QUESTION 25 Four algorithms have the following complexity functions: fin)=2n2(log,(n) + 1) fan) = 2" +n? +n fan) = 10n(n? + 2n + 1) faln) =n?(3+ yn) Under very large n. which of the following ordering does represent ordering of those algorithms from the fastest to the slowest? O f3,fa.f2. f1 fa.f.fa f2 O f2. fa: fa fı O f2. fa. fafi
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- 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?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 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?
- 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 13What is the leading term for the following expressions and specify the lowest Big O Complexity for each algorithm?Write an efficient algorithm for the following problem, and describe your reasoning. Determine the Time complexity and if you cannot find any polynomial time algorithm, then give a backtracking algorithm. Problem: Tower of Hanoi with Every Tower having some Disks Input: Each of the three towers contains roughly n/3 disks. Tower A contains floor(n/3) largest disks. Tower C contains ceiling(n/3) smallest disks. Tower B contains the remaining disks. The disks at each tower are already sorted according to the typical Tower of Hanoi rule. Output: A set of moves that transfers all the n disks to C maintaining the Tower of Hanoi rule that after each move, the smaller disks at a tower will always be above the larger ones.
- You will analyze three algorithms to solve the maximum contiguous subsequence sum problem, and then evaluate the performance of instructor-supplied implementations of those three algorithms. You will compare your theoretical results to your actual results in a written report. What is the maximum contiguous subsequence sum problem? Given a sequence of integers A1, A2, ..., An (where the integers may be positive or negative), find a subsequence Aj, ... , Ak that has the maximum value of all possible subsequences. The maximum contiguous subsequence sum is defined to be zero if all of the integers in the sequence are negative. Consider the sequence shown below. A1: -2 A2: 11 A3: -4 A4: 13 A5: -5 A6: 2 The maximum contiguous subsequence sum is 20, representing the contiguous subsequence in positions 2, 3, and 4 (i.e. 11 + (-4) + 13 = 20). The sum of the values in all other contiguous subsequences is less than or equal to 20. Consider a second sequence, shown below. A1: 1…Select the asymptotic worst-case time complexity of the following algorithm:AlgorithmInput: a1, a2, ..., an, a sequence of numbersn, the length of the sequencex, a numberOutput: ??For i = 1 to n-1For j = i+1 to nFor k = 1 to nIf ((ai)^2 + (aj)^2 = (ak)^2) Return( "True" )End-forEnd-forEnd-forReturn( "False" )a. ?(1)b. ?(?)c. ?(?2)d. ?(?3)Solve This D&AOA Question. Analyze your algorithm and find its complexity class.
- 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..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?(a) What “better-known”/simpler complexity class is equivalent to O(N log N2); briefly explain why. (b) Explain under what conditions sorted(set(l)) runs faster than set(sorted(l)) for a list l (they both produce the same answer); state the worst-case complexity class of each.