This article explores what Binary Trees are, some of it’s types and usecases and implementation of Binary Trees in C# to improve your data structure skills. Binary trees are a fundamental data structure used in computer science and programming. In a binary tree, each node can have at most two children, called the left child and right child. This simple structure has many applications, such as storing and organizing data, and performing various operations such as searching and sorting.
In this article, we’ll explore how binary trees work, how to implement them in C#, and some common use cases and applications.
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What is a Binary Tree?
A binary tree is a tree data structure where each node has at most two children. The topmost node in the tree is called the root, and nodes with no children are called a leafs. Each node has a value or data, which can be of any type.
In a binary search tree, the left child of a node has a smaller value than the node, and the right child has a larger value. This property is called the binary search tree property, and it allows us to perform various operations efficiently.
Implementing a Binary Tree in C#
In C#, we can implement a binary tree using classes and objects. We’ll create a class for the tree itself, and a class for the tree nodes.
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namespace Algorithms; public class BinaryTree<T> where T : IComparable<T> { public Node<T> Root { get; private set; } = null!; public void Add(T value) { if (Root == null) { Root = new Node<T>(value); } else { Root.Add(value); } } } public class Node<T> where T : IComparable<T> { public T Value { get; private set; } public Node<T> Left { get; private set; } = null!; public Node<T> Right { get; private set; } = null!; public Node(T value) => Value = value; public void Add(T newValue) { if (newValue.CompareTo(Value) < 0) { if (Left == null) { Left = new Node<T>(newValue); } else { Left.Add(newValue); } } else { if (Right == null) { Right = new Node<T>(newValue); } else { Right.Add(newValue); } } } } 
In this implementation, the BinaryTree<T>
and BinaryTreeNode<T>
classes are generic. You can pass them integer values to test them:
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var tree = new BinaryTree<int>(); foreach(var value in new[]{8,5,6,4,1,2}) tree.Add(value); 
The BinaryTree
class has a single property, Root
, which is the topmost node in the tree. The Add
method adds a new value to the tree, by calling the Add
method of the root node.
The BinaryTreeNode
class has three properties: Value
, Left
, and Right
. The Value
property is the integer value stored in the node. The Left
and Right
properties are the left and right children of the node, respectively. The Add
method adds a new integer value to the tree, by comparing the value to the current node and inserting it into the appropriate child node. Find the code including its tests in this Github repository. If you want to skyrocket your C# career, check out our powerful ASP.NET fullstack web development course that also covers testdriven development.
Binary Tree Traversal
Binary trees can be traversed in three different ways:
 Inorder
 Preorder,
 Postorder.
Inorder traversal visits the left subtree, then the node, then the right subtree.
Preorder traversal visits the node, then the left subtree, then the right subtree.
Postorder traversal visits the left subtree, then the right subtree, then the node.
Binary Tree Types
Here’s a table that summarizes some common types of binary trees, their characteristics, and use cases:
Type  Characteristics  Use Cases 

Full Binary Tree 


Complete Binary Tree 


Perfect Binary Tree 


Balanced Binary Tree 


Binary Search Tree (BST) 


AVL Tree 


RedBlack Tree 


Heap 


Trie 


Note that there are many other types of binary trees, and some of them may have overlapping characteristics or use cases.
Common Use Cases and Applications
Binary trees have many use cases and applications in computer science and programming. Here are a few common examples:
 Storing and organizing data: Binary trees are often used to store and organize data, such as elements in a search tree or a priority queue. The binary search tree property allows us to search for elements efficiently, and the tree structure allows us to perform operations such as inserting and deleting elements.
 Sorting: Binary trees can be used to sort data efficiently. By adding all the elements to a binary search tree and then traversing the tree in inorder, we can retrieve the elements in sorted order.
 Huffman coding: Binary trees can be used to implement Huffman coding, a lossless data compression technique. Huffman coding assigns shorter binary codes to frequently occurring characters, and longer codes to less frequently occurring characters, using a binary tree to build the codebook.
 Expression evaluation: Binary trees can be used to evaluate expressions in computer programs, such as mathematical expressions. By parsing the expression and building a binary tree, we can recursively evaluate the expression in a way that takes operator precedence into account.
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Conclusion
Binary trees are a fundamental data structure that is widely used in computer science and programming. In C#, binary trees can be implemented using classes and objects, and the binary search tree property allows us to perform efficient operations such as searching and sorting. Binary trees have many use cases and applications, including storing and organizing data, sorting, Huffman coding, and expression evaluation. By understanding binary trees and how to use them, we can become better programmers and problem solvers. Find the code for this article in this Github repository.
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