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Chapter 3 — Chapter 3 — Algorithms and Problem Solving

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Characterizing Computational Problems

Source: CS 11, Ch 3, 3.1

📘Easy summary

To solve a problem computationally we identify its inputs, desired outputs and the process that transforms inputs into outputs. Classifications: decision problems (output yes/no), search problems (find an item meeting criteria), optimization problems (find the best solution) and counting problems (count the ways a condition is met). Well-defined problems have clear goals, inputs, processes and outputs (is a number even?). Ill-defined problems lack clear definitions or have ambiguous goals and requirements ('How to reduce poverty in Pakistan').

⭐Key points

  • Decision, search, optimization, counting.
  • Well-defined: clear goals, inputs, process, output.
  • Ill-defined: vague goals.

🔬Diagram

Problem typesDecisionSearchOptimizationCountingProblems

🌿Real-life example

'Is 7 even?' is a well-defined decision problem.

💡Exam tip

  • Well-defined = clear goals, inputs, processes, outputs.

✅Quick check

1. A well-defined problem has:

2. Output yes/no:

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