2. Use the master theorem to find the following in O-notation: 1. T(n) = 4T(n/2) + n 2. T(n) = 4T(n/2) + n√n 3. T(n) = 4T(n/2) + n² 4. T(n) = 5T(n/2) + n 5. T(n) = 5T(n/2) + n√√n 6. T(n) 5T(n/2) + n² =

Q: Use mathematical induction to prove the statement.

A: Use mathematical induction to prove the statement.13+23+33+....+n3=[n(n+1)/2]2, for all integers…

Q: Explain alpha Beta pruning on the following diagram MAX MIN MAX MIN L E M B 3 N 3 F 0 P C 3 H Q/ R\…

A: Alpha beta pruning is an optimization technique for the minmax algorithm. This technique reduces the…

Q: The Big-0 of 0(2n+1) is the same as O(n).

A: Answer: True

Q: f( n) = n°logn and g( n) = 10n f( n) : |(g(n)) Big O Omega Theta

A: For n=8 f(n) = n2  log n = 8² log 8 = 64*3 = 192 g(n) = 10 n3 = 10*8³ = 5120

Q: Espress the mwer in ars aNTATiSis TIotation

A: In Asymptotic notations, there are three types of time complexities. That are: Best case time…

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: Based on the master theorem, what is the solution to T (n) = 16 (4) +n o e (n² log n) o e (n*) e…

A: - We have to get the complexity according to master's theorem.

Q: We need to calculate the summation of 12 + 22 + 32 + ... + n2 using some formula. Which of the…

A: In step 2, I have provided  ANSWER  with  brief  explanation-----------In step 3, I have provided…

Q: 1 g(n) = 4 · g(n/3) + log(n)

A: The solution for the above given question is given below:

Q: log(n + 1) is O(log n) while log(n² + 1) is not. O True O False

A: Below is the answer with explanation:

Q: 1. Ig(n² – 10n) = N(log(n)) 2. c2'g(n) = O(k2'9(n))

A: According to the question, we will have to prove that the given expressions are true or false. The…

Q: What is the Theta notation for the ff. : foo(n): 1: if n == 1 then 2: return 1 3: else 4: return n·…

A: The algorithm is linear, running in O(n) time because it executes once every time it decrements the…

Q: L= { w ∈ {0,1}* | w contains odd number of 0’s and even number of 1’s.} using only 5 states.   draw…

A: An NFA (Nondeterministic Finite Automaton) state diagram is a graphical representation of the states…

Q: Suppose that f(n) = n² + 10n + 100 and g(n) = n logn +1000n f(n) = O(g(n)) and f(n) = N(g(n)) ○ f(n)…

A: We are given two functions f(n) and g(n) and we are going to find out the relationship between the…

Q: Explain....... 1.Given f(n)=3nlgn+2. State if the following are true (T) or false (F): i) f(n)…

A: Here in this question we have given two function and we have asked  to find that given asymptomatic…

Q: Use the formal definition of the Big-Theta notation to prove that T(n) = 2 + 4n + n² + 3n3 belongs…

A: I have answered the question in step 2.

Q: f(n) — 103л+2 А. f(n) — О(9(n)) В. f(n) — N(9(п)) С. f(n) %3D Ө(9(n)) g(n) = 10"+7

A: Let's calculate value of f(n) and g(n) for different values of n.  For n=5,  F(n) = 1017 g(n) = 1012…

Q: 1. Use the definition of Big O notation to find the constants c, n。 which show that T(n) is O(f(n)).…

A: Big O notation is a mathematical notation used to describe the limiting behavior of a function when…

Q: Prove that"1+3+5+………..+(2n-1)= n2

A: We will prove this by 2 method.

Q: (zu) Uz/8 7/82

A: To prove that n3/2 ≠ Ω( n2 ), we need to show that there does not exist a constant c and a value n_0…

Q: Prove the following by using induction: 1(1!) + 2(2!) + 3(3!) +...... + n(n!) = (n + 1)! - 1, for n…

A:

Q: Given polynomials: P(x) = 4x3 + 5x2 -2x + 3 Q(x) = 2x3 -3x2 + x + 1 Calculate the product PQ(x) in…

A: Answer: I have given answer in handwritten format.

Q: Prove that the following is true for all positive integers n by using the Principle of Mathematical…

A: In mathematical induction method, first proves that a statement is true for the initial value. Then…

Q: For each of the following expressions, find if they are O(1), O(2"), O(n²), O(log n), O(n2022), O(n…

A: Below are the answers with reason:

Q: Consider f(n)= 7 log (7) ,    g(n)=  9 log (9)      which of the following is true? Theta = θ…

A: Consider f(n)= 7 log (7) , g(n)= 9 log (9) which of the following is true?   Theta = θ Omega = Ω…

Q: Put 0, 0, N in the right position, the same as the given example a) n² = .- (n), solution: n2 =…

A: First of all, we need to define the symbols as follows. θ = equal function(average case) O = worst…

Q: (n+4)(n+2) +1 belongs to: 2 O 0 (n) O 0 (n * log(n)) O 0 (n*) O e (n²)

A:

Q: Explain alpha Beta pruning on the following diagram MAX MIN MAX MIN L E B 3 M 2) (3) 3 F N O P A 3…

A: Alpha beta pruning is an optimization technique for the minmax algorithm. This technique reduces the…

Q: F= (A+B+C) (A+B+C) (A+B+C) = A+BE

A: Given information:- F=(A+B+C).(A+B+C').(A+B'+C') to prove : F=A+B.C'

Q: Assume that: 1) f(n) belongs to O(g(n)) and the formal proof for this statement uses c=3 and n0=1 2)…

A: SOLUTION: f(n) = O(g(n)) for c=3, n0 = 1 f(n) <= c*g(n) for all n>=n0 f(n) <= 3*g(n) for…

Q: 6. T(n) = 5T(n/2) + n²

A: Big O is a mathematical notation that describes the upper bound on growth rate of time complexity in…

Q: ferential equation using Simulink: cos cos (5t) + 4 exp exp (t) + 4ln(t) solve this i matlab simu

A: Given is true

Q: d. Distinguish between the following pairs of Big O notations and give practical examples to…

A: Time complexities are measured using the Big O notation.