or list that calculates how many iterations of the inner for loop there are for each iteration of the outer loop. (That is, when i = 1, how many “j" loops will occur? How about when i = 2? Etc.)In computer science and mathematics, the Josephus Problem (or Josephus permutation) is a theoretical problem. Following is the problem statement: There are n people standing in a circle waiting to be executed. The counting out begins at some point (rear) in the circle and proceeds around the circle in a fixed direction. In each step, a certain number (k) of people are skipped and the next person is executed. The elimination proceeds around the circle (which is becoming smaller and smaller as the executed people are removed), until only the last person remains, who is given freedom. Given the total number of persons n and a number k which indicates that k-1 persons are skipped and kth person is killed in circle. The task is to choose the place in the initial circle so that you are the last one remaining and so survive. For example, if n = 5 and k = 2, then the safe position is 3. Firstly, the person at position 2 is killed, then person at position 4 is killed, then person at position 1…Let w(n) and A(n) denote respectively, the worst case and average case running time of an algorithm executed on an input of size n. which of the following is ALWAYS TRUESEE MORE QUESTIONS