How would I prove that log2(32n) = O(n) (Big Oh of N) I got: 2 log2(3)...
How would I prove that log2(32n) = O(n) (Big Oh of N)
I got: 2 log2(3) n <= c * n , however, I do not know how to continue from this part.
Thanks
Homework Answers
big-O Definition: ---------------------- f(n) = O(g(n)) means there are positive constants c and k, such that 0 ≤ f(n) ≤ cg(n) for all n ≥ k. The values of c and k must be fixed for the function f and must not depend on n. 2 log2(3) n <= c * n Lets take f(n) = 2 log2(3) n and g(n) = n The above statement is true for all the values of c = 2 log2(3) = 3.169925001442312 and n > 0 So, we can say that f(n) = O(g(n)) 2 log2(3) n = O(n)
Add Answer to:
How would I prove that log2(32n) = O(n)
(Big Oh of N)
I got: 2 log2(3)...
1. Prove that log2(n) is O(n) 2. Prove that log(n!) is O(n log(n))
1. Prove that log2(n) is O(n) 2. Prove that log(n!) is O(n log(n))
How can I go prove ( sqrt( (n+1)^3 ) ) is Big Omega (n * sqrt(n))...
How can I go prove ( sqrt( (n+1)^3 ) ) is Big Omega (n * sqrt(n)) using the formal definitions of Big Oh, Big Theta, and Big Omega?
Formal Definitions of Big-Oh, Big-Theta and Big-Omega: 1. Use the formal definition of Big-Oh to prove that if f(n) is...
Formal Definitions of Big-Oh, Big-Theta and Big-Omega:
1. Use the formal definition of Big-Oh to prove that if f(n) is a decreasing function, then f(n) = 0(1). A decreasing function is one in which f(x1) f(r2) if and only if xi 5 r2. You may assume that f(n) is positive evervwhere Hint: drawing a picture might make the proof for this problem more obvious 2. Use the formal definition of Big-Oh to prove that if f(n) = 0(g(n)) and g(n)...
Let f(n) = 5n^2. Prove that f(n) = O(n^3). Let f(n) = 7n^2. Prove that f(n)...
Let f(n) = 5n^2. Prove that f(n) = O(n^3). Let f(n) = 7n^2. Prove that f(n) = Ω(n). Let f(n) = 3n. Prove that f(n) =ꙍ (√n). Let f(n) = 3n+2. Prove that f(n) = Θ (n). Let k > 0 and c > 0 be any positive constants. Prove that (n + k)c = O(nc). Prove that lg(n!) = O(n lg n). Let g(n) = log10(n). Prove that g(n) = Θ(lg n). (hint: ???? ? = ???? ?)???? ?...
(a) Prove that n log^3 n is O(n^2). Prove that n^3 is not O(n^2 log n)....
(a) Prove that n log^3 n is O(n^2). Prove that n^3 is not O(n^2 log n). (b) The multi Pop (i) method pops i items from the top of a stack. Analyse the amortized complexity of the multiPop (i) method.
Prove each of the following using the definition of Big-Oh. a)(?+1)5is O(?5) b)2?+1is O(2?) c)If ?(?)is...
Prove each of the following using the definition of Big-Oh. a)(?+1)5is O(?5) b)2?+1is O(2?) c)If ?(?)is a polynomial in ?, then ????(?)is ?(log?)
Please explain big O. I don't get it Prove the following, using either the definition of...
Please explain big O. I don't get it
Prove the following, using either the definition of Big-O or a limit argument. (a) log_2 (n) elementof O(n/log_2(n)) (b) 2^n elementof O(n!) (c) log_2(n^2) + log_2 (100n^10) elementof O(log_2 (n)) (d) n^1/2 elementof O(n^2/3) (e) log(3n) elementof O(log(2n)) (f) 2^n elementof O(3^n/n^2)
Prove that if f (n) = O (g (n)) and g (n) = Ohm (h (n)),...
Prove that if f (n) = O (g (n)) and g (n) = Ohm (h (n)), it is not necessarily true that f(n) = O (h (n)). You may assume that low degree (i.e., low-exponent) polynomials do not dominate higher degree polynomials, while higher degree polynomials dominate lower ones. For example, n^3 notequalto O (n^2), but n^2 = O (n^3). Prove that if f (n) = O (g (n)) and g (n) = Ohm (h (n)), it is not necessarily...
1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark...
1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark 1729 is O(1) b) 3 marks 2n2-4n -3 is O(n2) 2. [3 marks] Using the definition of Big-Oh, prove that 2n2(n 1) is not O(n2) 3. 6 marks Let f(n),g(n), h(n) be complexity functions. Using the definition of Big-Oh, prove the following two claims a) 3 marks Let k be a positive real constant and f(n) is O(g(n)), then k f(n) is O(g(n)) b)...
in my c++ class i need help with these question please Question 1. Indicate whether the...
in my c++ class i need help with these question please Question 1. Indicate whether the first function of each of the following pairs has a smaller, same, or larger order of growth (to within a constant multiple) than the second function. Use the correct notation to indicate the order of growth (f(n) ∈O(g(n)), Ω(g(n)), or Θ(g(n)) as applicable). Prove your statement using limits. (a) (lnn)2 and lnn2 (b) 42n+1 and 42n Question 2. Use the formal definitions of O,...
Formal Definitions of Big-Oh, Big-Theta and Big-Omega:
1. Use the formal definition of Big-Oh to prove that if f(n) is a decreasing function, then f(n) = 0(1). A decreasing function is one in which f(x1) f(r2) if and only if xi 5 r2. You may assume that f(n) is positive evervwhere Hint: drawing a picture might make the proof for this problem more obvious 2. Use the formal definition of Big-Oh to prove that if f(n) = 0(g(n)) and g(n)...
(a) Prove that n log^3 n is O(n^2). Prove that n^3 is not O(n^2 log n). (b) The multi Pop (i) method pops i items from the top of a stack. Analyse the amortized complexity of the multiPop (i) method.
Please explain big O. I don't get it
Prove the following, using either the definition of Big-O or a limit argument. (a) log_2 (n) elementof O(n/log_2(n)) (b) 2^n elementof O(n!) (c) log_2(n^2) + log_2 (100n^10) elementof O(log_2 (n)) (d) n^1/2 elementof O(n^2/3) (e) log(3n) elementof O(log(2n)) (f) 2^n elementof O(3^n/n^2)
Prove that if f (n) = O (g (n)) and g (n) = Ohm (h (n)), it is not necessarily true that f(n) = O (h (n)). You may assume that low degree (i.e., low-exponent) polynomials do not dominate higher degree polynomials, while higher degree polynomials dominate lower ones. For example, n^3 notequalto O (n^2), but n^2 = O (n^3). Prove that if f (n) = O (g (n)) and g (n) = Ohm (h (n)), it is not necessarily...
1. [5 marks Show the following hold using the definition of Big Oh: a) 2 mark 1729 is O(1) b) 3 marks 2n2-4n -3 is O(n2) 2. [3 marks] Using the definition of Big-Oh, prove that 2n2(n 1) is not O(n2) 3. 6 marks Let f(n),g(n), h(n) be complexity functions. Using the definition of Big-Oh, prove the following two claims a) 3 marks Let k be a positive real constant and f(n) is O(g(n)), then k f(n) is O(g(n)) b)...
Most questions answered within 3 hours.
-
You follow the lab procedure and at the end of Part 4C, you used
an average...
asked 14 minutes ago -
Write 250-450 words, about the following: • Analyze how a
servant leader in your organization or...
asked 17 minutes ago -
3. American and Japanese workers can each produce 4 cars a
year. An American worker can...
asked 20 minutes ago -
On October 1, 20X1, a company purchased a piece of land by
agreeing to pay the...
asked 32 minutes ago -
Jamie is doing a survey at her school about whether the students
feel the cafeteria food...
asked 37 minutes ago -
What are the roles of 3' and 5' untranslated regions in
mRNAs?
asked 39 minutes ago -
A domestic television receives antenna delivers a sky noise
power of -105 dBm to a matched...
asked 37 minutes ago -
What do you think are the chemical reactions involved in the
breathalyzer tests administered to potentially...
asked 53 minutes ago -
A random sample of 120 observations produces a mean of
38.2 from a population with a...
asked 1 hour ago -
The average area of land burned by forest fires every year in
Canada is 2.5 million...
asked 1 hour ago -
36. The basic difference between government bureaus and market
firms is that bureaus:
a. can...
asked 1 hour ago -
java
- A recursive method findR() to search for a number in list
(ArrayList)
- A...
asked 1 hour ago