A binary tree is a data structure that consists of a set of nodes organized in a hierarchical way, with a maximum of two children per node. The nodes at the top of the tree are called the root nodes, and the nodes at the bottom of the tree are called leaf nodes.
Each node in a binary tree has a value, and the nodes are organized in such a way that the value of any node in the left subtree of a node is less than the value of the node, and the value of any node in the right subtree is greater than the value of the node. This property is called the “binary search tree” property.
Here’s a diagram of a simple binary tree:
4
/ \
2 6
/ \ / \
1 3 5 7
In this tree, the root node has value 4, and the nodes with values 2 and 6 are its children. The nodes with values 1, 3, 5, and 7 are the children of the nodes with values 2 and 6.
Binary trees have a number of useful applications, including:
-Storing data in a sorted way, so that it can be searched efficiently (e.g. using the binary search algorithm).
-Implementing priority queues (e.g. using a heap).
-Implementing expression trees, which can be used to evaluate arithmetic expressions.