What is the best big-oh estimate of (n2+n!)*(n2+2n)?

Q: Given that EuV k=1 to n k = n(n+1)/2, evaluate Euu k=1 to n (k+1)

A:

Q: recurrence

A: Given : - A recurrence relation is mention in the above given question as, T(n) = 1/4 T(n/4) + 3/4…

Q: What are the theta values for the recurrences given below in Q1-Q3? (Show your work in details) (1)…

A:

Q: Show that the recurrence equation (n-1)tn-1+(n-1)tn-2 t₁ = 0 t₂ = 1 can be written as tn =…

A: Solution of the given recurrence equation is:

Q: Solve completely for a(n) a(n+2) = 3a(n+1)-2a(n) a(0)-3 a(1) =4

A: This is recurrence relation problem which uses distinct roots theorem.

Q: for the given 1,2,3 find the recurrences - the closed-form expression for n. 1) S(0) = 6 for n =…

A:

Q: (b) T(n)=T([n/2])+log2 n for n>l, T(1)=1. (n = 2k %3D (c) T(n)=E- T(i), T(0)=1. Li=0

A: Solution for (b):

Q: The solution to the recurrence cquation: T (2)=3T (2) - 1,T(1) = 1 is:

A: The answer for the recurrence equation is

Q: What is the value of the following summations? - Σ(2) k==7 5 j ΣΣ (+1) j=0 k=0

A: a) Given that ∑k=−77(k2)…

Q: Solve each recurrence, using O, N, or 0, whicheve is appropriate K(n)= K(n-2√√n + 1) + n.

A: Big Oh Notation (O):- Mathematically, suppose if f(n) describes the running time complexity of an…

Q: Solve the given recurrence equation by iterative method. n=1 T(n) =- 4T(n/2) + n?/ lg n n>1

A: Need to solve given recurrence equation using iterative method :  Where C is constant

Q: Use Mathemabieal nduction to Show that n-n is diusıble by 3

A: Given: use mathematical induction to show that n3-n  divisible by 3

Q: solve the following recurrances using any method T(n) = 7T(n/3) + n^2  and T(n) = 4T(n/2) +…

A: The Master Theorem provides a framework for solving recurrence relations of the form:T(n) = aT(n/b)…

Q: T(n) = 4T(n/2) +n is (n²)

A: The Master Theorem is a tool used to solve recurrence relations that arise in the analysis of…

Q: Consider the recurrence T (n) = 2T (n/2) + n log n. Provide a detailed proof why Master Theorem does…

A: The recurrenceT (n) = 2T (n/2) + n log n. Master Theorem is used to determine running time of…

Q: Solve the following recurrences (i.e. find a closed form expression for n). Any method is accepted.…

A: Solving recurrence relation.

Q: If set A has size m, and set B has size n, then what is the size of the cross product of A and B?…

A: Introduction: A set is a collection of distinct and well-defined objects, which can be numbers,…

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

A:

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: Use Master Method to deduce the time complexity of the following recurrence equations: T(n) =…

A: T(n) = aT(n/b) + f(n) If f(n) = Θ(n^c) where c < Logb(a) then T(n) = Θ(n^Logb(a)) If f(n) =…

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: What if k = 3? would it also include x5?

A: K-Nearest Neighbors (KNN) is a simple machine learning algorithm used for both classification and…

Q: Show that T(n) has the same order as S(n) where T(n) = 3nª – 5n? S(n) = nº

A: Defined the asymptomatic order of the  given functions

Q: Prove √15n2log(5n) + 0.4n +√n is Θ(n2log(n)) using definitions only

A:

Q: Please use definition of big-theta in your proof. i.e. find constants c1>0 and c2 >0 such that…

A: Here's the solution:

Q: an the master method be applied to the recurrence T(n) = 4T(n²) +n²logn Why or why not? Give an…

A: Here in this question we have given a recurrence realtion and we have asked that weather we could…

Q: Given the recurrence T(n) = T(n – 1) + O(n)          What is the corresponding big-O?     O(n)…

A: Explanation: The recurrence-relation is indeed a mathematical-formula that describes an algorithm's…

Q: What is s(s(s(0)))+s(s(s(s(0))))?

A: The expression "s(s(s(0)))+s(s(s(s(0)))))" appears to be using a notation for representing natural…

Q: If g(n) = O(f(n)),by using the definition of Big-Θ, prove that f(n) + g(n) = Θ(f(n)).

A: Hence proved. Show explanation below.

Q: Prove by cases for any integer n ,the number (n3-n) is even.

A: hay! in the following c++ code I proved any integer n , the number (n3-n) is even. PLEASE CHECKOUT…

Q: What is the regular expression for this grammer

A: For it their are two possibilities either m<n or m=n For m<n Regular Expression(First…

Q: Given that Eup k=1 to n k³ = n²(n+1)²/4, evaluate Zuu j=2 to n (j-1)3 by the change of summation…

A:

Q: U Use the iteration method to solve the recurrence T(n) = 4T(n/2) + n?

A: Here in this question we have asked to solve a recurrance relation using iteration method. T(n) =…

Q: Discuss the time and space complexity of k-means

A: The answer of time and space complexity of k-means

Q: (a) Show that T(n) = 3n²+ 10n + 1 is not (n²)

A: Answer: We need to shown the given tine complexity is not in θ(n2) So we will see in the more…

Q: log(n!) = O

A: Solution - In the given question, we have to prove log(n!) = θ(nlogn)

Q: Prove by using a flow proof. For all integers n, if n is odd, then 5n +7 is even.

A: Flow proof is a method by which we can prove a conclusion statement by using the given condition…

Q: please show the steps) Formula: T(n) = 4n + 2 + T(n-1)

A: Recurrence relation having n no. Of iterations  N no. Steps we are using to divide the equation into…

Q: What is the determinant of M? M = [1 0 2;      3 8 5;      1 1 3]

A: The determinant of a matrix can be obtained by using det command in MATLAB and thus the command and…

Q: Solve recurrence with backward substitution. G(1) = 11 G(n) = 5 + G(n/2)

A: - We need to unfold the equation for solving the demanded relation. - We need to use the backward…

Q: What is the truth set of p if p(x) represents x² > 1 and the domain is the integers?

A: Solution for the above question is solved in step 2:-

Q: e the following recurrences exactly: (a) T(1) = 8, and for all n ≥ 2, T(n) = 3T(n − 1) + 1

A: When we talk about recurrence relations, we are referring to equations which define a sequence based…

Q: Solve the following recurrence equation using the iterative Method, show the details of your…

A: We have to solve given recurrence relation using the iterative method.  In this, we will put n…

Q: Jse master method to solve T(n) = 4T | +

A: We are given a recurrence relation and we are going to solve it using Master's theorem. Please refer…

Q: Give an analysis of the running time (Big-Oh will do).   sum = 0;   for( i = 0; i < n; ++i )…

A: The solution is given below with explanation