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Consider the following functions from positives integers to real numbers 10, √n, n, log2n, 100/n. The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:
- a)log2n, 100/n, 10, √n, n
- b)100/n, 10, log2n, √n, n
- c)10, 100/n ,√n, log2n, n
- d)100/n, log2n, 10 ,√n, n
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Consider the following functions from positives integers to real numbe...
For the large number, value of inverse of number is less than a constant and value of constant is less than value of square root.
Therefore, 100/n < 10< log<sub>2</sub>n< √n< n
It can be proven by substituting any big number in all the functions.
Therefore, 100/n < 10< log<sub>2</sub>n< √n< n
It can be proven by substituting any big number in all the functions.
Most Upvoted Answer
Consider the following functions from positives integers to real numbe...
Explanation:
Asymptotic complexity is the measure of the rate at which the running time of an algorithm increases as the size of the input increases. In order to compare the asymptotic complexity of the given functions, we need to find the order of growth of each function.
The order of growth of a function is determined by the term with the highest degree in the function. For example, in the function f(n) = 3n^2 + 2n + 1, the term with the highest degree is n^2, so the order of growth is O(n^2).
Arranging the Functions:
We will arrange the given functions in increasing order of asymptotic complexity as follows:
1. log2n: This function grows at a slower rate than any polynomial function. Therefore, its order of growth is O(log n).
2. 100/n: This function has an inverse relationship with n, which means that its value decreases as n increases. Therefore, its order of growth is O(1/n).
3. 10: This function is a constant function, which means that its value does not depend on the input size n. Therefore, its order of growth is O(1).
4. n: This function grows linearly with the input size n. Therefore, its order of growth is O(n).
Conclusion:
Based on the above analysis, the correct arrangement of the given functions in increasing order of asymptotic complexity is option 'B' – 100/n, 10, log2n, n, n.
Asymptotic complexity is the measure of the rate at which the running time of an algorithm increases as the size of the input increases. In order to compare the asymptotic complexity of the given functions, we need to find the order of growth of each function.
The order of growth of a function is determined by the term with the highest degree in the function. For example, in the function f(n) = 3n^2 + 2n + 1, the term with the highest degree is n^2, so the order of growth is O(n^2).
Arranging the Functions:
We will arrange the given functions in increasing order of asymptotic complexity as follows:
1. log2n: This function grows at a slower rate than any polynomial function. Therefore, its order of growth is O(log n).
2. 100/n: This function has an inverse relationship with n, which means that its value decreases as n increases. Therefore, its order of growth is O(1/n).
3. 10: This function is a constant function, which means that its value does not depend on the input size n. Therefore, its order of growth is O(1).
4. n: This function grows linearly with the input size n. Therefore, its order of growth is O(n).
Conclusion:
Based on the above analysis, the correct arrangement of the given functions in increasing order of asymptotic complexity is option 'B' – 100/n, 10, log2n, n, n.
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Consider the following functions from positives integers to real numbers 10, √n, n, log2n, 100/n. The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:a)log2n, 100/n, 10, √n, nb)100/n, 10, log2n, √n, nc)10, 100/n ,√n, log2n, nd)100/n, log2n, 10 ,√n, nCorrect answer is option 'B'. Can you explain this answer?
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Consider the following functions from positives integers to real numbers 10, √n, n, log2n, 100/n. The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:a)log2n, 100/n, 10, √n, nb)100/n, 10, log2n, √n, nc)10, 100/n ,√n, log2n, nd)100/n, log2n, 10 ,√n, nCorrect answer is option 'B'. 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 from positives integers to real numbers 10, √n, n, log2n, 100/n. The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:a)log2n, 100/n, 10, √n, nb)100/n, 10, log2n, √n, nc)10, 100/n ,√n, log2n, nd)100/n, log2n, 10 ,√n, nCorrect answer is option 'B'. 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 from positives integers to real numbers 10, √n, n, log2n, 100/n. The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:a)log2n, 100/n, 10, √n, nb)100/n, 10, log2n, √n, nc)10, 100/n ,√n, log2n, nd)100/n, log2n, 10 ,√n, nCorrect answer is option 'B'. Can you explain this answer?.
Consider the following functions from positives integers to real numbers 10, √n, n, log2n, 100/n. The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:a)log2n, 100/n, 10, √n, nb)100/n, 10, log2n, √n, nc)10, 100/n ,√n, log2n, nd)100/n, log2n, 10 ,√n, nCorrect answer is option 'B'. 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 from positives integers to real numbers 10, √n, n, log2n, 100/n. The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:a)log2n, 100/n, 10, √n, nb)100/n, 10, log2n, √n, nc)10, 100/n ,√n, log2n, nd)100/n, log2n, 10 ,√n, nCorrect answer is option 'B'. 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 from positives integers to real numbers 10, √n, n, log2n, 100/n. The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:a)log2n, 100/n, 10, √n, nb)100/n, 10, log2n, √n, nc)10, 100/n ,√n, log2n, nd)100/n, log2n, 10 ,√n, nCorrect answer is option 'B'. Can you explain this answer?.
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Consider the following functions from positives integers to real numbers 10, √n, n, log2n, 100/n. The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:a)log2n, 100/n, 10, √n, nb)100/n, 10, log2n, √n, nc)10, 100/n ,√n, log2n, nd)100/n, log2n, 10 ,√n, nCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Consider the following functions from positives integers to real numbers 10, √n, n, log2n, 100/n. The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:a)log2n, 100/n, 10, √n, nb)100/n, 10, log2n, √n, nc)10, 100/n ,√n, log2n, nd)100/n, log2n, 10 ,√n, nCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Consider the following functions from positives integers to real numbers 10, √n, n, log2n, 100/n. The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:a)log2n, 100/n, 10, √n, nb)100/n, 10, log2n, √n, nc)10, 100/n ,√n, log2n, nd)100/n, log2n, 10 ,√n, nCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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