Practice Running Time of the Naive Algorithm - 8.5 | 8. Prime Numbers and GCD | Discrete Mathematics - Vol 3
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Running Time of the Naive Algorithm

8.5 - Running Time of the Naive Algorithm

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is a prime number?

💡 Hint: Think about what makes a number prime.

Question 2 Easy

Up to what integer do we check divisibility to determine if a number is prime using the naive algorithm?

💡 Hint: This relates to the definition of composite numbers.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What defines a prime number?

A number greater than 1 with exactly two positive divisors.
Any odd number.
A numeral with no even divisors.

💡 Hint: Focus on the divisors of the number.

Question 2

The naive algorithm checks divisibility up to which number?

The number itself
Its square root
Half of the number

💡 Hint: Visualization of divisors helps with this.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Create a comparison chart detailing time complexity and efficiencies between the naive algorithm and AKS.

💡 Hint: Consider using a graph as a visual for this comparison.

Challenge 2 Hard

Explain how the inefficiency of the naive algorithm can impact cryptographic systems.

💡 Hint: Connect the practical application of primes in security systems.

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