Is f (n) = 13n² + 6nyn log(3n²) – 4n logź(5n*) + 2n – 1 in N(n³)? Is f(n) in O(n²)? Is f (n) in N(n²)?

Q: Give the exact complexity classes of the functions:  (log n)2 + √n + log n10, (n/2) + log nlogn,…

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Q: 1. Find the big-theta of 5n^2 log n +3n^3 2. Find the c and n when 2^n +3n^2 is O(2^n) 3. Find c…

A: In this question, we have to find out the values of c and n for given functions and also find out…

Q: sum1 = 0; for (k=1; k<=n; k*=2) for (j=1; j<=n; j++) sum1++; sum2 = 0; for (k=1; k<=n; k*=2) for…

A: Рrimitive  орerаtiоns  аre  bаsiс  соmрutаtiоns  рerfоrmed  by  аn  аlgоrithm.  Exаmрles  аre…

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: Use induction to show that for all positive integers n (a) 13+23+33 + ... + n³ = (n(n+1)/2)². (b) 1.…

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Q: Prove that for any integer n, n6k-1 is divisible by 7 if gcd(n,7)=1 and k is a positive integer.

A: Given: Prove that for any integer n, n6k-1 is divisible by 7 if gcd(n,7)=1 and k is a positive…

Q: Implement SHANKS' ALGORITHM for finding discrete logarithms in Zp, where p is prime and à is a…

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

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Q: By using the definition of prove that 4√7n³ - 6n² + 5n − 3 € O(n¹.5). -

A: Defination of theta function Θ(g(n)) = { f(n): there exist positive constants c1, c2 and n0…

Q: Prove, for what value of c and no following is true: a. 3n³ + 20n² + 5 is O(n³) b. 5n? is 2(n) c.…

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Q: Demonstrate that n! equals O (nn).

A: According to the information given:- We have to prove n!=O(nn)

Q: Prove using definitions only that nªlog(n) is not O(nª).

A: Proof by contradiction Assume that nnlog(n) is O(nn) itself. So, by definition of BigO, there exists…

Q: Is O(n3) or O(n2) the correct upper bound of f(n) = 3n3+n2+50 ? Please explain why.

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Q: 1. Give asymptotic upper and lower bounds for T(n) (1) T(n) = 20T(n/9) + n'.5 (2). T(n) = 25T(n/625)…

A: Given the following we have to answer in asymptotic Upper and lower bound for T(n).

Q: 3. Put 0, 0, N in the right position, the same as the given example: a) n2 = .-· (n), solution: n2 =…

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Q: QUESTION 8 Show by induction that 21"-8" is divisible by 13 for all n20

A: This is a question on mathematical induction.

Q: Information entropy for classification of m tuples in D is calculated as follows: m I(D) =2 P, log2…

A: so your question is information entropy for classification of m tuples in D is calculated as  I(D) =…

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

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Q: Provide the prime implicants in a comma separated list (e.g., a & ~b, ~a & b) for the following…

A: The answer is given below:-

Q: The recurrence relation for the method is O A. T(n) = T(n-1) for n > 0 and T(0) = 1 B. T(n) =…

A: Given: Given a time complexity finding problem and we need to choose the correct option.

Q: Prove a) 1000000n2 + 0.0000001n5 is Ω(n3) b ) n! is Ω(2n) if you use an example c and n PLEASE…

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Q: Show that if f(n) is O(g(n)) and g(n) is e(h(n)) then f(n) is O(h(n))

A: θ-notation denotes tight bound. O-notation denotes upper bound. For a given function g(n), we denote…

Q: Question 2. (a) Show that there is no n EN such that n = 1 (mod 12) and n = 3 (mod 8). (b) Find a…

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

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Q: Question 3. Show that n³ +4n² + 1 n+3 = O(n*).

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Q: What is the order of an algorithm with running time f(n) = 2n3+5n2

A: Order of an algorithm means the worst case running time of algorithm.

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: Show that 6n2+8n+2 is O(n2)

A: We need to find k and n0 such that: 6n2 + 8n + 2 &lt;= kn2 for all n &gt;= n0 . Divide both sides by…

Q: 11.What is the order of growth of the recurrence relation A(n)-8A(n/8)+n? * A(n) € 8(n**3) A(n) €…

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Q: Given a sequence x(n), n from 0 to 3, where x(0)=-2,x(1)=4, x(2)=0 and X(3)= Evalute its DFT X(K)

A: DFT OF THE GIVEN SEQUENCE   X(K) 7  -2 + 1j  -11 + 0j -2 - 1j

Q: 2. The derivation of Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, ... (FIB(N – 1) + FIB(N – 2) If N>…

A: Fibonacci series is a series in which the nth element is the sum of previous two elements given that…

Q: 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…

A: The Answer is

Q: Show that n2 + 3n + 2 is O(n²). Show that 3" is N(n° + 4).

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Q: 2. The derivation of Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, .. (FIB(N – 1) + FIB(N – 2) If N> 2…

A: We write function named fibonacciRecursion according to the conditions provided and return the…

Q: For the following netlist write a code in python for VLSI placement with simulated annealing M2…

A: import Module import PortIn import PortOut import PortClk import ConfigParser from ordereddict…

Q: Construct the truth (tables) values of the given compound proposition: [(p^q'Ar) + (p O q)] – [(p' &…

A: XOR is represented by ⊕. AND is represented by ∧. OR is represented by ∨. ↔ represents…

Q: . Show that if p(n) is a polynomial of the form n3 + C2 n² + c1 n + Co, then p(n) = ©(n³).

A: - We need to show that if the polynomial is given in the form of the equation n3 + C2n2 + C1n + C0.…

Q: Compute big-oh of the given T(n) using the specified methods: A- Iteration Method:  1. T(n) =…

A: A 1.T(n) = 8T(n/2) + n 2 (T(1) = 1) T(n) = n 2 + 8T(n/2) = n 2 + 8(8T( n 2 2 ) + (n 2 ) 2 ) = n 2 +…

Q: for (m 10; m <= 11; m++) { cout << "Table of" << m << endl; for (n = 1; n <= 10; n++) {

A: GIVEN CODE int m;    int n;    for(m=10;m&lt;=11;m++){        cout&lt;&lt;"Table…

Q: Write down the growth order of n, log n, n^2, 1, n^3, n!, 2^n, nlogn in increasing sequence. With…

A: Growth Order as Follows  1 &lt; logn &lt; n &lt; nlogn &lt; n^2 &lt; n^3 &lt;2^n &lt; n!…

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

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

Q: Run the Miller-Rabin test for n = 2701 and the base a = 2. What conclusions would you draw about the…

A: Lets see the solution in the next steps

Q: Examples: SF = ZF = PF SF = ZF = MSB 3210 SUIT 0010 0011 0100 0101 5010 0011 0011 0010 0001 1001 이이…

A: Answer:- These are the different arithmetic flags used, it becomes set(1) or reset(0) depending upon…

Q: Compare the order of growth of 1. 2^n and n! 2. log |n| and √n

A: Here in this question we have given two function and we have to compare their order of growth.so we…

Q: The prefix search of the expression 8 (3- 1) + 2 x 5 is O a. 8 ÷ 3 – 1+2\tims5 O b. +-318 x 25 O c.…

A: Correct Option  d. None

Q: For each of the following expressions below, write the corresponding Big-Oh complexity Expression…

A: 1. O(2n) 2. O(n7)

Q: for (j = n - 1; j> 0; j = j - 1) Factorial ( n ) { if n=1 for (i = 0; i A[ i+ 1]) return n *…

A: Time complexity :  Time complexity is the total amount of time required by an algorithm to perform…

Q: n log2n - 2n <= log2 n! <= n log2n - n

A: Given :- In the above question, a sequence or relation is mention in the above given question   Need…

Q: (or disprove) that n2 is 2(n²+n)

A: We are given a function f(n) which is n2 and g(n) which is n2+ n and we are going to prove n2 is…