GATE CS 2017 Set 1 — Question 4
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Question
Consider the following functions from positive integers to real numbers:The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:
Correct answer
(B) (100)/(n), 10, ₂ n, √(n), n
Solution
To arrange the functions in increasing order of asymptotic complexity, we analyze their growth rates as :
1.: As , this function approaches 0. Its growth rate is less than constant ().
2.: This is a constant function, .
3.: Logarithmic growth, . We know that .
4.: Fractional power growth, . We know that .
5.: Linear growth, . We know that .
Combining these, the increasing order is:This matches option (B).Continue learning with Success Tracker
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