Distinguishing Between Problem Restatement and Abstract Representation in Problem-Solving

  1. Problem Restatement: In problem restatement, you rephrase the original problem in your own words while retaining its core essence. The purpose is to gain clarity, better understanding, and perhaps reveal hidden insights about what is being asked. You’re essentially asking, “What is the problem really asking me to do?” but in terms that make it clearer to you.

  2. Abstract Representation: Abstract representation takes it a step further by converting the problem into a formal model, often mathematical, or some sort of a data structure. This is usually devoid of any real-world context and is strictly technical. Here, you answer the question, “How can this problem be generalized and represented in a structured format?” You might represent entities as variables, relationships as equations, or complex structures as graphs, arrays, or trees.

Key Differences:

  1. Scope:

    • Problem restatement is often broader and takes into account the context in which the problem exists.
    • Abstract representation is focused on the technical aspects required for solving the problem.

  2. Formality:

    • Problem restatement is more informal and might even be conversational.
    • Abstract representation is more formal and technical.

  3. Purpose:

    • Restatement aims for clarity and understanding.
    • Abstract representation aims for a structured model suitable for algorithmic or mathematical treatment.

  4. Language:

    • Problem restatement uses natural language.
    • Abstract representation uses the language of mathematics or computational models.

  5. Target Audience:

    • Restatement often helps both the problem solver and anyone interested in understanding the problem.
    • Abstract representation mainly aids the problem solver in designing an algorithm or formula for the solution.

By understanding both, you set a strong foundation for problem-solving, making it easier to transition from understanding what needs to be solved to actually solving it.