Preorder Traversal of a Binary Tree

Perform a pre-order traversal on a given binary tree.

Pre-order traversal of a binary tree is a fundamental concept in graph theory and related fields. In a pre-order traversal, the nodes of the tree are recursively visited in this order: root node, then the left subtree, followed by the right subtree. This traversal strategy is useful in scenarios where you want to explore the structure of a tree starting from its root, giving priority to the left children before the right ones.

Understanding pre-order traversal is important because it lays the groundwork for more complex tree traversal techniques and algorithms. It is part of a trio of basic depth-first traversals including in-order and post-order, each with specific use cases depending on the nature of the problem. For instance, pre-order traversal is often used in prefix notation, which can be handy in applications involving expression trees.

Conceptually, pre-order traversal can also help in constructing a copy of the tree, evaluating prefix mathematical expressions, or providing a foundation for learning about more intricate tree structures such as AVL trees, B-trees, or even balancing algorithms. Mastering tree traversals is critical for students as they advance into more sophisticated topics in computer science, as trees are one of the fundamental data structures employed in algorithms and data handling.