18 Questions
What type of running time does O(n log n) denote?
Log-linear
In the context of big-O notation, what does O(1) denote?
Constant running time
What type of input size does O(n^2) represent in terms of running time?
Quadratic
If a function has a complexity of O(n), what is the order of growth for this function?
Linear
What is the best case scenario for finding an element in a list?
Minimum running time
How are elements added to or removed from a stack?
Only at the top end
What is the purpose of an algorithm?
To map inputs to outputs
Which statement best describes Big-O notation?
It represents the worst-case runtime behavior of an algorithm.
What is the exponential form of log3(27) = 3?
3^3 = 27
In evaluating log6(36) = x, what is the value of x?
2
Which statement accurately reflects the relationship between algorithms and programs?
A program is a specific implementation of an algorithm in a programming language.
What does Big-Theta notation classify?
The exact growth rate of a function within constant factors
What does it mean when f(x) is O(g(x)) in Big-O notation?
g(x) is an upper bound for f(x)
In Big-Omega notation, what does f(x) being Ω(g(x)) imply?
g(x) is a lower bound for f(x)
When f(x) is θ(g(x)), what relationship exists between the growth rates of f(x) and g(x)?
f(x) is a tight lower bound and a tight upper bound for g(x)
How is a direct proof useful in mathematics?
To demonstrate the validity of a claim using logical reasoning
What is the goal of Proof by Induction in mathematics?
To prove that something is true for all natural numbers
How do Big-Oh, Big-Omega, and Big-Theta notations help analyze algorithms?
By providing insights into the runtime efficiency of algorithms
Prepare for your midterm with this quick review covering key topics such as algorithms, simplifying expressions, direct proof, proof by induction, Big O notation, classifying the order of growth of functions, worst-case runtime behavior, stacks, queues, and binary trees. Understand the importance of correctness, unambiguity, and steps in algorithms.
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