The following articles describe various tree data structures. A tree is a hierarchical structure with a root node and its children, which in turn can have children of their own and thus form subtrees.
Algorithms and Data Structures
On this page, you find an overview of all articles about algorithms and data structures.
Latest Articles
Advent of Code 2025 – Java Solutions for All 12 Days, Explained
December 5, 2025All twelve Advent of Code 2025 puzzles solved in Java 25 – each with the algorithm explained, its time complexity, and the code on GitHub.
Advent of Code 2022 – Java Solutions for All 25 Days, Explained
December 1, 2022All 25 Advent of Code 2022 puzzles solved in object-oriented Java 19 – each with the approach explained and the code on GitHub.
Radix Sort Algorithm – Example, Java Code, Time Complexity
July 19, 2022Radix Sort step by step: LSD and MSD with an example, Java implementations, time and space complexity – and benchmarks against Quicksort.Tree Data Structure
Binary Tree: Types, Traversal, and Implementation in Java
What is a binary tree? Types (full, complete, perfect, balanced), traversal (pre-, in-, post-, level-order), and implementation in Java.
Binary Search Tree (BST) in Java: Insert, Search, Delete + Code
What is a binary search tree (BST)? Example, insert, search, and delete with Java code – plus a comparison with heap and hash table.
AVL Tree: Rotations, Balance Factor, and Java Code
What is an AVL tree? How to calculate its height and balance factor (BF)? How does AVL rotation work? How to (re-)balance an AVL tree?
Red-Black Tree (Fully Explained + with Java Code)
The red-black tree step by step: rules, rotations, insertion, and deletion with diagrams – plus a Java implementation and time complexity.Shortest Path Algorithms
Pathfinding or shortest path algorithms are used to find a path (or the shortest path) between two nodes within a graph.
What you’ll learn:
- What is the difference between “shortest path” and “pathfinding”?
- Which pathfinding algorithms are there?
- How do the most important pathfinding algorithms work (explained step by step)?
- When do you use which algorithm?
- How to determine the time complexities of the pathfinding algorithms?
- How to implement pathfinding algorithms in Java?
- What are “negative cycles” and how are they identified?
Shortest Path Algorithms in Java: Overview + Maze Example
Shortest path or pathfinding? The four main algorithms at a glance – and a maze algorithm explained step by step in Java.
Dijkstra’s Algorithm in Java: Example, Code, Time Complexity
Dijkstra’s algorithm explained step by step with an example – plus Java code, time complexity, and runtime measurements.
A* Search Algorithm: Example, Java Code, Time Complexity
How the A* search algorithm finds the fastest path with a heuristic: step by step with an example, Java code, and time complexity.
Bellman-Ford Algorithm: Example, Java Code, Time Complexity
Bellman-Ford step by step: negative edge weights, negative cycles, Java code, time complexity, and how it compares with Dijkstra.
Floyd-Warshall Algorithm: Matrix Example, Java Code, Complexity
Floyd-Warshall algorithm explained step by step: matrix example, Java code, O(n³) time complexity, transitive closure, and negative cycles.Algorithms and Data Structures in General
This category covers general articles about algorithms without any specific type of algorithm in mind, e.g., classifications of algorithms.
Array vs. Linked List: Differences and Time Complexity
What is the difference between Array and Linked List? What are the advantages and disadvantages? When should you use which data structure?
Big O Notation: Time Complexity Classes in Order, Explained
Big O notation and time complexity classes in order – with examples and diagrams, without math: O(1), O(log n), O(n), O(n log n), O(n²).
Binary Search in Java (Recursive + Iterative + JDK Methods)
How to implement binary search in Java – recursive, iterative, and with the JDK’s built-in methods. Plus: runtime comparison with linear search.Sorting Algorithms
If you need a refresher on how the most common sorting algorithms work and how they differ, this series is for you.
What you’ll learn:
- What are the most common sorting methods?
- In which characteristics do they differ?
- How to sort arrays and collections in Java?
- How each sorting algorithm works (using lots of visualizations and examples).
- How to derive a sorting algorithm’s time complexity, without complicated maths.
- How to implement each sorting algorithm in Java.
Sorting Algorithms: Time Complexity and Stability Compared
The most important sorting algorithms compared: time complexity, space, and stability from Insertion Sort to Radix Sort – with a table.
Sorting in Java: Arrays, Lists, Objects [Tutorial]
How to sort primitive data types and objects of any class in Java – also in parallel? And which sorting algorithms does the JDK use?
Insertion Sort Time Complexity (Best, Average, Worst), Java Code
How does Insertion Sort work, and why is it O(n²) in the average and worst case but O(n) in the best case? With Java code and measurements.
Selection Sort in Java – Algorithm, Code, Time Complexity
How does Selection Sort work? With illustrations and Java code. How do you determine its time complexity – and why is it not stable?
Bubble Sort – Algorithm, Source Code, Time Complexity
How does Bubble Sort work? With illustrations and Java code. Best, average, and worst case time complexity – without complicated math.
Quicksort in Java – Algorithm, Source Code, Time Complexity
How does Quicksort work? With illustrations, Java code, and benchmarks. How to determine its time complexity without complicated math?
Merge Sort – Algorithm, Java Source Code, Time Complexity
How does Merge Sort work? With illustrations and source code. How to determine its time complexity (without complicated math)?
Heapsort (Heap Sort) – Algorithm, Java Code, Time Complexity
How does heap sort work? Step by step with illustrations and Java code – and why its time complexity is O(n log n) even in the worst case.
Counting Sort – Algorithm, Java Code, Time Complexity, Stability
How does Counting Sort work? Step by step with diagrams and Java code – plus time complexity O(n + k), space complexity, and stability.Radix Sort Algorithm – Example, Java Code, Time Complexity
Radix Sort step by step: LSD and MSD with an example, Java implementations, time and space complexity – and benchmarks against Quicksort.
Free Bonus:
Big O Cheat Sheet
[7 Time Complexity Classes on 1 Page]
Use this 1-page PDF cheat sheet as a reference to quickly look up the seven most important time complexity classes (with descriptions and examples).
You get access to this PDF by signing up for my newsletter. I won’t send any spam, and you can opt-out at any time.
Stack
In this tutorial series, you will learn everything about the abstract data type “stack”, how to use it, and how to implement your own stack classes in Java.
Stack Data Structure: LIFO Principle, Push, Pop, Peek
The stack data structure explained: the LIFO principle, push, pop, and peek, typical applications, and time complexity.
Java Stack: Class, Methods, Alternatives, and Implementation
The Java Stack class by example, why ArrayDeque is better – and how to implement your own stack with push(), pop(), peek(), and isEmpty().
Implement a Stack Using an Array in Java
Implementing a stack in Java with an array, without Collections classes: first with a fixed size, then with an array that grows on demand.
Implement a Stack Using a Linked List in Java
Implement a stack using a singly linked list in Java: push and pop step by step, with diagrams, source code and a comparison with arrays.
Implement a Stack Using Queues
How to implement a stack with a queue (better said: with two queues)? Tutorial with images and Java code examples.
Reverse a Stack Using Recursion
How to reverse the order of the elements in a stack using recursion (i.e., without iteration)? Tutorial with images and Java code examples.
Difference Between Stack and Queue (Data Structures and Java)
What is the difference between stack and queue? LIFO vs. FIFO, terminology – and how the Java Stack class and the Queue interface differ.Queue
In this tutorial series, you will learn everything about the abstract data type “queue”, which methods it provides, how to use queues, when to use which queue implementation and how to program your own queues in Java.
Queue Data Structure: FIFO, Head and Tail, Enqueue, Dequeue
What is a queue? How the FIFO data structure works, what head and tail are, what enqueue and dequeue do, and where queues are used.Ring Buffer (Circular Buffer): How It Works and Where Java Uses It
Ring buffer explained: two indices, wrap-around, full vs. empty – and where Java uses it: ArrayDeque, ArrayBlockingQueue, LMAX Disruptor.
Java Queue: Methods, Implementations, and Examples
The Java Queue interface: all six methods with an example, the JDK implementations compared – and which thread-safe queue to use when.
Java BlockingQueue: Interface, Methods, and Example
What is a BlockingQueue in Java? put(), take(), offer() and poll() with timeout, bounded vs. unbounded – with an example and its output.
Java ConcurrentLinkedQueue: Thread-Safe Without Locks
ConcurrentLinkedQueue explained: lock-free via CAS, unbounded, non-blocking, why size() is O(n) – with a producer/consumer example.
Priority Queue in Java: PriorityQueue Explained (+ Examples)
What is a priority queue, and how does Java’s PriorityQueue work? Time complexity and examples – with and without a custom comparator.
Java LinkedBlockingQueue: Blocking Queue With Two Locks
Java LinkedBlockingQueue explained: blocking, thread-safe with two locks, optionally bounded – with a code example and when to use it.
Java ArrayBlockingQueue: Bounded Queue With a Single Lock
ArrayBlockingQueue explained: bounded, one lock for both ends, optional fairness – with an example and when LinkedBlockingQueue is better.
PriorityBlockingQueue: Thread-Safe Priority Queue (+ Example)
Java PriorityBlockingQueue: thread-safe, blocking PriorityQueue with a single lock. Characteristics, example, use with ThreadPoolExecutor.
Java DelayQueue: Delayed, getDelay(), compareTo() (+ Example)
Java DelayQueue: each element carries its own delay and can be taken only after it expires. Characteristics, Delayed, compareTo(), example.
Java SynchronousQueue: Direct Handoff Explained (+ Example)
Java’s SynchronousQueue has no capacity: put() waits for take() and vice versa. How the handoff works, and where the JDK uses it.
LinkedTransferQueue and TransferQueue in Java (+ Example)
Java’s LinkedTransferQueue: how transfer() waits for a consumer to take the element, the queue’s characteristics, and when to use it.
Implementing a Queue Using a Stack
How to implement a queue with a stack (more precisely: with two stacks)? Tutorial with illustrations and Java code examples.
How to Implement a Queue Using a Linked List in Java
Queue using a linked list in Java: head and tail references, enqueue and dequeue in O(1) – step by step with diagrams and source code.
Implement a Queue Using an Array in Java (Circular Array)
How to implement a queue with an array in Java – bounded, as a circular array, and growing on demand. Step by step with diagrams and code.
Priority Queue Implementation in Java Using a Min-Heap
Implementing a priority queue with a min-heap in Java: array representation, sift up and sift down step by step – with diagrams and code.Deque
In this tutorial series, you will learn everything about the abstract data type “deque”, which methods it provides, how to use deques, when to use which deque implementation and how to program your own deques in Java.
Deque Data Structure: What Is a Deque (Double-Ended Queue)?
What is a deque? How the double-ended queue works as a queue and as a stack, its operations at both ends, and where deques are used.
Java Deque: Methods, Implementations, and Examples
The Java Deque interface: all methods with an example, the four JDK implementations compared – and which one to use when.
BlockingDeque Interface in Java (+ Code Example)
How to use the BlockingDeque interface in Java? Overview of all blocking methods and comparison with the BlockingQueue interface.
Java ArrayDeque: How It Works, Example, vs. LinkedList and Stack
ArrayDeque explained: circular array, amortized O(1), no nulls, not thread-safe – with example and comparison to LinkedList and Stack.
Java LinkedList – List and Deque: Methods, Example, ArrayDeque
LinkedList explained: doubly linked, implements List and Deque, allows null – with example, methods per interface, and vs. ArrayDeque.
Java ConcurrentLinkedDeque: Thread-Safe Deque Without Locks
ConcurrentLinkedDeque explained: lock-free via CAS, unbounded, why size() is O(n), how it differs from ConcurrentLinkedQueue – with example.
Java LinkedBlockingDeque (+ Code Examples)
How to use the Java LinkedBlockingDeque? How does it work? What are its characteristics? When should you use it?
Implement a Deque Using a Circular Array in Java
How to implement a deque in Java with a circular array: bounded and unbounded, with diagrams of the index wrap-around and the growing step.
Java Deque vs. Stack: Why Deque Is the Better Choice
Deque or Stack in Java? How they differ in thread safety, iteration order, and API – and why you should use ArrayDeque instead of Stack.
Queue vs. Deque in Java: What’s the Difference?
Queue vs. deque: the data structures and the Java interfaces compared – including iteration and SequencedCollection since Java 21.Data Structures in Java
What are data structures? A data structure is a collection of related data values and their relationships with each other. It provides operations to read or modify the data.
Java data structures are, for example, collections, maps, and sets, trees, queues, deques, and stacks.
How to Declare and Initialize Arrays in Java
How to declare and initialize arrays in Java, fill and copy them, and convert lists, sets, and streams into arrays – including 2D arrays.
Java Array Length and Size: .length, 2D Arrays, Max Array Size
How to get and set the length of a Java array, including 2D arrays – plus an array’s memory use in Java 27 and the maximum array size.Advent of Code
In the following articles, you will find object-oriented, test-driven Java solutions for Advent of Code:
Advent of Code 2015 – Java Solutions for All 25 Days, Explained
All 25 Advent of Code 2015 puzzles solved in object-oriented Java – each with the approach explained and the code on GitHub.Advent of Code 2022 – Java Solutions for All 25 Days, Explained
All 25 Advent of Code 2022 puzzles solved in object-oriented Java 19 – each with the approach explained and the code on GitHub.Advent of Code 2025 – Java Solutions for All 12 Days, Explained
All twelve Advent of Code 2025 puzzles solved in Java 25 – each with the algorithm explained, its time complexity, and the code on GitHub.Want Even More Knowledge?
My blog features many articles on Java, software architecture, and performance — from foundational concepts to advanced patterns.
If you want to go deeper, check out my trainings: hands-on, easy to understand, and directly applicable to your day-to-day project work. Instead of theory, I teach principles that help you write code that is better, more maintainable, and more performant in the long run.
Explore the Java Trainings