(12 pts) Solve each of the following Do not only state your solution- Show how you...
Solve the following recurrences by repeatedly unrolling them, aka the method of substitution. You must show your work, otherwise you will lose points. Assume a base case of T(1) = 1. As part of your solution, you will need to establish a pat- tern for what the recurrence looks like after the k-th iteration. You must to formally prove that your patterns are correct via induction. Your solutions may include integers, n raised to a power, and/or logarithms of n....
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...
Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that T(n) is constant for n≤2. Make your bounds as tight as possible, and justify your answer. *Hint : You can use Master method to obtain Θ(.). (a) T(n) = 4T(n/4) + 5n (b) T(n) = 4T(n/5) + 5n (c) T(n) = 5T(n/4) + 4n (d) T(n) = 25T(n/5) + n^2 (e) T(n) = 4T(n/5) + lg n (f) T(n) = 4T(n/5) + lg^5 n...
3. Determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution using expansion/substitution and upper and/or lower bounds, when necessary. You may not use the Master Theorem as justification of your answer. Simplify and express your answer as O(n*) or O(nk log2 n) whenever possible. If the algorithm is exponential just give exponential lower bounds c) T(n) T(n-4) cn, T(0) c' d) T(n) 3T(n/3) c, T() c' e) T(n) T(n-1)T(n-4)clog2n, T(0) c' 3. Determine the...
solve using only one of the following methods: unrolling substitution, recurrence tree. Please show all your work! Please solve using only any of the following methods: unrolling substitution or recurrence tree (i.e tree diagram). Please show you. work! 74. |TCn3Tn-1)+ 1| if nz1, TCEB
Problem 2 Solve the following recurrences. You only need to obtain the asymptotic solution (in e) notation). If you use the master theorem, you must specify all parameters and briefly verify all conditions. 1. (5%) T(n) = 25T(F) + n2 +n, T(1) = 5.
(a) Solve using separation of variables. (Even if you already know the solution, show how to use separation of variables to find it.) Your solution should have one arbitrary constant. (b) Demonstrate that your solution satisfies the differential equation. You can do all relevant integrals in the problem by algebraic simplification, or with a u-substitution.
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.
r the recurrence relation o. Consider T(n) = Vn T(Vn) + n a. Why can't you solve this with the master theorem? b. S t involves a constant C, tell me what it is in terms of T(O), T(1), or whatever your inequality by induction. Show the base case. Then show the how that T( n)= 0(n lg ig n). First, clearly indicate the inequality that you wish to hen proceed to prove the inductive hypothesis inductive case, and clearly...
Please help me solve these problems, and show your work on the math related ones, thank you in advance! 12. A weatherman reports that the temperature will reach a high of 308.2 K. Your mother is freaking out about the weather report until you show her that 308.2K is equal to ... ^oC 13. If you plot a graph with Fahrenheit temperatures along the vertical axis and the corresponding Celsius temperatures along the horizontal axis, the slope of the will...