1. Find out the complexity of following algorithm 1. For I=1 to n 2. For J=1 to n 3. k= b[I] F = Linear_search(a,k) 4. 5. Print F 6. J=J*2
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![1. Find out the complexity of following algorithm
1. For I=1 to n
2.
For J=1 to n
k= b[I]
F = Linear_search(a,k)
3.
4.
5.
Print F
6.
J=J*2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd636ab5-23a0-4c65-8901-a05f53b89842%2F62cbdd74-fbf8-4f65-8553-076666a976d9%2Fpi3d1us_processed.jpeg&w=3840&q=75)
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- please answer with proper explanation and step by step. don't give Direct answer. Question: If an algorithm takes n^2 operations, and the computer can perform 100 billion operations per second, what is a reasonable estimate of how long it will take to sort 2 billion elements (assuming there is ample memory, the computer doesn't crash, etc.)? a. 1 second b. 1 minute c. 1 hour d. 1 day e. 1 month f. 1 year g. 1 decade h. 1 centuryQuestion 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: AnswerQ10. 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?
- Modeling the spread of a virus like COVID-19 using recursion. Let N = total population (assumed constant, disregarding deaths, births, immigration, and emigration). S n = number who are susceptible to the disease at time n (n is in weeks). I n = number who are infected (and contagious) at time n. R n = number who are recovered (and not contagiuous) at time n. The total population is divided between these three groups: N = S n + I n + R n There are several hidden assumptions here that may or may not apply to COVID-19, such as a recovered person is assumed to not be able to get the disease a second time, at least within the time window being examined. On week 0 (the start), you assume a certain small number of people have the infection (just to get things going). Everyone else is initially susceptible, and no one is recovered. There are two constants of interest: Let period = time period that it takes for an infected person to recover (recover meaning they become not infectious to…Consider the following non-recursive algorithm:Algorithm Euclid2(m, n)//Input: Integers m and n where m >=n//Output: Greatest Common Divisor of m and nwhile n ≠ 0 do r ← m mod n m← n n ← r return ma) What does this algorithm compute?b) What is the input size for this algorithm?c) What is the basic operation of this algorithm?d) How many times the basic operation is executed worst case scenario?e) How many times the basic operation is executed in best-case scenario?Consider the following algorithm and answer the following questions. procedure Algo1(a1, a2, . . . , an: integers) k := 0 for i := 1 to n if ai is even then k := i return k{k is the desired location(or 0 if there are no evens)} What does the given algorithm compute??? Execute the given algorithm and complete the following table by using the list 3, 5, 8, 10, 5, 2, 1, 7, 3, 13. i ai k 1 3 2 5 3 8 4 10 5 5 6 2 7 1 8 7 9 3 10 13
- Consider the following non-recursive algorithm: Algorithm Euclid2(m, n)//Input: Integers m and n where m >=n//Output: Greatest Common Divisor of m and nwhile n ≠ 0 do r ← m mod n m← n n ← r return m a) What does this algorithm compute?b) What is the input size for this algorithm?c) What is the basic operation of this algorithm?d) How many times the basic operation is executed worst case scenario?e) How many times the basic operation is executed in best-case scenario?There are situations in which a sequential search algorithm would be preferable, and there are others in which a binary search algorithm would be preferable, but what are some general guidelines for making this decision?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 ?1(?) = 3 ? log ? and ?2(?) = ? 6/5a) 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?
- Question 2 Q10. Consider the following algorithm: g1 = 8 g2 = 5 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?Please provide at least one example of an algorithm for each of the following complexity classes: log2n, n, n log2n, n2, n3, 2n, n!, Undecidable..Big-O notation. Suppose n is the input size, we have the following commonly seen functions in complexity analysis: f1(n) = 1, f2(n) = log n, f3(n) = n, f4(n) = n log n, f5(n) = n2, f6(n) = 2n, f7(n) = n!, f8(n) = nn. Intuitively, the growth rate of the functions satisfy 1 < log n < n < n log n < n2 < 2n < n! < nn. Prove this is true. Let f, g : N → R+, prove that Ω(f(n) + g(n)) = Ω(max{f(n), g(n)}). [Note: Proving this will help you understand that we can also leave out the insignificant parts in big-Ω notation and the result is still a lower bound, e.g., Ω(n2 + n log n + n) = Ω(n2).]
