Visualisation for Problem Solving

Overview

Visualisation in problem-solving involves creating a graphical or mental representation of how a program operates or how a problem is structured. It helps programmers and problem-solvers understand the flow of data, the logic of algorithms, and the relationships between different components.

By visualising a problem, developers can anticipate potential issues, plan solutions more effectively, and communicate their ideas.

What is Visualisation?

• Definition: A technique that involves representing a problem or a program's operation through diagrams, flowcharts, graphs, or other visual tools.
• Purpose: To simplify complex problems by providing a clear and structured view of the solution or process.

How Visualisation Helps in Problem-Solving

Creates a Mental Model:

• Visualisation helps build a mental image of how a program works or how data flows through an algorithm.
• Example: Visualising the steps of a sorting algorithm using an animation of data elements being rearranged.

Supports Planning:

• By visualising the problem, developers can plan the steps of an algorithm or the structure of a program in advance.
• Example: Drawing a flowchart to map out the decision-making process before writing code.

Identifies Errors Early:

• Visual representations can help spot logical errors, inefficiencies, or overlooked edge cases.
• Example: Visualising a recursive algorithm to identify incorrect base cases or infinite recursion.

Facilitates Communication:

Diagrams and visual tools make it easier to explain complex ideas to team members or stakeholders.

Common Visualisation Techniques

Flowcharts

• Description: Graphical representations of a process or algorithm, showing the sequence of steps and decision points.
• Purpose: To illustrate the flow of control in a program.

[Start] → [Input data] → [Process data] → [Output result] → [End]

Trace Tables

• Description: A table used to track the values of variables at each step of an algorithm.
• Purpose: To manually trace the execution of code and verify its correctness.

Step   | x   | y   | Result
---------------------------
Start  | 0   | 0   | 0
Step 1 | 1   | 0   | 1
Step 2 | 1   | 2   | 3

State Diagrams

• Description: Visualise the states of a system and the transitions between them.
• Purpose: To model systems with multiple states (e.g., a vending machine).

[Idle] → [Waiting for Input] → [Processing] → [Completed]

Graphs and Trees

• Description: Represent data structures or relationships between entities.
• Purpose: To visualise hierarchical structures (e.g., file systems) or connected data (e.g., social networks).
• Example: Binary search tree showing how nodes are traversed.

Algorithm Animations

• Description: Dynamic visualisations that show how algorithms operate step by step.
• Purpose: To help understand the flow and efficiency of algorithms like sorting or searching.
• Example: Animation of the Quick Sort algorithm showing partitioning and recursive sorting.

Benefits of Visualisation

• Enhances Understanding: Visual tools simplify complex problems, making it easier to grasp their structure and behaviour.
• Improves Problem-Solving: By seeing the problem and its solution visually, developers can better anticipate and address potential issues.
• Aids in Debugging: Trace tables and flowcharts help track the flow of data and identify where errors occur.
• Supports Collaboration: Visual representations are easier to share and discuss with others, improving teamwork and communication.

Note Summary