Data structures and algorithms: a complete guide for programmers

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Algorithms and data structures They are two pieces that fit together like a puzzle: one outlines the procedure for solving the problem, and the other determines where and how we store the information. While it may sound academic, mastering this pair is what separates a code that merely works from one that flies and scales without breaking.

If you want to pursue professional programming, prepare for technical interviews, or simply stop struggling with exercises like LeetCode and Codewars, you need a solid foundation in data structures and algorithmsThroughout this article you will see what they are, why they are so important, what main types exist, what basic operations they perform and what questions usually appear in exams and selection processes.

What are data structures and algorithms?

a data structure It is, basically, a specific way of organizing and storing information in memory to be able to operate on it efficiently. This organization is not random: it directly determines which operations are fast and which become costly (insert, search, delete, traverse, etc.).

When you choose the right data structure, your program can manage large volumes of data without breaking a sweat; when you choose poorly, even a small application can become slow, consume too much memory, or become impossible to maintain over time.

An algorithm It is a finite and ordered sequence of well-defined steps that transforms inputs into outputs to solve a specific problem. It's like a cooking recipe: it tells you what to do, in what order, and under what conditions, but it doesn't worry about how you store the ingredients in the refrigerator, which would be the data structure part.

In computer science, each algorithm is designed with the type of data it will work with in mind. The choice of data structure is not a minor detail: Structure and algorithm go hand in handAnd small changes in one of the two parts can either boost or sink performance.

From a theoretical perspective, authors such as Niklaus Wirth popularized the idea as early as the 70s that algorithms + data structures = programsDecades later, it remains just as true: it doesn't matter if you program in Java, Python, C++ or if you come from a bootcamp, what will be required of you in interviews and serious projects is knowing how to choose and combine both elements well.

Why are they so important in programming?

In any real-world application, however simple it may seem, you are always working with data: salaries, products, users, transactions, routes, documentsLog records, etc. The question isn't whether you're going to handle data, but how you're going to organize it so that your code is fast, clear, and easy to maintain.

Data structures are used to store information in an orderly and coherent manner according to the problem. Not the same Having to always access the first element, search by key, traverse in order, insert in the middle, or frequently delete; each usage pattern fits better with a different structure.

For their part, algorithms allow process that data efficiently: sort them, filter them, search for elements, find optimal routes, detect patterns with data mining, optimize resources, etc. Many problems that seem difficult become trivial when you find the right combination of algorithm and data structure.

In technical interviews for software development, it's rare to be asked a question that doesn't directly address these topics. Sometimes the question explicitly mentions the structure, such as "given a binary tree…", and other times it's implicit: "we want to count how many books each author has," which suggests using a hash table or key-value map.

Furthermore, formal and professional training often revolves around this area. Many universities and higher education programs include a subject on... Data structures and algorithms, with an official program, prerequisites, theory and practice sessions, exams and assignments, because it is considered a core subject for any software engineer.

Prerequisites and necessary foundations

To get the most out of studying data structures and algorithms, it's helpful to have some familiarity with a general-purpose programming language, such as Java, Python or C++You don't need to be a guru, but you do need to be comfortable with basic concepts such as variables, data types, conditionals, loops, functions, and parameter passing.

It also helps a lot to understand the idea of algorithmic complexity and Big O notation: how execution time or memory usage grows as the data size (n) increases. Knowing how to distinguish between O(1), O(log n), O(n), O(n log n), and O(n²) allows you to compare alternatives with sound judgment and justify your decisions.

Another important aspect is having had a bit of a fight with the solving problemsStructured programming exercises, small logic challenges, simple kata, etc. The more you train your "nose" to break down a problem into steps, the easier it will be to see which data structure fits each case.

Some curricula explicitly state prerequisites or corequisites For the Data Structures and Algorithms course, you need to have passed Programming Fundamentals, Programming I, or Discrete Mathematics. This makes sense: without a solid foundation in basic programming and some logic, it's easy to get frustrated with this subject.

Finally, having some familiarity with real-world practical environments (such as small web projects, scripts, or console applications) helps you better visualize what you're going to use each structure for, instead of seeing it as something purely academic.

Most commonly used data structures

In computer science there are many data structuresHowever, there is a group of "basic" functions that are repeated time and again: arrays (vectors), stacks, queues, linked lists, trees, graphs, tries, and hash tables. Understanding how they work, what operations they offer, and their typical costs is key to moving smoothly through programming.

Now we are going to review each one, with its main idea, typical operations and examples of problems that usually appear in classes, exercises and job interviews for developers.

Arrays

The array It is the simplest linear data structure and one of the most widely used. It consists of a contiguous block of memory that stores a collection of elements of the same type, accessible by an integer index, usually starting from zero.

Imagine an array of size 4 containing the values ​​1, 2, 3, and 4. Each position has a index (0, 1, 2, 3) and you can directly access any element with its index in constant time O(1). This makes arrays very efficient for random reading.

There are two main categories: one-dimensional arrays (a single row of elements) and multidimensional arrays (for example, matrices, which are arrays of arrays). Many programming languages ​​offer both variants natively or with slight differences in syntax and performance.

The basic operations on an array are usually:

• Insert: placing an element in a specific position, which in static arrays may involve shifting other elements.
• Get: accessing the element at a given index, typically O(1).
• Delete: delete or mark as empty the element at a specific position, usually by shifting elements to the left.
• Size: check how many elements are stored or the maximum capacity of the array.

In interviews and exams, exercises like these are very common. find the second minimum of an arrayFinding the first non-repeating integer, merging two already sorted arrays, or reordering positive and negative numbers while maintaining certain properties. All of this relies on index access and linear or double traversals.

Stacks

The battery It is a linear data structure that follows the LIFO principle: Last In, First Out. Imagine a stack of books placed one on top of the other: you can only take or put books from the top.

This behavior means that We only access the element that is at the top of the stackWe cannot remove the middle element without first removing the elements above it. This makes it an ideal structure for modeling action histories (undo), nested function calls, navigation (back/forward), etc.

Typical stack operations are:

• Push: insert a new item at the top.
• Pop: extract and return the element at the top, reducing the size of the stack.
• Top or peek: consult the top element without deleting it.
• isEmpty: check if the battery is empty.

In the context of interviews, problems such as the following are seen: evaluate expressions in postfix notation (RPN), sorting elements using only stacks, or checking if a string of parentheses (and other symbols) is properly balanced using push and pop.

In practice, many internal implementations of languages ​​(for example, the system call stack) work following these same principles, even though we don't see them directly.

Queues

The tail It's another linear data structure, but instead of following the LIFO principle, it uses the FIFO model: First In, First Out. The clearest analogy is a line of people waiting at a movie theater ticket booth.

In a standard queue, the elements are They add at the end and withdraw at the beginningFirst come, first served, making it ideal for managing pending tasks, operating system processes, server requests, print queues, etc.

Basic queue operations include:

• Enqueue: insert a new item at the end of the queue.
• Dequeue: remove and return the element located at the beginning.
• Front or top: consult the first item without removing it.
• isEmpty: check if the queue is empty.

In programming challenges, it's common for them to ask you, for example, implement a stack using two queues, reverse the first k elements of a queue without altering the rest, or generate binary numbers from 1 to n using the FIFO behavior of the queue.

Besides the basic tail, there are variations such as the circular tail, the priority queue or double queues (deque), which offer additional operations and improve performance in certain scenarios.

Linked lists

The linked list A linked list is also a linear structure, but internally it is very different from arrays. Instead of using a contiguous block of memory, it is made up of sparse nodes that are connected to each other by references or pointers.

Each node typically contains two parts: the data that are to be stored and a pointer (or several) that points to the next node in the sequence (and, in the case of doubly linked lists, also to the previous one). The list is managed through a reference to its head, which points to the first node, and in more complex lists a reference to the tail is also maintained.

There are two main variants:

• Singly linked list: each node points only to the next one; the path is usually in a single direction.
• doubly linked listEach node points to the next and previous node, facilitating bidirectional traversals and more efficient deletion operations.

Typical operations on linked lists include:

• InsertAtHead: insert a new node at the beginning of the list.
• InsertAtEnd: add a node to the end, updating the queue if it exists.
• Delete: remove a specific node, adjusting the pointers of neighboring nodes.
• DeleteAtHead: delete the first node and move the head to the next one.
• Search: traverse the list looking for a specific value.
• isEmpty: check if the head is null and therefore the list has no elements.

Problems such as these abound in classes and interviews reverse a linked list, detect if there is a cycle (usually using the "tortoise and hare" algorithm), obtain node N by counting from the end, or remove duplicate nodes, always handling pointers carefully.

Linked lists are widely used to implement hash tables with chainingadjacency lists in graphs, and dynamic data structures where elements are frequently inserted and deleted.

Trees

A tree It is a hierarchical data structure made up of nodes connected by edges. Unlike general graphs, a tree does not have cycles: there is always a root, children, parents, siblings, leaves, levels, and subtrees, with a "family" or "organizational chart" type organization.

Trees are very useful when we want represent hierarchical relationships or divide a problem into smaller subproblems: file systems, menus, DOM structures in browsers, decision trees in artificial intelligence, etc.

There are many varieties of trees, including:

• N-ary Tree: each node can have a variable (and possibly large) number of children.
• Balanced tree: keeps its branches at a similar depth to avoid performance degradation.
• Binary tree: each node has a maximum of two children (left and right).
• Binary Search Tree (BST): binary tree with the property that everything to the left of a node is smaller and everything to the right is larger (according to some ordering criterion).
• AVL tree, red-black, 2-3 and other variantsThese are balanced search trees that guarantee good complexity limits in insertion, deletion, and search operations.

In practice, the most frequent ones in exercises are the binary tree and the binary search treeTypical problems include calculating the height of the tree, finding the k-th maximum value in a BST, listing the nodes at a certain distance from the root, or determining the ancestors of a particular node.

Furthermore, traversal algorithms (preorder, inorder, postorder, level by level) are fundamental to many subsequent processes: sorted printing, expression evaluation, tree serialization and deserialization, etc.

Graphs

A graph It generalizes the concept of a tree by allowing cycles and multiple arbitrary connections between nodes. It consists of a set of vertices (nodes) and a set of edges that connect pairs of vertices, sometimes with an associated weight or cost.

There are several types of graphs: undirected (the edges have no sense of direction, the relationship is bidirectional) and directed (Edges have a starting point and a destination). They can also be classified as weighted or unweighted, connected or unconnected, with or without cycles, etc.

In code, graphs are usually represented in two basic ways:

• Adjacency matrix: a matrix where the cell indicates whether there is an edge between vertex i and j (and possibly the weight of the connection).
• Adjacency list: for each vertex a list of its neighbors is stored, which saves memory in sparse graphs.

The most classic traversal algorithms are the Breadth-first search (BFS) and in-depth search (DFS)Both are used as basic building blocks for a multitude of problems: checking if a graph is connected, detecting cycles, finding connected components, etc.

In technical tests, it's common to be asked to implement BFS and DFS, check if a graph forms a tree, count the number of edges, or search shortest paths between two nodes (for example, on a map of cities) using variants such as Dijkstra or BFS in unweighted graphs.

Tries or prefix trees

The trie (or prefix tree) is a tree-shaped data structure optimized for handling strings of characters, especially useful when working with word dictionaries, autocomplete systems, or prefix searches.

In a trie, each node typically represents a character, and the paths from the root to certain nodes mark complete wordsThe final word nodes are usually marked in some way (for example, with a Boolean indicator) to distinguish them from simple prefixes.

If we store the words “top”, “thus”, and “their” in a trie, we will share part of the initial path for all those that begin with the same letters, allowing for searches and suggestions by prefix in very efficient time, proportional to the length of the word we are looking for and not to the total number of words stored.

Common operations and problems with tries include: count how many words are stored, print all words in lexicographical order, sort elements of an array by insertion into a trie, generate valid words from a set of letters or build structures similar to a T9 dictionary.

In interview contexts, it's not the most basic structure they'll ask for, but it does appear regularly in companies that work with searches, word processing, or suggestion systems.

Hash tables and hashing

Hashing It is a technique for assigning a numeric key (hash) to each piece of data in a deterministic way, so that we can store and retrieve elements in almost constant time, using that key as an index in an internal structure, usually an array.

La hash table This is the data structure that leverages this mechanism. Each element is stored as a key-value pair: the key is transformed into a table index using a hash function, and the value (or a reference to it) is stored there. Later, to search, simply hash the key again and access the corresponding position.

The performance of a hash table depends crucially on three factors: the hash function chosen (you must distribute the keys well to avoid concentration), the table size (insufficient size causes many collisions) and the method for managing collisions (linking with linked lists, open addressing, etc.). This is similar to a index in databasewhere deciding on the appropriate structure improves searches and access.

Typical hash programming exercises often require, for example, find symmetric pairs in an arrayReconstructing the complete itinerary of a trip from individual flights, quickly checking if one array is a subset of another, or verifying if two arrays are disjoint, all by taking advantage of the approximate O(1) searches of the hash table.

In most modern languages, structures like map, dictionary, hash map or hash set They rely internally on hash tables, although a high-level interface is offered to the programmer.

How algorithms and data structures are related

The choice of data structure directly determines which algorithms make sense and what their complexity will be. A linear search algorithm on a unordered list It iterates through elements one by one; if we change the structure to a balanced search tree or hash table, we get much better times.

For example, if you want to repeatedly search for keys in a large collection, storing the data in a hash table or binary search tree It allows you to design search algorithms that are much faster than if you use a simple unsorted array. The same applies to priority queues and heaps for scheduling or shortest path algorithms.

Conversely, when designing an algorithm, you often realize that you need certain properties: index access, fast insertions at the beginning, hierarchical traversals, prefix searches, etc. These needs guide your choice of structure. arrays, lists, trees, graphs, hash tables, tries...

This appropriate combination of algorithm and data structure is what makes it possible for complex applications to be efficient and scalableWithout a good foundation, solutions tend to become slow, difficult to understand and maintain, or impossible to adapt as the volume of information grows.

Therefore, mastering algorithms and data structures is not a almost indispensable requirement for anyone aspiring to become a competent and competitive programmer in today's job market.

How to learn data structures and algorithms

Many people feel stuck when they try to learn on their own with platforms like LeetCode or CodewarsIt is common to start with "easy" exercises and still not know where to approach the problem, ending up looking at the solution and not being clear on how to reproduce it afterwards.

A practical approach usually combines several ingredients: a good theoretical explanation Each structure and algorithm includes visual examples, plenty of guided practice, and, if possible, support from someone with experience to help you refine your problem-solving skills.

In the Spanish-speaking world, there are professionals with extensive experience who have contributed to facilitating this learning. One example is the work of Teachers with experience in business and education who have published books and courses on programming fundamentals, Java, data structures and programming challenges with games, making these concepts accessible in a fun and applicable way to real projects.

It is also common for academies and training centers to include specific modules on data structures and algorithms within their programs for web developers or application programmers. In many cases, a particular approach is emphasized. very practical and project-based, with exercises of increasing difficulty and simulation of typical technical interview problems.

If you're stuck, following a structured route can help: start with arrays and lists, going through stacks and queues, then trees and basic graphs, and finally hash tables and tries, always alternating theoretical explanation, small code examples and lots of individual practice.

When preparing for interviews, it's advisable to review not only the structures but also the brute force algorithms and the associated classical algorithms (traversals, searches, sorting, simple backtracking, basic dynamic programming) and ensure you can explain aloud why you have chosen a particular structure and what the complexity of your solution.

Over time and some consistencyWhat at first seems like a wall ends up becoming a set of familiar tools that you use almost instinctively when faced with new problems.

A good understanding of what algorithms are, how the main data structures work, and how they relate to each other will allow you to write programs faster, clearer and more robustIt will open doors for you in demanding selection processes and ensure that your projects, both academic and professional, are based on a solid foundation with a future.