Homework Answers
f(n) = O(g(n)), if there exists c1 and n0 such that f(n)
c1*g(n) for all n
> n0
f(n) = 
(g(n), if there
exists c1 and n0 such that f(n) 
c1*g(n) for all n
> n0
Using basic operation we try to achieve the above inequalities and hence establish the relation between f(n) and g(n)
Add Answer to:
3. (10 pts) For each of the following functions f(n), prove the stated claim by providing...
1. a) Let f(n) = 6n2 - 100n + 44 and g(n) = 0.5n3 . Prove...
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...
Need help with 1,2,3 thank you. 1. Order of growth (20 points) Order the following functions...
Need help with 1,2,3 thank you.
1. Order of growth (20 points) Order the following functions according to their order of growth from the lowest to the highest. If you think that two functions are of the same order (Le f(n) E Θ(g(n))), put then in the same group. log(n!), n., log log n, logn, n log(n), n2 V, (1)!, 2", n!, 3", 21 2. Asymptotic Notation (20 points) For each pair of functions in the table below, deternme whether...
Let f(n) = 5n^2. Prove that f(n) = O(n^3). Let f(n) = 7n^2. Prove that f(n)...
Let f(n) = 5n^2. Prove that f(n) = O(n^3). Let f(n) = 7n^2. Prove that f(n) = Ω(n). Let f(n) = 3n. Prove that f(n) =ꙍ (√n). Let f(n) = 3n+2. Prove that f(n) = Θ (n). Let k > 0 and c > 0 be any positive constants. Prove that (n + k)c = O(nc). Prove that lg(n!) = O(n lg n). Let g(n) = log10(n). Prove that g(n) = Θ(lg n). (hint: ???? ? = ???? ?)???? ?...
1. For each of the following pairs of functions, prove that f(n)-O(g(n)), and / or that...
1. For each of the following pairs of functions, prove that f(n)-O(g(n)), and / or that g(n) O(f(n)), or explain why one or the other is not true. (a) 2"+1 vs 2 (b) 22n vs 2" VS (c) 4" vs 22n (d) 2" vs 4" (e) loga n vs log, n - where a and b are constants greater than 1. Show that you understand why this restriction on a and b was given. f) log(0(1) n) vs log n....
Compare the following pairs of functions f, g. In each case, say whether f- o(g) f-w(g), or f = Θ...
Compare the following pairs of functions f, g. In each case, say whether f- o(g) f-w(g), or f = Θ(g), and prove your claim. 157. f(n) -100n+logn, gn) (logn)2. 158,介f(n) = logn, g(n) = log log(n2). 159. . f(n)-n2/log n, g(n) = n(log n)2. 160·介介f(n)-(log n)106.9(n)-n10-6 . 161. (n)logn, g(n) (log nlog n 162. f(n) n2, gn) 3.
Compare the following pairs of functions f, g. In each case, say whether f- o(g) f-w(g), or f = Θ(g), and prove...
Formal Definitions of Big-Oh, Big-Theta and Big-Omega: 1. Use the formal definition of Big-Oh to prove that if f(n) is...
Formal Definitions of Big-Oh, Big-Theta and Big-Omega:
1. Use the formal definition of Big-Oh to prove that if f(n) is a decreasing function, then f(n) = 0(1). A decreasing function is one in which f(x1) f(r2) if and only if xi 5 r2. You may assume that f(n) is positive evervwhere Hint: drawing a picture might make the proof for this problem more obvious 2. Use the formal definition of Big-Oh to prove that if f(n) = 0(g(n)) and g(n)...
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)...
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...
Part I. (30 pts) (10 pts) Let fin) and g(n) be asymptotically positive functions. Prove or...
Part I. (30 pts) (10 pts) Let fin) and g(n) be asymptotically positive functions. Prove or disprove each of the following statements T a、 f(n) + g(n)=0(max(f(n), g(n))) 1. b. f(n) = 0(g(n)) implies g(n) = Ω(f(n)) T rc. f(n)- o F d. f(n) o(f(n)) 0(f (n)) f(n)=6((f(n))2)
1. (10 pts) For each of the following pairs of functions, indicate whether f = 0(g),...
1. (10 pts) For each of the following pairs of functions, indicate whether f = 0(g), f = Ω(g), or both (in which case f-6(1). You do not need to explain your answer. f(n) (n) a) n (b) n-1n+1 (c) 1000n 0.01n2 (d) 10n2 n (lg n)2 21 е) n (f) 3" (g) 4" rl. 72 i-0 2. (12 pts) Sort the following functions by increasing order of growth. For every pair of consecutive functions f(n) and g(n) in the...
state and prove divergence or convergence for each of the following series. f. 5 nn |(n+3)...
state and prove divergence or convergence for each of the following
series.
f. 5 nn |(n+3) n= ln 00 g. (2n-1) (n!) n=1 h. į vn + cos n n n=1 i. 2"n? n!
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...
Need help with 1,2,3 thank you.
1. Order of growth (20 points) Order the following functions according to their order of growth from the lowest to the highest. If you think that two functions are of the same order (Le f(n) E Θ(g(n))), put then in the same group. log(n!), n., log log n, logn, n log(n), n2 V, (1)!, 2", n!, 3", 21 2. Asymptotic Notation (20 points) For each pair of functions in the table below, deternme whether...
1. For each of the following pairs of functions, prove that f(n)-O(g(n)), and / or that g(n) O(f(n)), or explain why one or the other is not true. (a) 2"+1 vs 2 (b) 22n vs 2" VS (c) 4" vs 22n (d) 2" vs 4" (e) loga n vs log, n - where a and b are constants greater than 1. Show that you understand why this restriction on a and b was given. f) log(0(1) n) vs log n....
Compare the following pairs of functions f, g. In each case, say whether f- o(g) f-w(g), or f = Θ(g), and prove your claim. 157. f(n) -100n+logn, gn) (logn)2. 158,介f(n) = logn, g(n) = log log(n2). 159. . f(n)-n2/log n, g(n) = n(log n)2. 160·介介f(n)-(log n)106.9(n)-n10-6 . 161. (n)logn, g(n) (log nlog n 162. f(n) n2, gn) 3.
Compare the following pairs of functions f, g. In each case, say whether f- o(g) f-w(g), or f = Θ(g), and prove...
Formal Definitions of Big-Oh, Big-Theta and Big-Omega:
1. Use the formal definition of Big-Oh to prove that if f(n) is a decreasing function, then f(n) = 0(1). A decreasing function is one in which f(x1) f(r2) if and only if xi 5 r2. You may assume that f(n) is positive evervwhere Hint: drawing a picture might make the proof for this problem more obvious 2. Use the formal definition of Big-Oh to prove that if f(n) = 0(g(n)) and g(n)...
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...
Part I. (30 pts) (10 pts) Let fin) and g(n) be asymptotically positive functions. Prove or disprove each of the following statements T a、 f(n) + g(n)=0(max(f(n), g(n))) 1. b. f(n) = 0(g(n)) implies g(n) = Ω(f(n)) T rc. f(n)- o F d. f(n) o(f(n)) 0(f (n)) f(n)=6((f(n))2)
1. (10 pts) For each of the following pairs of functions, indicate whether f = 0(g), f = Ω(g), or both (in which case f-6(1). You do not need to explain your answer. f(n) (n) a) n (b) n-1n+1 (c) 1000n 0.01n2 (d) 10n2 n (lg n)2 21 е) n (f) 3" (g) 4" rl. 72 i-0 2. (12 pts) Sort the following functions by increasing order of growth. For every pair of consecutive functions f(n) and g(n) in the...
state and prove divergence or convergence for each of the following
series.
f. 5 nn |(n+3) n= ln 00 g. (2n-1) (n!) n=1 h. į vn + cos n n n=1 i. 2"n? n!
Most questions answered within 3 hours.
-
Which of the following pairs of ions have the same electron
configuration?
I: Br− and Se2−...
asked 11 minutes ago -
The Foremost Composite Materials Company is planning a two-day
sales conference for October 19-20. The conference...
asked 34 minutes ago -
3) Illustrate the observed pattern of relatedness of organisms
versus adaptations to specific conditions. This means...
asked 51 minutes ago -
In winter a lake has a 0.35 m thick ice layer over 1.10 m of
water....
asked 1 hour ago -
Assuming the following has been encrypted with a Vigenere cipher
below, use the method(s) and assumptions...
asked 2 hours ago -
How would I use switch statements to write a program that will
take an input of...
asked 2 hours ago -
Imagine a reaction in which methane gas combusts at a constant
pressure of 1 atm and...
asked 2 hours ago -
Two parallel wires (each 12 m in length) are separated by a
distance of 0.065 m...
asked 2 hours ago -
Suppose there were three masses at the corner of uniform
equilateral triangle. The masses are m1...
asked 2 hours ago -
Situation: A building that is 618 m above the ground floor. How
many times would a...
asked 2 hours ago -
help me and discuss one successful and one
unsuccessful international company/busines in Indonesia.whyit
succeed and why...
asked 2 hours ago -
I- Choose the best answer
Which of the following statements about the structure and
packaging of...
asked 2 hours ago