1) True or false?
a. n2 = O(n3)
b. 2n2 + 1 = O(n2)
c. n1/2 = O(log n)
d. log n = O(n1/2 )
e. log n + n1/2 = O(n2)
f. log n = O( n-1/2)
g. log n = O( 1/n )
h. log (n + 3) = q(n1/2)
i. n + n1/2= W( n2 - n )
a. n2 = O(n3) True b. 2n2 + 1 = O(n2) True c. n1/2 = O(log n) False d. log n = O(n1/2 ) True e. log n + n1/2 = O(n2) True f. log n = O( n-1/2) False g. log n = O( 1/n ) False h. log (n + 3) = W(n1/2) False i. n + n1/2= W( n2 - n ) False
Which of the following could be false? A. n2/(log(n)) = O(n2). B. (log n)1000 = O(n1//1000). C. 1/n = O(1/(log(n))). D. 2(log(n))^2 = O(n2). E. None of the above.
O(log(log(N))) < O(log(N)) a. True b. False O(N ) < O(log(N)) a. True b. False O( N5) < O(N2 - 3N + 2) a. True b. False O(2N) < O(N2) a. True b. False
a) Prove that running time T(n)=n3+30n+1 is O(n3) [1 mark] b) Prove that running time T(n)=(n+30)(n+5) is O(n2) [1 mark] c) Count the number of primitive operation of algorithm unique1 on page 174 of textbook, give a big-Oh of this algorithm and prove it. [2 mark] d) Order the following function by asymptotic growth rate [2 mark] a. 4nlogn+2n b. 210 c. 3n+100logn d. n2+10n e. n3 f. nlogn
n1 n2 6. Light rays cross interfaces from medium 1 into medium 2 and then into medium 3. Which of the following is true? n3 A) n1 > n2 and n2 > n3 B) n3 > n2 and n2 > n1 C) n2 > n1 and n2 > n3 D) None of the above
Can I get some help please :) 8. Determine whether or not the following are true and provide a full derivation explaining your answer for each. The domain of the functions of n below is the positive real numbers. For convenience, you may assume that the logs are in the base of your choice, but you should specify what base you are using in your derivation. (2 marks each) a. 6+n+is O(n3) b. 5(n log n +n) is O(n2) c....
True or false for each, and explain why (4 pts) The height of a binary tree is bounded by O(n2), where n is the size of the C. tree. d. (4 pts) dynamic array and O(1) time if L is a linked list. Given a list L of n > 2 elements, the following code takes O(n) time if L is a iterator i = L. iterator () i.next); i.next); i.remove ); binary tree T that has size n and...
1. a) Let f(n) = 6n2 - 100n + 44 and g(n) = 0.5n3 . Prove that f(n) = O(g(n)) using the definition of Big-O notation. (You need to find constants c and n0). b) Let f(n) = 3n2 + n and g(n) = 2n2 . Use the definition of big-O notation to prove that f(n) = O(g(n)) (you need to find constants c and n0) and g(n) = O(f(n)) (you need to find constants c and n0). Conclude that...
Please help me with question 13(c,f,h,i,k,m) 13. Show that the following equalities are correct: (a) 5n2 - 6n(n2) (b) n! - O(n) (c) 2n22"+ n logn-e(n22) (d) I012(n3) (h) 6n3/(log n+1)O(n3) (i) n1.001 + n logn (n1.001) (j) nkte + nk logn 6(nkte) for all fixed k and e, k 0 and e> 0 (1) 33n3 + 4n2 2(n2) (m) 33n3 + 4n23)
Monochromatic light of wavelength, λ is traveling in air. The light then strikes a thin film having an index of refraction n1 that is coating a material having an index of refraction n2. If n2 is larger than n1, what minimum film thickness will result in maximum reflection of this light? A B C D E F G H I J A λ/n1 B λ/4 C λ D λ/(4n2) E λ/n2 F λ/(2n1) G λ/(4n1) H λ/2 I λ/(2n2) J...
Monochromatic light of wavelength, λ is traveling in air. The light then strikes a thin film having an index of refraction n1 that is coating a material having an index of refraction n2. If n1 is larger than n2, what minimum film thickness will result in minimum reflection of this light? A B C D E F G H I J A λ/(4n2) B λ/n2 C λ/(4n1) D λ/(2n1) E λ/4 F λ G λ/2 H λ/(2n2) I λ/n1 J...