GATE CSE 2023 | Complexity Analysis and Asymptotic Notations Question 8 | Algorithms

GATE CSE 2023

MCQ (More than One Correct Answer)

-0

Let $$f$$ and $$g$$ be functions of natural numbers given by $$f(n)=n$$ and $$g(n)=n^2$$. Which of the following statements is/are TRUE?

$$f \in O(g)$$

$$f \in \Omega (g)$$

$$f \in o(g)$$

$$f \in \Theta (g)$$

GATE CSE 2022

MCQ (Single Correct Answer)

-0.33

Which one of the following statements is TRUE for all positive functions f(n) ?

f(n²) = $$\theta$$(f(n)²), when f(n) is a polynomial

f(n²) = o(f(n)²)

f(n²) = O(f(n)²), when f(n) is an exponential function

f(n²) = $$\Omega$$(f(n)²)

GATE CSE 2021 Set 1

MCQ (Single Correct Answer)

-0.33

Consider the following three functions.

f₁ = 10ⁿ, f₂ = n^logn, f₃ = n^√n

Which one of the following options arranges the functions in the increasing order of asymptotic growth rate?

f₁ , f₂, f₃

f₂, f₁, f₃

f₃, f₂, f₁

f₂, f₃, f₁

GATE CSE 2020

MCQ (Single Correct Answer)

-0.33

For parameters a and b, both of which are $$\omega \left( 1 \right)$$,
T(n) = $$T\left( {{n^{1/a}}} \right) + 1$$, and T(b) = 1.
Then T(n) is

$$\Theta \left( {{{\log }_a}{{\log }_b}n} \right)$$

$$\Theta \left( {{{\log }_{ab}}n} \right)$$

$$\Theta \left( {{{\log }_b}{{\log }_a}n} \right)$$

$$\Theta \left( {{{\log }_2}{{\log }_2}n} \right)$$

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Finite Automata and Regular Language Push Down Automata and Context Free Language Undecidability Recursively Enumerable Language and Turing Machine

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