If f(n) took 30 seconds for an n = 100 then how long would it take to process n = 400 if f(n) was of order: 1. O(N) 2. O(N^2)

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: Order the following functions by their growth rate: O(Log N), O(N°), O(1), O(N), O(2N), O(N Log N),…

A: The given functions are O (Log N), O(N4), O(1), O(N), O(2N), O(N Log N), O(N2) The order of the…

Q: 30 GeD 40 Print 50 Print 60 Data True False

A: Lets see the solution.

Q: Q2\ Compute IDFT using Matrix method for X(k) = [6, - 2 + 2j, -2, - 2 - 2 - 2j] then calculate the…

A: To compute the Inverse Discrete Fourier Transform (IDFT) using the matrix method for  X(k) = [6, -2…

Q: 5. Find the O(g) estimate for each of the following functions. The order of g should be as small as…

A: The O(g) of the given functions

Q: Prove or disprove: (a) 100n 2 − 65n + 10 ∈ O(n 2 ) (b) n 3 log n + 2n 2 + 3 ∈ O(n 3 )

A: The required answer is in subsequent steps.

Q: Please answer all questions and show all work 8. If f(n) = n³ and g(n) = 17,000,000n² Show that g(n)…

A: As per Big-O notation, if f(n) = O(g(n)) then f(n) <= c.g(n) such that c >0 , n>n0 and n0…

Q: Match the following 10 functions into 5 pairs. f(n) should be paired with g(n) if f(n) = O(g(n)).…

A: Solution:   Given,

Q: sorting algorithm is in O(n2) in the worst case. It takes 2 seconds to sort 10,000  records, i.e. n…

A: As per the given information, we are supposed to solve the two parts provided.

Q: Solve by matlab using to print the element of secondary diagonal for a matrix A(N,N), where I…

A: Solve by matlab                .............. using to print the element of secondary diagonal for a…

Q: In each of the following show whether f(n) = O(g(n)) and/or f(n) = Ω(g(n)): (a) f(n) = 20n + logn,…

A: Defined the given function

Q: For some constant c and recurrence T(n) 2 the runtime is polynomial with an exponent larger than 1…

A: The given recurrence relation T(n)<qT(2n​)+cn is a representation of the time complexity of an…

Q: and h(n) = 0(n). Then %3D

A:

Q: Problem 3: Order the following functions by asymptotic growth rate 2log(n) 5n + 32 log(n) 5n3 4.n.…

A: We are going to arrange given functions by asymptotic growth rate. Smallest function<…

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: Suppose f(n) = 19n³ and h(n) = 20n³ + n+ 23. Prove or disprove whether f(n) E N(h(n)) %3D Use the…

A: Here, we have to prove or disprove whether f(n) belongs to Ω(h(n)). As per the definition of Big…

Q: Prove that if f(n) = O(n) + 0(n ^2) + O(n^ 3) then f(n) = (n ^3)

A: In the realm of algorithmic analysis and computational complexity, Big O notation is a fundamental…

Q: Find the base Let m=(313), and n=(322)4. 4 expansion of m+n. A (635)4 B (32312)4 C (21323) 4

A: This question can be solved by as first converting both the number in decimal system and then…

Q: Use induction to verify that T(n)=O(n^3) where T(n) ≤ 3T(n/2) + 4T(n/3) + n^3

A: The recurrence relation is a formula that describes a series based on a rule that determines the…

Q: Explain step by step and provide all correct answers

A: The Chinese Remainder Theorem (CRT) is a powerful tool in number theory, often used to simplify…

Q: It can be shown that if gcd(m,n) = 1 then Ф(mn) = Ф(m) Ф(n). Use this property and the above result…

A: gcd(m,n) = 1 means that m and n have no common factors

Q: using python language print out an output solving for the particular and homogeneous solution of…

A: This is very simple. You can do this in one line. I will show you the easiest method to solve this…

Q: Determine if ∀a, b ∈ N, f(n) = a^n , g(n) = b^n , then it follows that f ∈ Θ(g).

A: f(n)=a^n g(n)=b^n Given a,b∈ N where a,b>0 Let k∈ N  such that a<=kb a^n<=(kb)^n

Q: I need an algorithm which gets n numbers from 1 to k and has a process in O(n+k). Then whenever we…

A: Given: We are given a problem in which there are "n" numbers and each number can be anything from 1…

Q: Let d p(n) = [a¡n', i=0 where ad > 0, be a degree-d polynomial in n, and let k be a constant. Use…

A: SOLUTION -   e. If k <d, then p(n) = w(nk).     Below I have added the image of the solution -…

Q: Problem 2 - 40 points The value of sin(x) can be approximated using a Maclaurin series x³ x5 sin(x)…

A: Complete Solution Again, before starting this problem, we note that the Taylor series expansion at x…

Q: Provide solution thanks 2

A: Given :-Use the definition of big Theta, to find an f(n) that satisfies the expression: nlogn + 2n2…

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: Prove or disprorve the following: Please show ypur solution 1. T(n) = 3n^3 + 2n - 4 is O(n^3

A: The big-O notation is a type of asymptotic notation that is used to describe the order of growth of…

Q: 1 + 3 + 5 + ....... + (2n-1) = n^2 P(k+1) Prove the induction

A: Induction Proof: It is used to prove the particular sequence is true. There are three steps in this…

Q: The diagram below shows roads connecting towns near to Rochdale. The numbers on each arc represent…

A: Answer: We need to write the find the minimum path from source to destination using the Dijkstra's…

Q: What is the worst-case running time complexity of matrix substraction? select one: a.O(n^2.5)…

A: Given:- What is the worst-case running time complexity of matrix substraction? select one:…

Q: Formally prove or disprove the following claim, using any method T(n) = 3T(n/2) + 5 is O(n^log2(3))

A: Time complexity of the program is the total time required to execute the code. There are three types…

Q: please answer the following A) d(n) is O(F(n)) and f(n) is O(g(n) ) show that d(n) is O(g(n)) B)…

A: f(n) is O(g(n)), and there are constants c2 and n2 such that f(n) <= c2 * g(n) for all n >=…

Q: n2 Example 1 Find O bound for f (n) n %D 2 2

A: Answer: Here is the theta bound condition: c1*g(n)<=f(n)<=c2*g(n) we will apply this condition…

Q: The solution is on paper 2- Consider the following function : g (n) = 2n³ + 3n - 20

A: Solution - In the given question, we have to find the value of j so that all the given conditions…

Q: iii. 5+ 2cos(n) = Theta (1) iv. Show that (3/2)n^2 +2n-3 = Q (n^2)

A:

Modular linear equation

Modular arithmetic is a system of arithmetic for integers, whose values reset to zero and begin to increase again, after reaching a certain predefined value, called the modulus (modulo). Modular arithmetic is widely used in computer science and cryptography.