Problem Solving and Programming

This section covers the essential programming techniques and computational methods used to solve problems effectively with computers. The focus on modularity, recursion, and advanced problem-solving techniques enables students to develop efficient and reusable solutions in their programming.

Programming Techniques

Programming Constructs: Sequence, Iteration, Branching

Sequence: The order in which statements or instructions are executed. It follows a linear progression.

Iteration: Repeating a set of instructions using loops (e.g., for, while). It continues until a condition is met.

Branching: Decision-making within a program using conditional statements (if, else, switch). Different paths are taken based on certain conditions.

Recursion

Recursion: A function calls itself to solve a smaller instance of the same problem.

Advantages: Simplifies problems like tree traversal.

Disadvantages: Can be less efficient than iteration as it uses more memory (stack).

Comparison to Iteration: Recursion breaks problems down into sub-problems, whereas iteration repeatedly executes a block of code until a condition is met.

Global and Local Variables

Global Variables: Declared outside functions and accessible from anywhere in the program. Useful for sharing data between multiple parts of a program but can lead to unexpected side effects.

Local Variables: Declared within functions and only accessible within that function. Helps avoid conflicts between variables and ensures functions are more modular.

Modularity, Functions, and Procedures

Modularity: Breaking a program into smaller, manageable parts (modules) that can be developed and tested separately.

Functions: Sub-programs that return a value. They take parameters and return results.

Procedures: Sub-programs that do not return a value but perform specific tasks.

Parameter Passing:

By Value: A copy of the data is passed to the function, so changes do not affect the original data.

By Reference: The memory address of the data is passed, allowing the function to modify the original data.

Use of an IDE (Integrated Development Environment)

An IDE helps develop and debug programs with features like:

Code Editor: For writing and formatting code.

Compiler/Interpreter: To convert code into machine language.

Debugger: Helps identify and fix errors by providing step-by-step execution.

Auto-Completion: Suggests code completions to speed up writing.

Syntax Highlighting: Helps identify keywords, variables, and errors.

Use of Object-Oriented Techniques

Object-Oriented Programming (OOP) is based on objects and classes:

Classes: Blueprints for creating objects. They define properties (attributes) and behaviours (methods).

Objects: Instances of classes.

Key Concepts:

Inheritance: Allows a class to inherit properties and methods from another class.

Encapsulation: Protects the internal state of an object by restricting access to some components.

Polymorphism: Methods in different classes can have the same name but behave differently.

Abstraction: Hides the complex details of an object and only exposes what is necessary.

Computational Methods

Features of a Problem Solvable by Computational Methods

A problem can be solved computationally if:

It can be broken into smaller tasks.

The solution can be expressed in a logical sequence of steps.

There is a clear input and output.

Problem Recognition

Identifying when a situation can be transformed into a computational problem. Recognising patterns, inefficiencies, or areas where automation could improve efficiency.

Problem Decomposition

Breaking down a complex problem into smaller, more manageable components. Each component is easier to solve and understand, and can often be developed independently.

Use of Divide and Conquer

A strategy that recursively breaks down a problem into smaller sub-problems until they are simple enough to be solved directly. Example: Binary search.

Use of Abstraction

Simplifying a problem by removing unnecessary details. It helps focus on the key parts of the problem to find a solution without getting bogged down by irrelevant information.

Applying Knowledge of Advanced Techniques to Solve Problems

Backtracking

A recursive method for solving problems incrementally. If a solution fails, it backtracks and tries another approach. Used in problems like maze solving or constraint satisfaction.

Data Mining

The process of discovering patterns in large datasets using algorithms and statistical methods. Applied in fields such as market analysis and fraud detection.

Heuristics

An approach to problem-solving that uses practical methods or "rules of thumb" to produce solutions that may not be optimal but are good enough, especially when exact methods are too slow.

Performance Modelling

Analysing and predicting how a system will perform under different conditions. It helps in optimising system efficiency, often used in software testing and network analysis.

Pipelining

A technique where multiple stages of a process are overlapped to improve efficiency. Commonly used in CPU design where different stages of instruction execution are handled simultaneously.

Visualisation

The process of representing data or algorithms visually to better understand their structure or behaviour. Examples include flowcharts, graphs, and charts for complex data analysis.