What is the tightest big-O of 1/1+ 1/2+1/3+...+1/n2? Recall that for any base b, we have log, n = k log, n (this fact.may or may not be useful to get the answer). %3D A) O(1) B) O(n) C) O(log n) D) O(log n) A O C D.

Q: Formally prove or disprove the following claim, using any method T(n) = 4T(n/2) + n is (n^2)

A: In this question we have been given a recurrence relation claim where we need to disprove or prove…

Q: Let T(n) = T(n-2)+2T([])+n, for all n and T(n) E N(n²). 2 3. T(1) = T(2) 1. Prove that T(n) E O(2")…

A: Explanation given in step 2

Q: Let f(n)= 32n*+ 12 n² log n. Then f(n)= O(?), f(n)= Q(?), f(n)=0 (?) Replace question marks with the…

A: ANS: option (b) is correct. NOTE: I am unable to type 'omega' symbol and 'theta' symbol from…

Q: Let f(n)-12 logs (8n* +16n) + 5n0.05 Which of the following is true? (Select one.) ○ f(n) € 0 (1)…

A: We are given a function which has logarithmic and polynomial growth in it. We are suppose to find…

Q: O-notation (Upper Bound - Worst Case) 14 O(g(n)) = {f(n): there exist positive constants c and no…

A: Here is the explanation regarding time complexity:

Q: the definition that 2n2 + 100n log n + 1000 = O(n2)

A: Proved the  given asymptotic functions

Q: Evaluate the following problem to determine which value of N is the Big-O notation in the problem.…

A: Introduction Big-O notation: Big-O notation is a mathematical tool used to describe the upper bound…

Q: Consider T(n) = 6T(n/2) + n³; then T(n) is equal to %3D Select one: O a. (n² log n) O b. O(n³) O c.…

A: Given that, T(n) = 6T(n/2) +n3

Q: Analyse the below algorithm acc average-case efficiencies in terms асс Algo1(A[0..n-1], k) i=0 while…

A: Step 1: Algol(A[0..n-1], k)1=0while i<n and A[i] != k do 1=1+1if i < n return i else return -1

Q: f(n) = 0 (g(n)) implies.. O a. f(n) g(n) O c. f(n) = g(n) O d. f(n) > g(n)

A: As per our guidelines we are supposed to answer only one question. Kindly repost the remaining…

Q: Given f(n) and g(n). Is f(n) = O(g(n))? Select one: a. Yes b. No c. None d. May

A: Lets see the solution.

Q: Which statement is true? • not deciable• log(2) n < O (√n)• log(2) n = O (√n)• log(2) n > O…

A: STEP-1 The correct is (" log(2) n > O (√n)") Option("4")

Q: Consider the recurrence: T(N) = 9T(N/9)+N(lgN)4   Fill in the answers below. If a log is needed,…

A: The above question is answered in step 2:-

Q: Understand the running order of 7 functions O(1), O(n log n), O(n), O(n2 ), O(n3 ), O(log n), O(an…

A: The asymptotic upper bound of a function, often denoted using "big-Oh" notation (O()), can be…

Q: If we solve T(n) = T(n/2) + 0(n), we obtain T(n) = 0(n log n). "True False (Randomized) Quicksort…

A: answer :-   FALSE  T(n)=T(n/2)+Thetha (n)                                       , thetha(n) can…

Q: iven that (n) = 2T(n/2) +n for n >= 2, ou can assume n= 2k and T(1) = 1 ind the kth step…

A: Dear Student, The answer to your question is given below -

Q: : a. [(a mod n) - (b mod n)] mod n = (a - b) mod n

A:

Q: Prove or disprove the following statements: 1)Suppose that  f(n) = Θ(nlogn) and g(n) = Θ(n2/logn).…

A: 1. The given statement can be prove f(n) = Θ(nlogn) and g(n) = Θ(n2/logn). Then, h(n) = f(n) x g(n)…

Q: 3. Show that k ln k = 0(n) implies k = o("/nn)- 4. Is 2n+1 0(2")? Is 22n = 0(2")? %3D %3D

A: 3.

Q: T(n) = 12 + T(n/2) + c, for n> 1 T(1) = a O (n²) o (ni ) O(n log n) O (2")

A: In forwarding substitution, we start with the base case i.e. n =1 and try to work our way up till n…

Q: T (n) is taken as the ground state T (1) = 10. For numbers back to T (n + 1) = 2n + T (n), n> = 1.…

A: T (n) is taken as the ground state T (1) = 10. For numbers back to T (n + 1) = 2n + T (n), n> =…

Q: at sum = 0 or (int i sum++ unr

A: The efficiency of any code depends on value of time to execute that particular code on any device…

Q: Let ENFA = {N | N is an NFA and L(N) = Ø}. Prove that ENFA is in P.

A: Ans

Q: Prove that the sum of an even integer and an odd integer is odd. Let n₁ be an even integer, and let…

A: Here we proved that the sum of an even integer and an odd integer is odd

Q: Show that T(n) = O(n³) where T(n) = 1 + 2 + 3+...+n

A: Here in this question we have given a function and we have asked dto prove big-oh asymptomatic…

Q: 1. Prove that 1 i log i = O(n² log n). i=1

A: - We need to work on the expression of complexity.

Q: he following code:

A: The worst case time complexity is defined as the maximum time algorithm will take. It is represented…

Q: %D What is T(n) = 6T(n/7)+n, Vn >2 and T(1) = 1. O O(n) O O(log n) loge O 0(1) O(n log n) No valid…

A:

Q: It is found that the number of primitive operations required by an algorithm is log n!, where n is…

A: It is found that the number of primitive operations required by an algorithm is log n!, where n is…

Q: f(n) = n/ log n and g(n) = n(log n)? Select one: O a. f=Ø(g) O b. f=N(g) O .f=O(g) O d. None of…

A: Actually, algorithm is an step by step process.

Q: The power function can be defined as follows: What is the worst-case running time complexity of…

A: So Below is the answer to this question. Time complexity is most important for every algorithm,…

Q: Given two sorted arrays, each of length n, we can merge them into a sorted array in O(n) time. True…

A: First Question: Given two sorted arrays, each of length n, we can merge them into a sorted array in…

Q: For any n large enough, prove n/3 k=0 n 3k- 2n/3 = O(1). 3. For any n large enough, prove E" ) - =…

A: According to the question , we have to prove that the given equation time complexity is O(1). The…

Q: Show that f(n) is Θ(g(n)) for the correct function g(n). Prove your result using the definitions…

A: f(n) = n 1.5 log(2n) + n 2 log(n 2 ) + √ n:-

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

A: Given that,  f,g:Z+⟶R, and f(n)=nlog2(n) for n∈Z+ and also f∉O(g) That means we want g(n) which is…

Q: 3. Find f(2), f(3), ƒ(4), and f(5) if f is defined sively by f(0) = -1, f(1) = 2, and for n = 1, 2,…

A: Given that f(0)=-1 and f(1)=2   a)f(n + 1) = f(n) + 3f(n - 1) Now for n=1 we have: f(1+1)=…

Q: Show that n! = 0(n").

A:

Q: You are given N cents (integer N) Break up N cents into coins of 1 cent, 2 cent, 5 cents. Using a…

A: When given an amount of money represented in cents, the task is to break it down into the fewest…

Q: (5) T(n) = 2 T(n/2)+n/log n (6)T(n) a T(n/b) + n log n %3D (7) T(n) = log 1 + log2 + log3 + + log n…

A: Note: In part 6, a and b is not given . so, we can not decide on that .. Master Theorem  Case-02:…

Q: If f = (log n)^2, g = n log n; what is the relationship between f and g? Choose all that applies.…

A: The Answer is in Below Steps

Q: RSA How do you find a ‘p’ and ‘q’ given a number n and φ(n)? Using x^2 - [n-φ(n)+1]x+n = 0 to find p…

A: Solution given for the question,  RSA How do you find a ‘p’ and ‘q’ given a number n and φ(n)? Using…

Q: Use MATLAB to solve the following: Compute and draw v[n]*x[n] 1- (a) v[n] = 2"u[n] and x[n] = u[n]

A: It is defined as a script, which contains a set of commands exactly as you would type them at the…

Problems on numbers

Number theory is one of the most appealing topics in mathematics. Given one or more numeric values, a numeric algorithm performs some computation. The use of number theory in computing is important for applications like in the case of cryptographic algorithms. Number theory is also used in various applications such as calculating hash functions or in information security. Euclid’s algorithm is one of the oldest number-theoretic algorithms which is used to calculate the greatest common divisor of two numbers.