Algorithm: Working with Algorithms

Introduction to Algorithms

An algorithm is a well-defined sequence of steps or instructions designed to perform a specific task or solve a particular problem.
Each step in an algorithm is precise and unambiguous, following a logical order. An algorithm should always produce an output, given a valid set of inputs.
Algorithms are widely used in problem-solving scenarios in mathematics, computer science, engineering and more.

Definiteness: Every step in an algorithm is clear and unambiguous.
Finiteness: The algorithm terminates after a finite time.
Input: An algorithm has zero or more well-defined inputs.
Output: An algorithm produces one or more outputs.
Effectiveness: An algorithm should be simple, generic and practical so that it can deal with all problem instances.

Divide and conquer: A problem is divided into smaller sub-problems until they can be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.
Dynamic programming: This methodology is similar to divide and conquer. However, sub-problem solutions are remembered to avoid multiple calculations of the same sub-problem.
Greedy method: This involves building up a solution to the problem by always choosing the next step that offers the most immediate benefit or profit.
Backtracking: This approach is used when the problem involves searching a large solution space. It systematically explores all paths in the solution space.

The time complexity of an algorithm quantifies the amount of time taken by the algorithm to run, as a function of the length of the input. It’s usually expressed using Big O notation.
The space complexity of an algorithm quantifies the amount of space or memory taken by an algorithm to run, as a function of the length of the input.
In general, the goal is to choose or design algorithms with acceptable time and space requirements.

Pseudocode is a high-level description of an algorithm. It uses the structural conventions of a programming language but is intended for human reading rather than machine reading.
A flowchart is a type of diagram that represents an algorithm or process, showing the steps as boxes of various kinds, and their order by connecting these with arrows.
Both pseudocode and flowcharts are useful tools for designing, understanding and communicating algorithms.