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Semester 1 · Autumn 2025

Week 2 – Clique and Algorithms

Computationally Hard Problems 02450 · Week 2 Focus: Clique and Algorithms

What Is an Algorithm?

  • Definition:
    An algorithm is an unambiguous, abstract description of a method for solving a problem.

    • Unambiguous: Everyone following the steps obtains the same result.

    • Abstract: Independent of machine or programming language.

Example: Recipe for baking bread — inputs (ingredients) → series of exact steps → output (bread). This emphasizes deterministic, clearly defined input–output behavior

Algorithm Complexity

Algorithms consume resources:

  • ⏱ Time (primary measure)
  • 💾 Memory
  • 💽 I/O or storage access
  • 🌐 Network use, parallelism, power, etc.

We normally analyze time complexity.

In the form of worst case and best case

#TODO

Excercice