Question

Let H(n) = H(n/2) + log(n). Give matching upper and lower bounds for H(n) with the...

Let H(n) = H(n/2) + log(n). Give matching upper and lower bounds for H(n) with the following techniques:

1. Using a recursion tree

2. By substitution

3. Using the master theorem

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Give asymptotic upper and lower bounds for T .n/ in each of the following recurrences. Assume...
Give asymptotic upper and lower bounds for T .n/ in each of the following recurrences. Assume that T .n/ is constant for sufficiently small n. Make your bounds as tight as possible, and justify your answers. a) T(n) = T(n/2) +T(n/4)+T(n/8)+n b) T(n) = T(n-1) +1/n c) T(n)= T(n-1) +lg n d) T(n) = T(n-2) +1/lgn
Master Theorem: Let T(n) = aT(n/b) + f(n) for some constants a ≥ 1, b >...
Master Theorem: Let T(n) = aT(n/b) + f(n) for some constants a ≥ 1, b > 1. (1). If f(n) = O(n logb a− ) for some constant > 0, then T(n) = Θ(n logb a ). (2). If f(n) = Θ(n logb a ), then T(n) = Θ(n logb a log n). (3). If f(n) = Ω(n logb a+ ) for some constant > 0, and af(n/b) ≤ cf(n) for some constant c < 1, for all large n,...
Solve the following recurrence relations. If possible, use the Master Theorem. If the Master Theorem is...
Solve the following recurrence relations. If possible, use the Master Theorem. If the Master Theorem is not possible, explain why not and solve it using another approach (substitution with n = 3h or h - log3(n). a. T(n) = 7 * n2 + 11 * T(n/3) b. T(n) = 4 * n3 * log(n) + 27 * T(n/3)
3. Let x be a number between 400 and 900 (i.e. the lower and upper bounds...
3. Let x be a number between 400 and 900 (i.e. the lower and upper bounds for x are 400 and 900 respectively). • Anna knows that the remainder of dividing x over 11 is 10. • Bob knows that x ≡ 4 (mod 13). • Carl knows that x Mod 17 is equal to 13. a) Find x. b) Show that when only Anna and Bob share their information, we cannot find a unique solution for x. c) What...
Solve the following recurrences: (a) T(n) = T(n=2) + O(n), with T(1) = 1. Solve this...
Solve the following recurrences: (a) T(n) = T(n=2) + O(n), with T(1) = 1. Solve this two times: one with the substitution method and one with the master theorem from CLRS. When you use the master theorem, carefully show the values for the parameters a; b. For the following cases you can use your preferred method. In either case, show your work: (b) T(n) = 2T(n/2) + O(1), T(1) = 1. (c) T(n) = 3T(n/2) + O(1), T(1) = 1....
How do you find the margin of error from the lower and upper bounds of a...
How do you find the margin of error from the lower and upper bounds of a confidence interval? [1 sentence] What is the effect of increasing the standard deviation on the margin of error? [2 sentences] Why does increasing the confidence level result in a larger margin of error? [2 sentences] Why would you be more likely to use a T-interval in a real-world situation than a Z-interval? [2 sentences] When do you use the t-distribution to determine the confidence...
Let h(n) = n3 − 8n2 + 75. Give a careful proof, using the definition on...
Let h(n) = n3 − 8n2 + 75. Give a careful proof, using the definition on page 48, that h(n) is in Ω(n2).
1. y=∫upper bound is sqrt(x) lower bound is 1, cos(2t)/t^9 dt using the appropriate form of...
1. y=∫upper bound is sqrt(x) lower bound is 1, cos(2t)/t^9 dt using the appropriate form of the Fundamental Theorem of Calculus. y′ = 2. Use part I of the Fundamental Theorem of Calculus to find the derivative of F(x)=∫upper bound is 5 lower bound is x, tan(t^4)dt F′(x) = 3. If h(x)=∫upper bound is 3/x and lower bound is 2, 9arctan t dt , then h′(x)= 4. Consider the function f(x) = {x if x<1, 1/x if x is >_...
Determine the convergence/divergence of the following series using the integral test: a.) ∑= (1)/n(In(n))^2 (Upper limit...
Determine the convergence/divergence of the following series using the integral test: a.) ∑= (1)/n(In(n))^2 (Upper limit of sigma is ∞ ,and the lower limit of sigma is n=2) b.) ∑ (n-4)/(n^2-2n+1) (Upper limit of sigma is ∞ and the lower limit of the sigma is n=2 c.)∑ (n)/(n^2+1) (Upper limit of sigma ∞ and the lower limit sigma is n=1) d.) ∑ e^-n^2 (Upper limit of sigma ∞ and the lower limit sigma is n=1)
Analysing Asymptotic Bounds (Marks: 3) Prove the following using the definition of asymptotic order notation. Example:...
Analysing Asymptotic Bounds (Marks: 3) Prove the following using the definition of asymptotic order notation. Example: 15n 3 + 10n 2 + 20 ∈ O(n3 ) Hint: Consider C = 15 + 10 + 20 = 45 and n0 := 1. Then 0 ≤ 12n 3 + 11n 2 + 10 ≤ Cn3 for all n ≥ n0. a) n 2 + 3n 2 /(2+cos(n)) ∈ O(n 2 ) b) 2n 2 (log n) ∈ Ω(n(log n) 2 ) c)...