1.) T(n) = T(n/3) + c f(n) = versus nlog, a = Which is growing faster: f(n) or nlos, a? Which case of the Master Theorem does that potentially put us in? If you're potentially in case one or three, is it possible to find an epsilon which makes either f(n) = O(nlogs a-) (if you're in case one) or f(n) = N(nlossa+e) (if you're in case three) true? Choose one or show an inequality. If you're potentially in case three and there is an e, try to find a constant d < 1 such that af (n/b) ≤df (n) for large enough n's. What can you conclude?

Q: There are N frogs (numbered 1 through N) in a line. For each valid i, the i-th frog is initially at…

A: Algorithm: At first, we have to take the input of the scenario. Then we will develop the main logic…

Q: Let f,g:Z+⟶R, and f(n)=nlog2(n) forn∈Z+.  For which function g(n)below is f∉O(g)

A: The answer is given below step.

Q: There are N frogs (numbered 1 through N) in a line. For each valid i, the i-th frog is initially at…

A: Read the number of test cases. For each test case, read the number of frogs and their weights and…

Q: Practice Exercise # 3: For each of the following recurrences, give an expression for the runtime T…

A: Masters Theorem It is a beneficial technique for fixing recurrence equations as it immediately…

Q: If two functions f(n) and g(n) grow at the same rate asymptotically, what else can we say about…

A:

Q: Big-O notation is defined as follows: The function f(n) is O(g(n)) if there are positive integers c…

A: Answer :-

Q: Consider the function f:N×N¬N defined recursively by: 1) Base case: Let meN and define 0,m) = 0 2)…

A: ANSWER: Leave the assertion alone P(n): f(n,3*m)= 3*f(n,m) given f(0,m)=0 and f(x,m)= f(x-1,m)+m.…

Q: Let f(n) y g(n) two positive asymptotic functions. Prove or disprove the following conjectures: a)…

A:

Q: • For each of the following pairs of functions, either f(n) is O(g(n)), f(n) is Q(g(n)), or f(n) =…

A: The fundamental thought of asymptotic examination is to have a proportion of the effectiveness of…

Q: 2. Draw the K-Map and give the minimized result from the following Boolean function: Z= f(A,B,C) =…

A:

Q: 4. f(n) = O(g(n)) implies g(n) = N(f(n)) 5. f(n) = O((f(n))²)

A: Solution: We provided solution for your equation:

Q: Prove the following by induction, substitution, or by definition that 13n+ 10 = O(n²). Definition of…

A: Big O means worst case time complexity and it is the tightest upper bound of the function. That…

Q: Let A = {(N1, N2) | N1 and N2 are NFAS and L(N1)N L(N2) = Ø}. Show that A is %3D decidable.

A: Given that, A={ &lt;N1, N2&gt; | N1 and N2 are NFAs and L(N1)∩L(N2)=∅} That means N1 and N2 are…

Q: 1. f(n) = O(g(n)) implies g(n) = O(f(n)) 2. f(n)+g(n) = (min(f(n), g(n))) 3. f(n) = (f())

A: Solution: We have to prove and disprove each of the following. 1. f(n) = O(g(n)) implies g(n) =…