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4. (5 points) Use the substitution method to prove the guess that is indeed correct when...
(a) Use the recursion tree method to guess tight 5 asymptotic bounds for the recurrence T(n)-4T(n/2)+n. Use substitution method to prove it.
Subject: Algorithm solve only part 4 and 5 please. need urgent. 1 Part I Mathematical Tools and Definitions- 20 points, 4 points each 1. Compare f(n) 4n log n + n and g(n)-n-n. Is f E Ω(g),fe 0(g), or f E (9)? Prove your answer. 2. Draw the first 3 levels of a recursion tree for the recurrence T(n) 4T(+ n. How many levels does it have? Find a summation for the running time. (Extra Credit: Solve it) 3. Use...
(Weight: 3090) Use substitution, summation, or recursion tree method to solve the f ollowi recurrence relations. (a) T(n) = 2T(n/2) + nign (b) T(n) 2T(n-1)+5" 7(0) = 8
d. (4 pts) Fill in the asymptotic complexity (not the exact solution) of the work represented by the following summations for an input of size n. Write complexities in simplest form. ) (1) Ź 2' = 01 — (3) Z(64) = 01_ (2) (Si +5) = 01 - (4) I"3n =01_ logn ) ) e. (5 points) Consider the recurrence T(n) = 4T(n/2) +n , T(2) = 8. and a proposed closed-form solution T(n) = n² + 2n Suppose we...
Use the method of Laplace transforms and the accompanying proof results to solve the initial value problem. + y'' +9y' + 18y = f(t); y(O) = 0, y'(0) = 0 Here, f(t) is the periodic function defined in the graph to the right. Click the icon to review the results of a proof. Choose the correct answer to the initial value problem below. 1 O A. y(t) == (1-2-3t) 2 6 3 B. y(t) = - Ite - 5t t(t...
Please do exercise 129: Exercise 128: Define r:N + N by r(n) = next(next(n)). Let f:N → N be the unique function that satisfies f(0) = 2 and f(next(n)) =r(f(n)) for all n E N. 102 1. Prove that f(3) = 8. 2. Prove that 2 <f(n) for all n E N. Exercise 129: Define r and f as in Exercise 128. Assume that x + y. Define r' = {(x,y),(y,x)}. Let g:N + {x,y} be the unique function that...
PLEASE ANSWER ALL! SHOWS STEPS 2. (a) Prove by using the definition of convergence only, without using limit theo- (b) Prove by using the definition of continuity, or by using the є_ó property, that 3. Let f be a twice differentiable function defined on the closed interval [0, 1]. Suppose rems, that if (S) is a sequence converging to s, then lim, 10 2 f (x) is a continuous function on R r,s,t e [0,1] are defined so that r...
how do u do 6? F-'(C-D)= F-'(C)-F-'(D). 4. (10 points) In following questions a function f is defined on a set of real numbers. Determine whether or not f is one-to-one and justify your answers. (a) f(x) = **!, for all real numbers x #0 (6) f(x) = x, for all real numbers x (c) f(x) = 3x=!, for all real numbers x 70 (d) f(x) = **, for all real numbers x 1 (e) f(x) = for all real...
For part (a), please prove the answer. 5. Let S = {1, 2, 3, 4} and let F be the sets of all functions from S to S. Let R be the relation on F defined by: For all f,g EF, fRg if and only if fog(1)-2. (a) Is R reflexive? symmetric? transitive? (b) Is it true that that there exists f E F so that fRf? Prove your answer. (c) Is it true that for all f F, there...
For this lab you will write a Java program that plays a simple Guess The Word game. The program will prompt the user to enter the name of a file containing a list of words. These words mustbe stored in an ArrayList, and the program will not know how many words are in the file before it starts putting them in the list. When all of the words have been read from the file, the program randomly chooses one word...