Practice - Proving NP-Completeness by Reduction (The 'Domino Effect')
Practice Questions
Test your understanding with targeted questions
What does NP-complete mean?
💡 Hint: Think about what it means for a problem to be verified quickly.
Name a known NP-complete problem.
💡 Hint: Consider foundational problems in computer science.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is an NP-complete problem?
💡 Hint: Recall the definitions of NP and NP-hard.
The process of reducing a known NP-complete problem to another problem demonstrates what?
💡 Hint: Think about the implications of transformations.
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Challenge Problems
Push your limits with advanced challenges
Argue whether the Hamiltonian cycle is NP-complete by constructing a polynomial-time reduction from the Traveling Salesperson Problem.
💡 Hint: Think about how defining a cycle relates to optimizing a total distance.
Using 3-SAT, show how you can convert a general SAT instance to a reduction that highlights this problem's NP-completeness.
💡 Hint: Focus on manipulating clauses of various sizes.
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