Data Structure and Algorithm in Java
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Data Structure and Algorithm in Java Question 1. (21 points) Solve the following recurrences using master...
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
Solve the following using iteration method. Note: T(1) = 1. 2. recurrences GE) T(п) 2T 2.1 3 Т(п) 2T (п — 2) + 5 2.2 Solve the following using Master Theorem. 3. recurrenсes T(п) log n n 4T .3 3.1 n 5T 2 n2 log n T(п) 3.2 Solve the following using iteration method. Note: T(1) = 1. 2. recurrences GE) T(п) 2T 2.1 3 Т(п) 2T (п — 2) + 5 2.2 Solve the following using Master Theorem. 3....
3. Solve the follwoing recurrences using the master method. (a) T(n) = 4T (n/2) + navn. (8 pt) (b) T(n) = 2T (n/4) + n. (8 pt) (c) T(n) = 7T(n/2) +n?. (8 pt)
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.
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.
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
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
Problem 1 Use the master method to give tight asymptotic bounds for the following recurrences. a) T(n) = T(2n/3) +1 b) T(n) = 2T("/2) +n4 c) T(n) = T(71/10) +n d) T(n) = 57(n/2) + n2 e) T(n) = 7T(1/2) + 12 f) T(n) = 27(1/4) + Vn g) T(n) = T(n − 2) +n h) T(n) = 27T(n/3) + n° lgn
Part A Analyze the following recurrences and show their time complexity functions using (I) iteration method and (2) Master Theorem. AI. T(n) = 2T 3 A2. T(n) = 3T 2n АЗ. Т(п) — Т(п — 2) + 3 А4. Т(п) — 2Т (п — 1) + 1 A5. T(n)= 4T +n log n A6. T(n) = 3T +n log n n2 A7. T(n) = 27 Part B Do 2.3-4 (р39) and Problem 2-1 (р39) Part C Implement MERGE-SORT() algorithm that...
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