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Midterm Quick Review 1: Main Topics in Algorithms and Proofs

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Questions and Answers

What type of running time does O(n log n) denote?

Logarithmic
Log-linear (correct)
Exponential
Linear

In the context of big-O notation, what does O(1) denote?

Constant running time (correct)
Logarithmic running time
Exponential running time
Linear running time

What type of input size does O(n^2) represent in terms of running time?

Exponential
Logarithmic
Quadratic (correct)
Linear

If a function has a complexity of O(n), what is the order of growth for this function?

Linear (D) Signup and view all the answers

What is the best case scenario for finding an element in a list?

Minimum running time (B) Signup and view all the answers

How are elements added to or removed from a stack?

Only at the top end (A) Signup and view all the answers

What is the purpose of an algorithm?

To map inputs to outputs (D) Signup and view all the answers

Which statement best describes Big-O notation?

It represents the worst-case runtime behavior of an algorithm. (D) Signup and view all the answers

What is the exponential form of log3(27) = 3?

3^3 = 27 (C) Signup and view all the answers

In evaluating log6(36) = x, what is the value of x?

2 (B) Signup and view all the answers

Which statement accurately reflects the relationship between algorithms and programs?

A program is a specific implementation of an algorithm in a programming language. (B) Signup and view all the answers

What does Big-Theta notation classify?

The exact growth rate of a function within constant factors (D) Signup and view all the answers

What does it mean when f(x) is O(g(x)) in Big-O notation?

g(x) is an upper bound for f(x) (B) Signup and view all the answers

In Big-Omega notation, what does f(x) being Ω(g(x)) imply?

g(x) is a lower bound for f(x) (C) Signup and view all the answers

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) (D) Signup and view all the answers

How is a direct proof useful in mathematics?

To demonstrate the validity of a claim using logical reasoning (A) Signup and view all the answers

What is the goal of Proof by Induction in mathematics?

To prove that something is true for all natural numbers (B) Signup and view all the answers

How do Big-Oh, Big-Omega, and Big-Theta notations help analyze algorithms?

By providing insights into the runtime efficiency of algorithms (A) Signup and view all the answers

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