Algorithmic Problems

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Algorithmic problems involve following a finite and rigid set of procedures with limited predictive decisions to reach a solution. Commonly found in mathematics, science, and computer science, these problems emphasize procedural knowledge and calculation skills. 

Table of Contents

When to use

  • A learner needs to practice and master a specific procedure or algorithm, such as long division, equation factoring, or following a recipe.
  • The goal is to develop procedural fluency and automaticity in performing specific tasks.
  • Can use for activity only or introductory lesson.
  • Use as an introduction to ‘rule using’ pattern, mathematical pattern, problem solving patterns.
  • Any time you are applying a rule or following a procedure, or steps in a process.
  • When the order of the steps in the procedure matters. Changing the steps may change the output.

Pattern Requirements

  • A well-defined problem with a clear set of procedures to follow.
  • Opportunities for learners to practice and apply the algorithm to different situations.

Pattern Structure

  1. Understand the problem

    Carefully read and analyze the problem statement, making sure you understand the input, output, and constraints involved.

  2. Identify the algorithm

    Determine the type of algorithm or procedure required to solve the problem. This may involve recalling a known algorithm or developing a new one based on the problem's requirements.

  3. Break down the problem

    Decompose the problem into smaller, manageable subproblems or steps. This will help you better understand the overall structure and flow of the algorithm. (This will often be combined with step 2.)

  4. Develop the algorithm

    Create a step-by-step procedure for solving the problem, incorporating the subproblems or steps identified in the previous step. Make sure the algorithm is clear, concise, and logically sound.

  5. Implement the algorithm

    Translate the algorithm into code or a series of instructions that a computer or another system can execute. Ensure that your implementation is efficient and adheres to the problem's constraints.

  6. Test/Practice the algorithm

    Run the algorithm on sample inputs and outputs to verify its correctness. Debug and refine the algorithm as needed, ensuring it accurately and efficiently solves the problem

  7. Analyze the algorithm

    Evaluate the algorithm's performance in terms of time and space complexity. This will help you understand the efficiency and scalability of the algorithm when applied to larger or more complex problems.

  8. Review and refine

    Reflect on the problem-solving process and the algorithm you developed. Determine if there are any improvements or optimizations that can be made to enhance the algorithm's performance or make it more robust.

  9. Apply the algorithm

    Use the algorithm to solve the given problem, as well as similar or related problems that may arise in the future.

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