## Tree Traversal

### Tree Traversal

Tree traversal is the process of visiting and inspecting all the nodes of a tree data structure in a systematic order. Trees are hierarchical structures with a root node and child nodes, and tree traversal is a fundamental technique used in computer science and programming for various purposes, such as searching, printing, and manipulating data within the tree.

## Applications

### Applications of tree traversal

**Searching**

Tree traversal is used to search for specific elements or nodes within tree data structures, aiding in data retrieval.

**Sorting**

In-order traversal of binary search trees provides sorted lists, which are used in sorting algorithms like binary tree sort.

**Expression Evaluation**

Tree traversal helps evaluate mathematical expressions represented as expression trees, facilitating arithmetic operations.

**Parsing**

It’s essential for parsing structured data like XML and HTML, allowing the extraction and processing of information.

**Compilers and Interpreters**

In compilers and interpreters, syntax trees are traversed to generate machine code or execute code statements.

**Decision Trees**

Machine learning employs tree traversal for decision-making and classification based on input features.

**Graph Algorithms**

Tree traversal forms the foundation of graph algorithms like BFS and DFS, used for pathfinding, connected components, etc.

**Family Trees and Genealogy**

In genealogy software, tree traversal is used to explore family relationships and ancestral histories.

**File System Navigation**

Operating systems and file management utilities utilize tree traversal to navigate file directories and list directory contents.

**Database Indexing**

Tree traversal is crucial in B-trees for efficient data searching and indexing within databases.

**Web Crawling**

It’s used in web crawling and web scraping to explore website structures and extract data.

**Game Development**

Game engines leverage tree traversal to process and update game object hierarchies and render scenes efficiently.

**Tree-based Data Structures**

AVL trees, Red-Black trees, and Tries use tree traversal for balancing, searching, and prefix matching.

**Robotics and Path Planning**

In robotics, tree traversal is vital for path planning and navigation, aiding robots in making decisions based on sensory input.

## Inorder

### In-order Tree Traversal

In-order traversal is primarily used to visit nodes in sorted order. It’s commonly employed in binary search trees (BSTs) to retrieve elements in ascending order.

**Technique**

- You visit the nodes of a binary tree in the following order: left child, current node, right child.
- This method is often used with binary search trees to obtain the nodes in sorted order.
- The result is a sorted list of the nodes when applied to a binary search tree.

**Applications**

- Searching: Finding elements within a binary search tree.
- Sorting: Constructing sorted lists from BSTs or other binary trees.
- Expression Evaluation: Evaluating mathematical expressions stored in expression trees.
- Checking for Validity: Validating the structure of a binary tree.
- Checking for Balanced Trees: Determining if a binary tree is balanced.

## Preorder

### Preorder Tree Traversal

Pre-order traversal is used to perform actions on nodes before their children. It’s often used to copy a tree structure, evaluate expressions, and explore hierarchical data.

**Technique**

- In pre-order traversal, you visit the current node before its child nodes. The order is: current node, left child, right child.
- Pre-order traversal is useful for copying the tree structure or evaluating expressions in expression trees.

**Applications**

- Copying a Tree: Creating a duplicate of a binary tree.
- Expression Evaluation: Evaluating mathematical expressions in expression trees.
- Creating Prefix Expressions: Transforming an infix expression to a prefix expression (used in compilers).
- Tree Serialization: Storing a tree’s structure for later reconstruction.

## Postorder

### Post-order tree traversal

Post-order traversal is used to perform actions on nodes after their children. It’s often used in applications that require processing subtrees before the current node.

- In post-order traversal, you visit the current node after its child nodes. The order is: left child, right child, current node.
- Post-order traversal is often used in deleting nodes from a tree, as it ensures that child nodes are deleted before their parent nodes.

**Applications**

- Deleting Nodes: Safely removing nodes from a tree to avoid memory leaks.
- Calculating Expressions: Evaluating mathematical expressions in expression trees by visiting operators after their operands.
- Memory Management: Releasing resources associated with tree nodes (used in garbage collection).
- Determining Tree Height: Calculating the height of a binary tree.

## Breadth First

### Breadth First Traversal

Level-order traversal, also known as breadth-first traversal, visits the nodes level by level, from left to right.

It is suitable for exploring all nodes at a particular level before moving on to the next level.

Level-order traversal is often used in tree-based data structures like binary trees or n-ary trees.

## Depth Traversal

### Depth First Traversal

Depth-first traversals explore a tree by following a path as deeply as possible before backtracking.

- In-order, pre-order, and post-order as all examples of depth first traversal.

DFS is typically implemented using recursion or a stack data structure.

## Resources

### Resources