# Sarah Gerrard # The Fundamentals of Algorithms

Before delving deep into the intricacies of the individual algorithms, let's first take a moment to discuss some of the basics. This article will explore the fundamentals of algorithms, from simple sorting techniques to more complex graph algorithms. Furthermore, we will discuss common operations that we perform on algorithms and how to choose the best ones for a given problem.

## Algorithmic basics

Algorithms are at the core of computer programming - they are a set of instructions that a computer follows to solve a particular problem or accomplish a specific task. Like data structures, they are essential tools for developers, as they allow us to create efficient, reliable, and scalable software.

Algorithms, however, aren't just about solving problems - they also help us reason about our code and make sure it is correct. By breaking down complex tasks into smaller, more manageable pieces, we can write code that is easier to understand, maintain, and modify over time.

More practically, algorithms are used to speed up computation, minimize errors, and improve the performance of our programs. In carefully selecting and implementing the right algorithm for a task, we can make sure that our code is optimized for it, leading to faster and more reliable software.

In the next few sections of this article, we'll explore the fundamentals of algorithms, including types, characteristics, and common operations.

## Algorithm Types

### Sorting

Sorting algorithms are used to arrange a list of elements in a particular order. Some of the most common sorting algorithms are:

• Bubble sort: compares adjacent elements and swaps them if they are in the wrong order.

• Selection sort: selects the smallest element and swaps it with the first element, then selects the next smallest and swaps it with the second element, and so on.

• Insertion sort: inserts elements into the correct position, one at a time.

• Merge sort: divides the list into two halves, sorts each half recursively, and then merges them back together.

• Quick sort: selects a pivot element and partitions the list into elements less than the pivot and elements greater than the pivot, then sorts each partition recursively.

• Heap sort: a comparison-based algorithm that uses a binary heap data structure to sort a list of elements. It works by first building a max heap from the given list of elements, then repeatedly extracting the maximum element from the heap and placing it at the end of the list. This process continues until the entire list is sorted in ascending order.

### Searching

Searching algorithms are used to find a specific element in a list. Some of the most common search algorithms are:

• Linear search: checks each element in the list until the target element is found.

• Binary search: divides the list in half and checks if the target element is in the first half or the second half, then repeats the process until the target element is found.

### Recursion

This is a technique where a function calls itself repeatedly until a specific condition is met. This allows for elegant solutions to complex problems that would be difficult to solve iteratively.

### Graphs

Graph algorithms are used to analyze and manipulate graphs, which are data structures that consist of vertices (nodes) and edges that connect them. Some of the more common ones are:

• Breadth-first search: visits all the vertices in a graph at a given level before moving on to the next level.

• Depth-first search: visits all vertices by exploring as far as possible along each branch before backtracking.

• Dijkstra's algorithm: finds the shortest path between a given vertex and all other vertices in a weighted graph.

• Bellman-ford algorithms: finds the shortest path between a given vertex and all other vertices in a weighted graph, even in the presence of negative edge weights.

• Topological sort: arranges the vertices of a directed acyclic graph in a linear order that respects the partial order defined by the edges.

### Divide and conquer

This is a technique used to solve problems by breaking them down into smaller subproblems, solving each subproblem independently, and then combining the solutions to solve the original problem. Some common algorithms that use this method are:

• Quick sort

• Merge sort

• Binary search

### Dynamic programming

Dynamic programming is a method for solving problems by breaking them down into smaller subproblems and solving each subproblem only once, storing the solutions in a table to avoid redundant computations.

This method is used in a wide range of applications, from optimizing code to solving complex mathematical problems.

## An algorithms job

Algorithms are used to solve various computational problems. They are designed to operate on different types of data structures to perform different operations, such as sorting, searching, and graph manipulation.

As an example, sorting algorithms are used to arrange a list of elements in a specific order. Each algorithm has a unique way of sorting the data and has its advantages and disadvantages in terms of time and space complexity. Additionally, searching algorithms are used to locate a specific element.

Other algorithms, like recursion, divide-and-conquer, and dynamic programming, are used to solve complex problems. Recursion is when a function repeatedly calls itself until a specific condition is met; divide-and-conquer is a problem-solving technique that breaks down a problem into smaller sub-problems, solves each sub-problem independently, then combines to solve the original problem; and dynamic programming is used for solving problems by breaking them down into smaller sub-problems and storing the solutions in a table to avoid redundant computations.

In practice, different algorithms have different use cases depending on the data size, problem complexity, and desired time and space complexity. Understanding each algorithm independently will help you select the appropriate algorithm for your problem.

## Key Takeaways

In conclusion, algorithms are crucial tools for solving computational problems and are used in various applications, from sorting and searching to graph manipulation and complex problem-solving techniques like recursion and dynamic programming. By selecting and implementing the appropriate algorithm for a given task, programmers can significantly improve the performance and efficiency of their programs, reduce errors, and make their code more adaptable to changing needs.

By learning about algorithms and data structures, developers can create efficient, reliable, and scalable software that solves complex problems and meets the needs of their users.

Make sure to follow my blog as we go into depth about some common data structures and algorithms!