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Consider the following functions:
f(n) = 2^n
g(n) = n!
h(n) = n^logn
Q. Which of the following statements about the asymptotic behavior of f(n), g(n), and h(n) is true?
  • a)
     f(n) = O(g(n)); g(n) = O(h(n))
  • b)
    f(n) = Ω(g(n)); g(n) = O(h(n))
  • c)
    g(n) = O(f(n)); h(n) = O(f(n))
  • d)
    h(n) = O(f(n)); g(n) = Ω(f(n))
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Consider the following functions:f(n) = 2^ng(n) = n!h(n) = n^lognQ. Wh...
According to order of growth: h(n) < f(n) < g(n) (g(n) is asymptotically greater than f(n) and f(n) is asymptotically greater than h(n) ) We can easily see above order by taking logs of the given 3 functions
lognlogn < n < log(n!) (logs of the given f(n), g(n) and h(n)).
Note that log(n!) =
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Most Upvoted Answer
Consider the following functions:f(n) = 2^ng(n) = n!h(n) = n^lognQ. Wh...
Ω(g(n)); g(n) = O(h(n))c)f(n) = Θ(g(n)); g(n) = O(h(n))d)f(n) = O(g(n)); g(n) = Θ(h(n))

Answer:
d) f(n) = O(g(n)); g(n) = Θ(h(n))

Explanation:
- f(n) = 2^n: grows exponentially
- g(n) = n!: grows super-exponentially (more precisely, it grows factorially)
- h(n) = n^logn: grows slower than g(n) but faster than f(n) (more precisely, it grows faster than any polynomial but slower than any exponential)

Since f(n) grows slower than g(n), we have f(n) = O(g(n)). Since g(n) and h(n) are both super-exponential, we have g(n) = Θ(h(n)). Therefore, the correct statement is d) f(n) = O(g(n)); g(n) = Θ(h(n)).
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Consider the following functions:f(n) = 2^ng(n) = n!h(n) = n^lognQ. Which of the following statements about the asymptotic behavior of f(n), g(n), and h(n) is true?a)f(n) = O(g(n)); g(n) = O(h(n))b)f(n) =Ω(g(n)); g(n) = O(h(n))c)g(n) = O(f(n)); h(n) = O(f(n))d)h(n) = O(f(n)); g(n) =Ω(f(n))Correct answer is option 'D'. Can you explain this answer?
Question Description
Consider the following functions:f(n) = 2^ng(n) = n!h(n) = n^lognQ. Which of the following statements about the asymptotic behavior of f(n), g(n), and h(n) is true?a)f(n) = O(g(n)); g(n) = O(h(n))b)f(n) =Ω(g(n)); g(n) = O(h(n))c)g(n) = O(f(n)); h(n) = O(f(n))d)h(n) = O(f(n)); g(n) =Ω(f(n))Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the following functions:f(n) = 2^ng(n) = n!h(n) = n^lognQ. Which of the following statements about the asymptotic behavior of f(n), g(n), and h(n) is true?a)f(n) = O(g(n)); g(n) = O(h(n))b)f(n) =Ω(g(n)); g(n) = O(h(n))c)g(n) = O(f(n)); h(n) = O(f(n))d)h(n) = O(f(n)); g(n) =Ω(f(n))Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following functions:f(n) = 2^ng(n) = n!h(n) = n^lognQ. Which of the following statements about the asymptotic behavior of f(n), g(n), and h(n) is true?a)f(n) = O(g(n)); g(n) = O(h(n))b)f(n) =Ω(g(n)); g(n) = O(h(n))c)g(n) = O(f(n)); h(n) = O(f(n))d)h(n) = O(f(n)); g(n) =Ω(f(n))Correct answer is option 'D'. Can you explain this answer?.
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