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Advanced Topic 37 of 51 Theory & Discrete Math

NP-Completeness

Hardest problems in NP to which all NP reduces.

How it works

A problem is NP-complete if it is in NP and every NP problem reduces to it in polynomial time. Solving one in P would show P = NP.

Where it is used

SAT, 3-coloring, Hamiltonian cycle, subset sum.

Common pitfall

NP-hard problems need not be in NP.

Where it fits in the course

NP-Completeness is topic 37 of 51 in Theory & Discrete Math, rated Advanced. It follows Class NP. The next topic is Cook-Levin Theorem.

Practice and explore

How to study this topic

  1. Read the explanation above and restate the definition in your own words.
  2. Open the interactive lesson and answer its mini quiz.
  3. Read the common pitfall, then write a short example that avoids it.
  4. Check your understanding in the Theory & Discrete Math quiz, and revisit the topic if you miss a question.

Frequently asked questions

What is NP-Completeness?
Hardest problems in NP to which all NP reduces. It belongs to Theory & Discrete Math and is an advanced-level topic.
Where do people use NP-Completeness?
SAT, 3-coloring, Hamiltonian cycle, subset sum.
What is the most common mistake with NP-Completeness?
NP-hard problems need not be in NP.
What should I learn before this topic?
Start with Class NP, the topic just before it in Theory & Discrete Math.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Theory & Discrete Math quiz.
Is NP-Completeness hard to learn?
It is an Advanced topic. Expect to read the explanation more than once and to connect it with earlier topics. Working through a small example by hand helps most.
How long does it take to learn NP-Completeness?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to NP-Completeness?
Class NP, Cook-Levin Theorem, Class P are closely connected. The full list is in the related topics section of this page.
What should I study after NP-Completeness?
Continue with Cook-Levin Theorem, the next topic in Theory & Discrete Math.

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