Indicate whether the first function of each of the following pairs has a smaller, same or...
Indicate whether the first function of each of the following pairs has a smaller, same or larger order of growth (to within a constant multiple) than the second function. Justify your answer
(1) n(n2+1) and 2000 n2 + 34 n
(2) ln n and lg n
(3) 2n-1 and 2n
(4) 2 n2 and 0.001 n3 – 2 n
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Indicate whether the first function of each of the following
pairs has a smaller, same or...
Hello, I would like to get help with the following question, thanks in advance. Order the...
Hello, I would like to get help with the following question, thanks in advance. Order the following functions according to their asymptotic growth rate. Justify the ordering. n2 --- n! --- (lg n)! --- (3/2)n --- ln ln n --- nlg(n) --- n2n ---- ln n --- en ---- n ---- sqrt(n) ---- 1 --- n(1/lg n) --- ln2(n) --- 2n --- lg(n!)
For each of the following functions, indicate the class Θ(g(n)) the function belongs to. ( Use...
For each of the following functions, indicate the class Θ(g(n)) the function belongs to. ( Use the simplest g(n) possible in your answers). Prove your assertions. a. ( n2 + 1)10 b. 2n+1 + 3n-1 c. [ log2 n ] d. 2n lg(n+2)2 + ( n+2)2 lg n/2 e. ( 10n2 + 7n + 3)1/2
in my c++ class i need help with these question please Question 1. Indicate whether the...
in my c++ class i need help with these question please Question 1. Indicate whether the first function of each of the following pairs has a smaller, same, or larger order of growth (to within a constant multiple) than the second function. Use the correct notation to indicate the order of growth (f(n) ∈O(g(n)), Ω(g(n)), or Θ(g(n)) as applicable). Prove your statement using limits. (a) (lnn)2 and lnn2 (b) 42n+1 and 42n Question 2. Use the formal definitions of O,...
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...
Order the following functions by growth rate: N, squrerootN, N1.5, N2, NlogN, N log logN, Nlog2N,...
Order the following functions by growth rate: N, squrerootN, N1.5, N2, NlogN, N log logN, Nlog2N, Nlog(N2), 2/N,2N, 2N/2, 37, N2 logN, N3. Indicate which functions grow at the same rate.
For each set of ordered pairs, indicate whether it is a function. If not, briefly explain...
For each set of ordered pairs, indicate whether it is a function. If not, briefly explain why it is not a function. (a) { (2, 2) , (2, -3) , (2, 0) } (b) { (2, 2) , (-3, 2) , (0, 2) } (c) { (2, 2) , (-3, -3), (0, 0) }
1 question) Arrange the following in the order of their growth rates, from least to greatest:...
1 question) Arrange the following in the order of their growth rates, from least to greatest: (5 pts) n3 n2 nn lg n n! n lg n 2n n 2 question)Show that 3n3 + n2 is big-Oh of n3. You can use either the definition of big-Oh (formal) or the limit approach. Show your work! (5 pts.) 3 question)Show that 6n2 + 20n is big-Oh of n3, but not big-Omega of n3. You can use either the definition of big-Omega...
Here are some common orders of growth, ranked from no growth to fastest growth: Θ(1) — constant time takes the same amount of time regardless of input size Θ(log n) — logarithmic time Θ(n) — linear t...
Here are some common orders of growth, ranked from no growth to
fastest growth:
Θ(1) — constant time takes the same amount of time regardless
of input size
Θ(log n) — logarithmic time
Θ(n) — linear time
Θ(n log n) — linearithmic time
Θ(n2 ) — quadratic time
Θ(n3 ), etc. — polynomial time
Θ(2n), Θ(3n), etc. — exponential time
(considered “intractable”; these are really, really horrible)
In addition, some programs will never terminate if they get
stuck in an...
8.26 Indicate whether the final volume of gas in each of the following is the same,...
8.26 Indicate whether the final volume of gas in each of the following is the same, larger, or smaller than the initial volume, if pres- sure and amount of gas do not change: a. A volume of 505 mL of air on a cold winter day at -15 °C is breathed into the lungs, where body temperature is 37 °C. b. The heater used to heat the air in a hot-air balloon is turned off. c.A balloon filled with helium...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci number. By definition Fibonnaci(0) is 1, Fibonnaci(1) is 1, Fibonnaci(2) is 2, Fibonnaci(3) is 3, Fibonnaci(4) is 5, and so on. Your function may only use a constant amount of memory (i.e. no auxiliary array). Argue that the running time of the function is Θ(n), i.e. the function is linear in n. 2. (10 points) Order the following functions by growth rate: N, \N,...
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...
Order the following functions by growth rate: N, squrerootN, N1.5, N2, NlogN, N log logN, Nlog2N, Nlog(N2), 2/N,2N, 2N/2, 37, N2 logN, N3. Indicate which functions grow at the same rate.
Here are some common orders of growth, ranked from no growth to
fastest growth:
Θ(1) — constant time takes the same amount of time regardless
of input size
Θ(log n) — logarithmic time
Θ(n) — linear time
Θ(n log n) — linearithmic time
Θ(n2 ) — quadratic time
Θ(n3 ), etc. — polynomial time
Θ(2n), Θ(3n), etc. — exponential time
(considered “intractable”; these are really, really horrible)
In addition, some programs will never terminate if they get
stuck in an...
8.26 Indicate whether the final volume of gas in each of the following is the same, larger, or smaller than the initial volume, if pres- sure and amount of gas do not change: a. A volume of 505 mL of air on a cold winter day at -15 °C is breathed into the lungs, where body temperature is 37 °C. b. The heater used to heat the air in a hot-air balloon is turned off. c.A balloon filled with helium...
1. (10 points) Write an efficient iterative (i.e., loop-based) function Fibonnaci(n) that returns the nth Fibonnaci number. By definition Fibonnaci(0) is 1, Fibonnaci(1) is 1, Fibonnaci(2) is 2, Fibonnaci(3) is 3, Fibonnaci(4) is 5, and so on. Your function may only use a constant amount of memory (i.e. no auxiliary array). Argue that the running time of the function is Θ(n), i.e. the function is linear in n. 2. (10 points) Order the following functions by growth rate: N, \N,...
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