20 Questions
What is the purpose of complexity theory in computer science?
To analyze the efficiency of algorithms
Which problem is considered one of the most important open questions in computer science?
P = NP
In Landau's Big O notation, if f(n) grows slower than g(n), what does it mean?
f(n) is in small o of g(n)
If f(n) = 10n + 24 and g(n) = n^2, which function is greater for small values of n?
f(n)
What does it mean if f(n) is at most of the same order of magnitude as g(n)?
f(n) is in big O of g(n)
What would be the relationship between f(n) and g(n) if f n ∈ Ω(g n)?
f(n) grows at least as fast as g(n)
What condition does small o require for the function g compared to f?
g is larger than f only for arguments greater than a threshold
Which notation allows for multiple sign changes between f and c * g for n < n0?
Small o
What is the main difference between small o and big O?
Small o is a subset of big O
When is a function considered to grow exponentially?
When its growth rate is faster than a polynomial function
Which notation is used to upper bound the growth of a function?
O
In the Θ notation, what does it mean when f ∈ Θ(g)?
f grows exactly at the same rate as g
For which functions is the statement f ∈ O(n^2) true?
3n^2 + n
What does it mean when a function is in the Ω notation?
The function grows at least as fast as the stated function
Which notation is used to give a lower bound on the growth of a function?
Ω
If f(n) = n^2 + 3n and g(n) = 5n - n^2, which statement is true?
f(n) ∈ O(n^2)
What does it indicate if a function is in the small-o notation?
The function grows slower than the stated function
Which notation would be most useful when estimating computational effort precisely?
( \Theta ) - Theta notation
'f(n) ∈ Θ(g(n))' implies __________.
'f(n) ∈ Ω(g(n))' implies 'f(n) ∈ O(g(n))'
Which statement correctly explains Ω and O notation relationship?
O provides an upper bound while Ω provides a lower bound.
Learn about the importance of determining the computability of functions in theoretical computer science, as well as assessing algorithm efficiency in terms of runtime and memory requirements. Explore complexity theory and the notorious P=NP problem.
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