Introduction to Algorithms and Programs

An algorithm is a step-by-step procedure for solving a problem or achieving a specific goal.
A program is a sequence of instructions written to perform a specific task with a computer.
Algorithms can be expressed in many kinds of notations, including natural languages, pseudocode, flowcharts, drakon-charts, programming languages or control tables.

Types of Algorithms

Recursive Algorithms

Recursive algorithms call themselves with smaller instances of the same problem.
They are effective for problems that can be divided into smaller, identical problems.
Recursive algorithms can often be more elegant and simpler to understand than their iterative counterparts.

Brute Force Algorithms

Brute force algorithms simply try all possible options until a satisfactory solution is found.
These algorithms are simple to understand and implement but are often very inefficient.

Divide and Conquer Algorithms

Divide and conquer algorithms break the problem down into independent sub-problems, solve each sub-problem individually, and then combine the solution to the sub-problems to solve the main problem.
Unlike brute-force algorithms, they are more efficient and reduce the amount of computation by breaking down the problem.

Greedy Algorithms

Greedy algorithms choose the best option at each step as it aims for global optimisation, meaning they make locally optimal choices at each step in the hope that these choices will lead to a globally optimal solution.

Steps in Algorithm Development

Problem Definition

The problem must be clearly defined in terms of the given input and the expected output.

Algorithm Design

Use analytical and observational skills to design a solution to the problem.
This often involves identifying a pattern or using a problem-solving strategy such as divide and conquer or brute force.

Algorithm Implementation

Draft the algorithm in pseudocode or a flowchart.
Once designed, the algorithm needs to be converted into a program using a programming language.

Algorithm Testing

Conduct thorough testing to ensure correctness.
This involves running the program with various inputs and comparing the output with expected results.

Algorithm Analysis

Evaluate the efficiency of the algorithm.
This includes analysing the time complexity and space complexity.

Key Concepts of Programming

Sequence

In sequence structure, the instructions are executed in the order they appear.

Selection

In selection or decision structures, a condition is tested. If the condition is true, an action is carried out. Otherwise, a different action is performed.

Iteration

In iteration or loop structures, a set of instructions is executed repeatedly until a particular condition is met.
There are different types of loops available including while, for and do-while loops.

Writing Programs

Begin by analysing the problem, outlining the solution, and breaking it down into manageable parts.
Write and test each part, one by one.
Once all parts are working correctly, integrate them together to create the final program.

Remember: Effective programming requires not just understanding of the programming language, but also strong problem-solving skills. You need to be able to devise a plan (an algorithm) for solving a given problem and then implement that plan (write the program).