Explain the principle of how a binary tree works and its main properties.

A binary tree is a data structure where each node has at most two children: left and right. Main properties:

• Each node contains a value and references to its left and right children.
• The left child usually contains a value less than or equal to the parent's value (in a binary search tree).
• The right child contains a value greater than the parent's value.
• It is used for efficient search, insertion, and deletion of elements.

Example: In a binary search tree, searching for an element takes time proportional to the height of the tree, which gives logarithmic complexity in a balanced tree.