Consider the following functions from positives integers to real numbers 10 n n log2n 100n The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is gate computer science 2017

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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: -gate computer science 2017

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


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Answers

D) 100/n, 10, log˅2n, √n, n 

Explanation
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. 10 is constant, not affected by value of n. √n Square root and log2n is logarithmic. So log2n is definitely less than √n n has linear growth and 100/n grows inversely with value of n. For bigger value of n, we can consider it 0, so 100/n is least and n is max. So the increasing order of asymptotic complexity will be :
100/n < 10 < log2n < √n < n
So, option (b) is true.


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