Data structures and algorithms: a complete guide for programmers

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Algorithms and data structures are two pieces that fit together like a puzzle: one defines 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 code that merely works from code that flies and scales without breaking.

If you want to pursue a career in 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 algorithms . Throughout this article, you'll learn what they are, why they're so important, the main types that exist, the basic operations they perform, and the types of questions that typically appear on exams and in selection processes.

What are data structures and algorithms?

A data structure is, essentially, a specific way of organizing and storing information in memory to allow for efficient manipulation. This organization is not random: it directly determines which operations are fast and which become costly (inserting, searching, deleting, traversing, etc.).

When you choose the right data structure, your program can handle 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 is a finite, 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 hand , and small changes in either can significantly improve or degrade performance.

From a theoretical perspective, authors like Niklaus Wirth popularized the idea that algorithms + data structures = programs as early as the 70s . Decades later, this remains just as true: regardless of whether you program in Java, Python, C++, or come from a bootcamp, what will be required in interviews and serious projects is the ability to choose and combine both elements effectively.

Why are they so important in programming?

In any real-world application, no matter how simple it may seem, you're always working with data: salaries, products, users, transactions, routes, documents , log 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 organized and coherent way, depending on the problem. It's not the same to always access the first element, search by key, iterate in order, insert in the middle, or frequently delete; each usage pattern is better suited to a different structure.

Algorithms, for their part, allow us to process this data efficiently : sorting, filtering, searching for elements, finding optimal paths, detecting patterns through data mining , optimizing resources, and so on. 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 called Data Structures and Algorithms , with an official syllabus, prerequisites, lectures and practical 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 an expert, but you should be comfortable with basic concepts like variables, data types, conditionals, loops, functions, and parameter passing.

It's also incredibly helpful to understand the concept of algorithmic complexity and Big O notation: how execution time or memory usage increases 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 objectively and justify your decisions.

Another important aspect is having some experience with problem-solving : structured 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, such as having 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 become 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, rather than seeing it as something purely academic.

Most commonly used data structures

In computer science, there are many data structures , but there's a group of "basic" ones that are repeated time and again: arrays (vectors), stacks, queues, linked lists, trees, graphs, try-sums, and hash tables. Understanding how they work, what operations they offer, and their typical costs is key to becoming proficient in programming.

Next, we will 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

An array 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 an 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 such as finding the second minimum value in an array , finding the first unique integer, merging two sorted arrays, or reordering positive and negative numbers while maintaining certain properties are very common. All of these rely on index access and linear or double traversals.

Stacks

A stack 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 leave books from the top.

This behavior means that we can only access the element at the top of the stack . We 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), and so on.

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 evaluating expressions in postfix notation (RPN), ordering elements using only stacks, or checking if a string of parentheses (and other symbols) is correctly balanced using push and pop are seen.

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

Queues

A queue is 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, items are added at the end and removed from the beginning . The first item in is the first item served, making it ideal for managing pending tasks, operating system processes, server requests, print queues, and so on.

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 is common to be asked, for example, to implement a stack using two queues , to reverse the first k elements of a queue without altering the rest, or to generate binary numbers from 1 to n using the FIFO behavior of the queue.

In addition to the basic queue, there are variants such as the circular queue , the priority queue, or double queues (deque), which offer additional operations and improve performance in certain scenarios.

Linked lists

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 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.

In classes and interviews, problems abound such as reversing a linked list , detecting if there is a cycle (usually using the "tortoise and hare" algorithm), obtaining node N by counting from the end, or eliminating duplicate nodes, always carefully manipulating pointers.

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

Trees

A tree 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 of organization.

Trees are very useful when we want to 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 common types used in exercises are the binary tree and the binary search tree . Typical problems include calculating the height of the tree, finding the k-th maximum value in a binary search tree, listing the nodes at a certain distance from the root, or determining the ancestors of a specific 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 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 (edges have no direction, the relationship is bidirectional) and directed (edges have a origin 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 breadth-first search (BFS) and depth-first search (DFS) . Both are used as building blocks for a multitude of problems: checking if a graph is connected, detecting cycles, finding connected components, etc.

In technical tests, it is common to be asked to implement BFS and DFS, check if a graph forms a tree, count the number of edges, or look for shorter 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 entire words . Word-ending 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 us to perform 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: counting how many words are stored , printing all words in lexicographical order, sorting array elements by insertion into a try, generating valid words from a set of letters, or building 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 search, text processing, or suggestion systems.

Hash tables and hashing

Hashing 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.

The hash table 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 rehash the key and access the corresponding position.

The performance of a hash table depends crucially on three factors: the chosen hash function (it must distribute the keys well to avoid concentrations), the size of the table (an insufficient size leads to many collisions), and the method for handling collisions (chaining with linked lists, open addressing, etc.). This is similar to a database index , where deciding on the appropriate structure improves searches and access.

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

In most modern languages, map, dictionary, hash map or hash set structures are internally supported by hash tables, even though 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 how complex they will be. A linear search algorithm on an unordered list traverses elements one by one; if we change the structure to a balanced search tree or hash table, we achieve much faster results.

For example, if you want to repeatedly search for keys in a large collection, storing the data in a hash table or a binary search tree allows you to design much faster search algorithms 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, try-it loops, and so on.

This proper combination of algorithm and data structure is what makes complex applications efficient and scalable . Without a solid 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 an almost essential 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 trying to learn on their own with platforms like LeetCode or Codewars . It's common to start with "easy" exercises and still not know where to begin, ending up looking at the solution and not being clear on how to reproduce it afterward.

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

In the Spanish-speaking world, there are professionals with extensive experience who have helped facilitate this learning. One example is the work of teachers with experience in both business and education who have published books and courses on programming fundamentals, Java, data structures, and game-based programming challenges, presenting these concepts in an engaging way that is applicable to real-world 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, they emphasize a highly practical, project-based approach , with exercises of increasing difficulty and simulations of typical technical interview problems.

If you're stuck, it can help to follow a structured route: start with arrays and lists , move on to 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.

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 make sure you can explain out loud why you have chosen a specific structure and what the complexity of your solution is.

With time and some perseverance , what 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 solid understanding of algorithms, how the main data structures work, and how they relate to each other will allow you to write faster, clearer, and more robust programs , open doors in demanding selection processes, and ensure that your academic and professional projects are built on a solid and future-proof foundation.