Define the height of a binary tree.

The height of a binary tree is the longest path from the root node to any leaf node.

In more detail, the height of a binary tree is a measure of the maximum number of edges in the longest path from the root node to any leaf node. In other words, it is the maximum level of any leaf node. The height of a tree can also be seen as the depth of the tree's deepest node.

In a binary tree, each node has at most two children, referred to as the left child and the right child. The root node is the topmost node, and the leaf nodes are the nodes that have no children. The height of a binary tree is often used in the analysis of algorithms, as it can significantly impact the time complexity of operations such as search, insert and delete.

It's important to note that an empty tree (a tree with no nodes) has a height of -1, and a tree with only one node (the root) has a height of 0. This is because the height of a tree is defined as the number of edges in the longest path, not the number of nodes.

To calculate the height of a binary tree, you can use a recursive algorithm. Starting from the root node, you traverse down each subtree, incrementing a counter for each edge you pass. When you reach a leaf node, you return the counter. The height of the tree is the maximum counter value returned from the left and right subtrees.

Understanding the concept of tree height is crucial for understanding more complex data structures and algorithms, such as AVL trees and B-trees, which are used in many areas of computer science, including database systems and file systems.