Algorithms:
Please explain each step! Thanks!
Algorithms: Please explain each step! Thanks! (20 points) Use the Master Theorem to solve the following...
5) For each of the following recurrences state whether the Master theorem can be applied to solve the recurrence or not. If the Master theorem can be used, then use it to determine running time for the recurrence. If the Master theorem cannot be applied, then specify the reason (you don't need to solve the recurrence). a) T(n) = 4T(n/3)+n2
1. [12 marks] For each of the following recurrences, use the “master theorem” and give the solution using big-O notation. Explain your reasoning. If the “master theorem” does not apply to a recurrence, show your reasoning, but you need not give a solution. (a) T(n) = 3T(n/2) + n lg n; (b) T(n) = 9T(3/3) + (n? / 1g n); (c) T(n) = T([n/41) +T([n/4])+ Vn; (d) T(n) = 4T([n/7])+ n.
4. (20 points) For each of the following recurrences, give an expression for the runtime T(n) if the recurrence can be solved with the Master Theorem. Otherwise, explain why the Master Theorem does not apply. Justify your answer (1) T(n) = 3n T(n) + n3 (2) T(n)-STC)VIOn* (3 Tn)T)+ n logn (4) T(n) T(n-1) + 2rn (5) T(n) 16TG)+n2
Using the Master Theorem discussed in class, solve the following recurrence relations asymptotically. Assume T(1) = 1 in all cases. (a) T(n) = T(9n/10) + n (b) T(n) = 16T(n/4) + n^2 (c) T(n) = 7T(n/3) + n^2 (d) T(n) = 7T(n/2) + n^2 (e) T(n) = 2T(n/4) + √n log^2n.
Recurrence equations using the Master Theorem: Characterize each of the following recurrence equations using the master method (assuming that T(n) = c for n < d, for constants c > 0 and d > = 1). T(n) = c for n < d, for constants c > 0 and d greaterthanorequalto 1). a. T(n) = 2T(n/2) + log n b. T(n) = 8T(n/2) + n^2 c. T(n)=16T(n/2) + (n log n)^4 d. T(n) = 7T(n/3) + n
Question 6 (20 points) Solve the following recurrences using the Master Theorem. T(n) = 2T (3/4)+1 T(n) = 2T (n/4) + va 7(n) = 2T (n/4) +n T(n) = 2T (3/4) + n
Given the following find-min function, write the recurrence and solve it using the master theorem. Assume the worst case, i.e. the tree is imbalanced and skewed to the left. int find_min (TreeNode* tree) // returns the minimum value in a binary search tree { if (tree == NULL) throw (EmptyTreeException()); else if (tree -> left == NULL) return(tree->info); else { return find_min(tree->left); } }
Subject: Algorithm solve only part 4 and 5 please. need urgent. 1 Part I Mathematical Tools and Definitions- 20 points, 4 points each 1. Compare f(n) 4n log n + n and g(n)-n-n. Is f E Ω(g),fe 0(g), or f E (9)? Prove your answer. 2. Draw the first 3 levels of a recursion tree for the recurrence T(n) 4T(+ n. How many levels does it have? Find a summation for the running time. (Extra Credit: Solve it) 3. Use...
Write a recurrence relation describing the worst case running time of each of the following algorithms, and determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution by using substitution or a recursion tree. You may NOT use the Master Theorem. Simplify your answers, expressing them in a form such as O(nk) or (nklog n) whenever possible. If the algorithm takes exponential time, then just give an exponential lower bound using the 2 notation. function...
1. Solve the recurrence relation T(n) = 2T(n/2) + n, T(1) = 1 and prove your result is correct by induction. What is the order of growth? 2. I will give you a shortcut for solving recurrence relations like the previous problem called the Master Theorem. Suppose T(n) = aT(n/b) + f(n) where f(n) = Θ(n d ) with d≥0. Then T(n) is: • Θ(n d ) if a < bd • Θ(n d lg n) if a = b...