Use the Master Method to solve the following three recurrence relations and 6. state the complexity orders of the corresponding recursive algorithms. (a) T(n) = 27(99n/100) + 100n (b) T(n) = 16T(n/2) + n°Ign (c) T(n) = 16T(n/4) + n2 %3!
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- Question 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: AnswerUse the Master Theorem to find the complexity class ( Θ notation ) of the following recurrences a) T(n) = 4T(n/2) + n3 b) T(n) = 4T(n/3) + n c) T(n) = 4T(n/3) + n2Lecture: Analysis of Algorithms >> Time Complexity and Recursion << Please consider the following function and determine the Big-O notation using recurrence relation. int fun(int n){ if (n == 0 || n == 1) return n; if (n%3 != 0) return 0; return fun(n/3); }
- 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?Using the substitution method, Prove that the running time of the following recursive relation is O(N) T(n) = T(n / 2) + T(7n / 10) + O(n)Data Structures and Algorithms Solve the following recurrence relations. x(n) = x(n − 1) + 5 for n > 1, x(1) = 0 x(n) = x(n − 1) + n for n > 0, x(0) = 0 x(n) = x(n/2) + n for n > 1, x(1) = 1
- Please explain!! Solve the recurrence: T(n)=2T(2/3 n)+n^2. first by directly adding up the work done in each iteration and then using the Master theorem. Note that this question has two parts (a) Solving IN RECURSION TREE the problem by adding up all the work done (step by step) andConsider a divide-and-conquer algorithm that calculates the sum of all elements in a set of n numbers by dividing the set into two sets of n/2 numbers each, finding the sum of each of the two subsets recursively, and then adding the result. What is the recurrence relation for the number of operations required for this algorithm? Answer is f(n) = 2 f(n/2) + 1. Please show why this is the case.Please explain Solve the recurrence: T(n)=2T(2/3 n)+n^2. first by directly adding up the work done in each iteration and then using the Master theorem. Note that this question has two parts (a) Solving IN RECURSION TREE the problem by adding up all the work done (step by step) and (b) using Master Theorem
- Provide the non-recursive implementation of the following Euclid algorithm.What is the running time of the algorithm?int gcd(int m, int n) { if (n == 0) return m; return gcd(n, m % n);}Design a divide-and-conquer algorithm for the problem of finding the longest sequence of consecutive negative numbers in a list of negative and positive numbers. Find the time complexity of your algorithm (type recurrence relation first). Example input: [2, 5, 0, -3, -5, 0, -1, -2, -1, 2]; Output: [-1, -2, -1] assum : In this example there are two consecutive sequences of negative numbers. [-3, -5] and [-1, -2, -1]. Since the second one is longer, that is the output.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?