Tree traversal algorithms are methods for visiting every node in a tree data structure, such as a binary tree or a n-ary tree, in a specific order. The three most common tree traversal algorithms are:

**Pre-order traversal:**The algorithm visits the root node first, then recursively visits all the nodes in the left subtree, and finally recursively visits all the nodes in the right subtree. This algorithm is often used to create a copy of the tree.**In-order traversal:**The algorithm recursively visits all the nodes in the left subtree, then visits the root node, and finally recursively visits all the nodes in the right subtree. This algorithm is often used to sort the elements in a binary search tree.**Post-order traversal:**The algorithm recursively visits all the nodes in the left subtree, then recursively visits all the nodes in the right subtree, and finally visits the root node. This algorithm is often used to delete all the nodes in a tree.

Additionally, there is also level-order traversal that visits the level of the node by level, and breadth-first. It is useful in some algorithms such as in finding the shortest path in a graph. It is important to note that the order of traversal can have a significant impact on the performance of the algorithm and the results it produces, so it’s crucial to choose the right traversal method for the task at hand.

**There are several benefits of using tree traversal algorithms in your code, some of which include:**

- Traversing a tree: Tree traversal algorithms allow you to visit every node in a tree data structure in a specific order, which is useful for tasks such as searching for a specific node, printing all the nodes in a tree, or creating a copy of a tree.
- Efficiency: Tree traversal algorithms can be implemented using recursion, which can make the code more readable and maintainable. Additionally, by using the specific traversal algorithm that best suits your needs, you can improve the efficiency of your code by reducing the number of operations required to visit all the nodes in a tree.
- Data manipulation: Tree traversal algorithms can be used to manipulate the data stored in a tree, such as sorting the elements in a binary search tree or deleting all the nodes in a tree.
- Debugging: Tree traversal algorithms can be used to help debug your code by providing a way to visualize the data stored in a tree and to check that the tree is being modified correctly.
- Graph traversal: Tree traversal algorithms can also be used in graph traversal, like depth-first search algorithms.
- Others: Tree traversal algorithms can be used to implement other algorithms like expression evaluation, Huffman coding, and many others.

Overall, tree traversal algorithms can be a powerful tool for working with tree data structures and can help you to write more efficient and maintainable code.

**Preorder traversal**

Preorder traversal is a method of visiting every node in a tree data structure, such as a binary tree or a n-ary tree, in a specific order. The **preorder traversal algorithm** visits the root node first, then recursively visits all the nodes in the left subtree, and finally recursively visits all the nodes in the right subtree. The basic idea behind preorder traversal is to visit the root node first, and then recursively visit the left and right subtrees of the root node.

The algorithm starts at the root node of the tree, and performs the following steps:

- Visit the root node: This step involves processing the data stored in the root node, for example, by printing it out or adding it to a data structure.
- Recursively visit the left subtree: After visiting the root node, the algorithm moves on to the left subtree of the root node. In this step, the algorithm applies the same preorder traversal algorithm to the left subtree, starting with its root node.
- Recursively visit the right subtree: After visiting the left subtree, the algorithm moves on to the right subtree of the root node. In this step, the algorithm applies the same pre-order traversal algorithm to the right subtree, starting with its root node.

It is important to note that the algorithm is recursively applied to the left and right subtrees of the root node, which means that the algorithm is called again with the root node of the left and right subtrees as the new starting point. The recursion continues until it reaches

**Boundary traversal of a binary tree**

Boundary traversal of binary tree is a method of visiting all the nodes that form the boundary of a binary tree. The nodes on the boundary of a binary tree include the leaf nodes and the nodes on the leftmost and rightmost paths from the root to a leaf node.

The **algorithm for boundary traversal of a binary tree** typically involves traversing the tree in a specific order:

First, visit the root node of the tree.

Traverse the leftmost path from the root to a leaf node, visiting all the nodes on that path. Traverse all the leaf nodes in the tree. It can be done by visiting the left subtree and then the right subtree in the in-order traversal

Traverse the rightmost path from the root to a leaf node, visiting all the nodes on that path. The traversal should be done in reverse order, meaning starting from the rightmost leaf, going up to the rightmost leaf of the right subtree and a leftmost leaf of the left subtree.

It is important to note that when traversing the rightmost path, we need to avoid visiting the leaf nodes that were already visited in step 3, and we also need to avoid visiting the root node that we have already visited in step 1. It is worth noting that the order of traversal of the leftmost and rightmost paths, and leaf nodes can be different depending on the application, but the overall idea of visiting the nodes that form the boundary of the binary tree is the same.