Choosing an appropriate library for a programming task requires careful consideration of several factors. Firstly, evaluate the functionality of the library to ensure it aligns with your project's requirements. It should offer the features and capabilities needed without excessive, unnecessary functionalities. Secondly, assess the library's reliability and performance by reviewing its documentation, update history, and community feedback. A well-maintained library with frequent updates and a positive reputation is preferable. Thirdly, consider the compatibility of the library with your existing codebase and technologies. It should integrate smoothly without causing conflicts. Additionally, check the licensing terms to ensure they are compatible with your project's goals and distribution plans. Finally, consider the ease of use and learning curve. A library with comprehensive documentation and a supportive community can significantly reduce the time needed to learn and implement it. Balancing these factors helps in selecting a library that not only meets the immediate needs but also supports long-term project sustainability and growth.

While external libraries offer many advantages, they also come with potential risks and disadvantages. One primary concern is dependency issues. Relying on external code means that if the library is no longer maintained or updated, your project could face significant challenges, including security vulnerabilities and compatibility problems with newer technologies. Another risk is the introduction of bugs or errors from the external code, which can affect the stability and reliability of your project. Additionally, there's the issue of license restrictions. Some libraries may have licensing terms that could restrict the usage or distribution of your software. Also, over-reliance on libraries can lead to bloat, where a project becomes laden with unnecessary functionalities, increasing its size and potentially impacting performance. Lastly, using libraries often means that developers need to understand and adapt to the coding style and conventions used in the library, which can add a learning curve and potentially increase development time.

Function overloading is a programming concept where multiple functions can have the same name but differ in parameters (type, number, or both). It allows a function to perform different operations based on the arguments passed to it, increasing the flexibility and readability of the code. In pseudocode, function overloading can be represented by defining multiple functions with the same name but with different parameter lists. For example:

FUNCTION add (number1, number2)

RETURN number1 + number2

END FUNCTION

FUNCTION add(number1, number2, number3)

RETURN number1 + number2 + number3

END FUNCTION

Here, the add function is overloaded with two variations: one that adds two numbers and another that adds three. The correct function is chosen based on the number of arguments passed when the function is called. This concept is particularly useful in scenarios where a similar operation needs to be performed, but the input might vary in terms of quantity or type.

The use of external libraries significantly reduces both the development time and cost of a project. By incorporating these libraries, developers can leverage pre-existing, tested, and optimised code, which eliminates the need to develop complex functionalities from scratch. This reuse of code accelerates the development process, as developers can focus on the unique aspects of their project rather than reinventing the wheel. Additionally, libraries often come with extensive documentation and community support, which aids in quick resolution of issues and learning. In terms of cost, using libraries can decrease the need for extensive manpower and resources dedicated to writing and testing new code. This is especially beneficial for small teams or individual developers who might have limited resources. However, it's crucial to ensure that the chosen libraries are reliable, well-maintained, and compatible with the project's requirements to avoid potential issues that could arise from outdated or incompatible code.

Creating a custom function is recommended in scenarios where specific, unique requirements of a project cannot be effectively addressed by built-in or library functions. This includes situations where:

• Unique Logic: The project requires a function that performs a specific task not covered by existing functions, or where the existing functions do not meet the precise requirements.
• Performance Optimisation: Custom functions can be tailored for performance, especially in scenarios where existing functions may not be efficient enough, or where performance is a critical aspect of the project.
• Control and Security: Custom functions offer complete control over the code, which is crucial in scenarios where security and predictability are paramount. It eliminates any unforeseen risks associated with external code.
• Simplicity and Size: Sometimes, existing libraries may be too large or complex for a simple task. In such cases, a custom function can provide a more straightforward and lightweight solution.
• Educational or Learning Purposes: Writing custom functions can be an invaluable learning experience, offering deeper insights into the programming concepts and logic involved.

However, it's essential to weigh the benefits of creating a custom function against the time and resources required for development and testing. If an existing function can be adapted with minor modifications, it may be more efficient than building a new one from scratch.