## Table of content

- Introduction
- Understanding Binary Trees
- Types of Binary Trees
- Operations on Binary Trees
- Real-life Examples of Binary Trees
- Code Examples for Binary Trees
- Conclusion
- References

### Introduction

Binary trees are a fundamental concept in computer science and programming that every beginner should familiarize themselves with. So, what exactly are binary trees? Well, a binary tree is a tree-like data structure where each node has at most two children. These children are referred to as the left child and the right child.

The concept of binary trees dates back to the mid-19th century, where they were first studied by mathematicians as a way to explore the structure of hierarchical organization. Today, binary trees serve as a cornerstone of computer science and programming, with practical applications in fields such as data analysis, artificial intelligence, and machine learning.

In this article, we'll explore the fascinating world of binary trees in programming. We'll look at the properties and rules of binary trees, as well as their real-life applications. Additionally, we'll dive into code examples in a variety of programming languages to give you a practical understanding of how binary trees are implemented. By the end of this article, you'll have a foundational understanding of binary trees and be able to apply this knowledge to your own programming projects.

### Understanding Binary Trees

Binary trees are an essential data structure in computer science, which is used to manage and process large amounts of data efficiently. Understanding the concept of trees is necessary to grasp binary trees fully. Trees are hierarchical data structures that consist of a collection of nodes arranged in a specific order. Nodes are connected by edges, and the top of the tree is called the root. Each node can have zero or more children, and every child can have its children.

Binary trees differ from conventional trees in that each node can have at most two children, which are referred to as the left child and the right child. The binary tree's structure makes it easy to search, insert, and delete data compared to other data structures. The nodes of a binary tree can only have zero, one, or two children, and the order matters. The left child of a node is always smaller than the parent node, while the right child is always greater than the parent node.

is imperative because it's used to implement numerous data structures and algorithms such as binary search trees, heaps, huffman coding, etc. Binary trees are used in programming languages like Java, C, C++, and Python to store data efficiently. In Java, for instance, binary trees are used to store collections of objects in the Java collections framework.

In conclusion, learning about binary trees and how they operate is pertinent for any programmer who wants to develop efficient algorithms and data structures. gives you the power to process data with lightning speed and the ability to store colossal amounts of data with maximum efficiency. Below we'll discuss real-life code examples to help you grasp the power of binary trees.

### Types of Binary Trees

Binary trees come in a variety of forms, each with its own unique characteristics and uses. Here are some of the most common :

### Full Binary Trees

A full binary tree is one in which every node has either 0 or 2 children. In other words, there are no nodes with only 1 child. Full binary trees are useful for certain types of binary search algorithms and are often used as the basis for other types of trees, such as AVL trees and Red-Black trees.

### Complete Binary Trees

A complete binary tree is one in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible. Complete binary trees are useful for implementing priority queues and other types of data structures.

### Balanced Binary Trees

A balanced binary tree is one in which the depth of any two leaf nodes is at most 1. Balancing a tree helps ensure that the tree remains efficient (i.e., has a logarithmic time complexity) when searching, inserting, and deleting nodes. Examples of balanced binary trees include AVL trees and Red-Black trees.

### Binary Search Trees (BSTs)

A binary search tree is one in which each node stores a value that is greater than all the values in its left subtree and less than all the values in its right subtree. This property makes BSTs useful for implementing efficient search algorithms. In fact, many of the most common data structures and algorithms, such as sets, maps, and priority queues, are implemented using BSTs.

Understanding the different is key to harnessing their power and using them to solve real-world problems. By knowing which type of tree is best suited for a given task, programmers can create efficient and effective solutions that can scale to meet the needs of any application.

### Operations on Binary Trees

Binary trees are an essential data structure in computer science, often used to store and manipulate hierarchical data like file systems, company structures, and game trees. Like any data structure, binary trees require various operations to modify and access their contents. Some common binary tree operations include inserting new nodes, deleting existing nodes, and searching for particular nodes.

Insertion is one of the fundamental operations on binary tress. In this case, a new node is added to a binary tree to preserve the tree's binary search property. Simply put, this means that the value of every node on the left branch is less than the value of the parent node, while the value of every node on the right branch is greater than the parent node. Inserting a new node requires traversing the tree and comparing the node's value with those of the existing nodes, until an appropriate empty spot is found.

Deleting a node from a binary tree is another useful operation. Here, the node is removed from the tree and its children are reassigned to preserve the binary search property. Depending on the specific implementation of the binary tree, deleting a node can be challenging since it can affect the tree's structure.

Searching for a node within a binary tree involves traversing the tree to find the node with the specified value. The search typically starts from the root node, moving down the tree until the target node is found or reached a leaf node, indicating that the target node is not in the tree.

Overall, operations like insertion, deletion, and searching of nodes, among others, make binary trees a versatile data structure for managing hierarchical data. With real-life code examples, understanding the concepts and practical applications of binary trees is easy for beginners.

### Real-life Examples of Binary Trees

Binary trees may sound like a complicated concept, but they are prevalent in our everyday lives. For example, imagine a family tree. Each family member has two parents, except for the first generation, who have no parents or two children. This structure represents a binary tree, where each node has either zero or two children.

Another real-life example of binary trees is the way file systems are organized on computers. The root directory serves as the root of the tree, with each folder representing a node branching out with its respective files and subfolders. This structure allows for efficient searching and sorting of files.

In the field of biology, binary trees are used to represent evolutionary relationships between species. Each node represents a specific species, with two children representing the split into two different evolutionary paths.

In the realm of finance, binary trees are used for option pricing. The tree represents the possible outcomes of an investment decision, with the value of each node corresponding to the expected payoff of an option at a certain point in time. This allows investors to make informed decisions regarding their investments.

Overall, binary trees play a crucial role in various fields, and understanding their properties and applications can greatly benefit individuals in both their personal and professional lives.

### Code Examples for Binary Trees

Binary trees are an important data structure in programming, used to organize information and perform efficient searches. Here are some real-life code examples that demonstrate the versatility and power of binary trees:

**Example 1: Building a Binary Search Tree**

```
class TreeNode:
def __init__(self, val = 0, left = None, right = None):
self.val = val
self.left = left
self.right = right
class BST:
def __init__(self):
self.root = None
def insert(self, val):
if not self.root:
self.root = TreeNode(val)
return
curr = self.root
while curr:
if val < curr.val:
if curr.left:
curr = curr.left
else:
curr.left = TreeNode(val)
break
elif val > curr.val:
if curr.right:
curr = curr.right
else:
curr.right = TreeNode(val)
break
```

In this code example, we are building a binary search tree (BST). The BST is an ordered binary tree where the value of each node is greater than or equal to the values in its left subtree and less than or equal to the values in its right subtree. The `insert`

function takes a value as input, and inserts it into the correct position in the BST. If the BST is empty, it creates a new root node with the input value. If not, it traverses the tree until it finds the correct position to add the new node.

**Example 2: Inorder Traversal of a Binary Tree**

```
class TreeNode:
def __init__(self, val = 0, left = None, right = None):
self.val = val
self.left = left
self.right = right
def inorderTraversal(root):
res = []
def inorder(root):
if not root:
return
inorder(root.left)
res.append(root.val)
inorder(root.right)
inorder(root)
return res
```

In this code example, we are performing an inorder traversal of a binary tree. Inorder traversal visits each node in the order of left child, node, and right child. This function takes a binary tree as input, and returns a list of the node values in order. It does this by using a recursive helper function `inorder`

to traverse the left subtree, visit the node, and then traverse the right subtree. `res`

keeps track of the node values visited in order.

**Example 3: Binary Tree Level Order Traversal**

```
class TreeNode:
def __init__(self, val = 0, left = None, right = None):
self.val = val
self.left = left
self.right = right
def levelOrder(root):
if not root:
return []
queue = [root]
res = []
while queue:
level_nodes = []
for i in range(len(queue)):
node = queue.pop(0)
level_nodes.append(node.val)
if node.left:
queue.append(node.left)
if node.right:
queue.append(node.right)
res.append(level_nodes)
return res
```

In this code example, we are performing a level order traversal of a binary tree. Level order traversal visits each node in order of each level, from left to right. This function takes a binary tree as input, and returns a list of lists where each inner list represents a level of nodes. It does this by using a queue to keep track of the nodes at each level. We start with the root node in the queue, and then for each node, we add its left and right children to the queue to be processed in the next level. `res`

keeps track of the node values at each level.

### Conclusion

To conclude, binary trees with zero or two children are a fundamental concept in computer science and programming. Understanding how they work and how to implement them in your code can greatly improve your software design, data processing, and algorithm development skills. By following the examples and steps outlined in this article, you can start building your own binary trees with confidence and creativity.

Whether you're a programming novice or an experienced developer, binary trees with zero or two children offer endless possibilities for organizing, searching, and manipulating data. You can use them to create powerful search engines, sorting algorithms, and artificial intelligence tools that can revolutionize the way we interact with the world around us.

Furthermore, binary trees were not invented by computer scientists but have been around for centuries. It is fascinating to see how such a seemingly complex concept has its roots in simple everyday human activities.

In , we hope that this article has provided you with a compelling introduction to binary trees with zero or two children and that you continue to explore the exciting world of programming and computer science. Keep learning, experimenting, and building, and you'll be amazed by the incredible things you can accomplish.

### References

If you're interested in learning more about binary trees, there are plenty of resources available online. Here are some of our top picks:

- Binary Trees on Wikipedia: A comprehensive overview of binary trees, including their structure, properties, and applications.
- Visualizing Binary Trees: An interactive tool that allows you to create and explore binary trees in real time.
- "Binary Trees" chapter from "Introduction to Algorithms": This book is widely considered the "bible" of computer science, and its explanation of binary trees is no exception.
- Codecademy's "Learn Data Structures" course: A great option for beginners who want to learn about data structures and algorithms, including binary trees, through hands-on coding exercises.

Additionally, many programming languages have built-in functions or modules for working with binary trees. Here are some links to official documentation for a few popular languages: