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Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2, f3 and f4?
f1(n) = 2^n
f2(n) = n^(3/2)
f3(n) = nLogn
f4(n) = n^(Logn)
f2(n) = n^(3/2)
f3(n) = nLogn
f4(n) = n^(Logn)
- a)f3, f2, f4, f1
- b)f3, f2, f1, f4
- c)f2, f3, f1, f4
- d)f2, f3, f4, f1
Correct answer is option 'A'. Can you explain this answer?
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Which of the given options provides the increasing order of asymptotic...
f1(n) = 2^n
f2(n) = n^(3/2)
f3(n) = nLogn
f4(n) = n^(Logn)
f2(n) = n^(3/2)
f3(n) = nLogn
f4(n) = n^(Logn)
Except f3, all other are exponential. So f3 is definitely first in output. Among remaining, n^(3/2) is next. One way to compare f1 and f4 is to take Log of both functions. Order of growth of Log(f1(n)) is Θ(n) and order of growth of Log(f4(n)) is Θ(Logn * Logn). Since Θ(n) has higher growth than Θ(Logn * Logn), f1(n) grows faster than f4(n). Following is another way to compare f1 and f4. Let us compare f4 and f1. Let us take few values to compare
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Which of the given options provides the increasing order of asymptotic...
Asymptotic complexity refers to the rate at which a function grows as its input size increases. It is often expressed using big-O notation, which provides an upper bound on the growth rate of the function. In this question, we are given four functions f1, f2, f3, and f4, and we need to determine their asymptotic complexity in increasing order.
The given functions are:
f1(n) = 2^n
f2(n) = n^(3/2)
f3(n) = nLogn
f4(n) = n^(Logn)a
To determine their asymptotic complexity, we can compare their growth rates as n increases.
1. f1(n) = 2^n
This function grows very quickly as n increases. As n approaches infinity, the function approaches infinity at an exponential rate. Therefore, its asymptotic complexity is O(2^n).
2. f2(n) = n^(3/2)
This function grows more slowly than f1(n) but faster than f3(n) and f4(n). As n approaches infinity, the function approaches infinity at a polynomial rate. Therefore, its asymptotic complexity is O(n^(3/2)).
3. f3(n) = nLogn
This function grows more slowly than f2(n) but faster than f4(n). As n approaches infinity, the function approaches infinity at a rate that is slower than any polynomial, but faster than a logarithmic rate. Therefore, its asymptotic complexity is O(nLogn).
4. f4(n) = n^(Logn)a
This function grows more slowly than f3(n) and f2(n), but faster than f1(n). As n approaches infinity, the function approaches infinity at a rate that is slower than any polynomial or logarithmic rate. Therefore, its asymptotic complexity is O(n^(Logn)a).
Therefore, the increasing order of asymptotic complexity of the given functions is f3, f2, f4, f1.
The given functions are:
f1(n) = 2^n
f2(n) = n^(3/2)
f3(n) = nLogn
f4(n) = n^(Logn)a
To determine their asymptotic complexity, we can compare their growth rates as n increases.
1. f1(n) = 2^n
This function grows very quickly as n increases. As n approaches infinity, the function approaches infinity at an exponential rate. Therefore, its asymptotic complexity is O(2^n).
2. f2(n) = n^(3/2)
This function grows more slowly than f1(n) but faster than f3(n) and f4(n). As n approaches infinity, the function approaches infinity at a polynomial rate. Therefore, its asymptotic complexity is O(n^(3/2)).
3. f3(n) = nLogn
This function grows more slowly than f2(n) but faster than f4(n). As n approaches infinity, the function approaches infinity at a rate that is slower than any polynomial, but faster than a logarithmic rate. Therefore, its asymptotic complexity is O(nLogn).
4. f4(n) = n^(Logn)a
This function grows more slowly than f3(n) and f2(n), but faster than f1(n). As n approaches infinity, the function approaches infinity at a rate that is slower than any polynomial or logarithmic rate. Therefore, its asymptotic complexity is O(n^(Logn)a).
Therefore, the increasing order of asymptotic complexity of the given functions is f3, f2, f4, f1.
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Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2, f3 and f4?f1(n) = 2^nf2(n) = n^(3/2)f3(n) = nLognf4(n) = n^(Logn)a)f3, f2, f4, f1b)f3, f2, f1, f4c)f2, f3, f1, f4d)f2, f3, f4, f1Correct answer is option 'A'. Can you explain this answer?
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Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2, f3 and f4?f1(n) = 2^nf2(n) = n^(3/2)f3(n) = nLognf4(n) = n^(Logn)a)f3, f2, f4, f1b)f3, f2, f1, f4c)f2, f3, f1, f4d)f2, f3, f4, f1Correct answer is option 'A'. 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 Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2, f3 and f4?f1(n) = 2^nf2(n) = n^(3/2)f3(n) = nLognf4(n) = n^(Logn)a)f3, f2, f4, f1b)f3, f2, f1, f4c)f2, f3, f1, f4d)f2, f3, f4, f1Correct answer is option 'A'. 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 Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2, f3 and f4?f1(n) = 2^nf2(n) = n^(3/2)f3(n) = nLognf4(n) = n^(Logn)a)f3, f2, f4, f1b)f3, f2, f1, f4c)f2, f3, f1, f4d)f2, f3, f4, f1Correct answer is option 'A'. Can you explain this answer?.
Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2, f3 and f4?f1(n) = 2^nf2(n) = n^(3/2)f3(n) = nLognf4(n) = n^(Logn)a)f3, f2, f4, f1b)f3, f2, f1, f4c)f2, f3, f1, f4d)f2, f3, f4, f1Correct answer is option 'A'. 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 Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2, f3 and f4?f1(n) = 2^nf2(n) = n^(3/2)f3(n) = nLognf4(n) = n^(Logn)a)f3, f2, f4, f1b)f3, f2, f1, f4c)f2, f3, f1, f4d)f2, f3, f4, f1Correct answer is option 'A'. 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 Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2, f3 and f4?f1(n) = 2^nf2(n) = n^(3/2)f3(n) = nLognf4(n) = n^(Logn)a)f3, f2, f4, f1b)f3, f2, f1, f4c)f2, f3, f1, f4d)f2, f3, f4, f1Correct answer is option 'A'. Can you explain this answer?.
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Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2, f3 and f4?f1(n) = 2^nf2(n) = n^(3/2)f3(n) = nLognf4(n) = n^(Logn)a)f3, f2, f4, f1b)f3, f2, f1, f4c)f2, f3, f1, f4d)f2, f3, f4, f1Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2, f3 and f4?f1(n) = 2^nf2(n) = n^(3/2)f3(n) = nLognf4(n) = n^(Logn)a)f3, f2, f4, f1b)f3, f2, f1, f4c)f2, f3, f1, f4d)f2, f3, f4, f1Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Which of the given options provides the increasing order of asymptotic complexity of functions f1, f2, f3 and f4?f1(n) = 2^nf2(n) = n^(3/2)f3(n) = nLognf4(n) = n^(Logn)a)f3, f2, f4, f1b)f3, f2, f1, f4c)f2, f3, f1, f4d)f2, f3, f4, f1Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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