A binary tree is a tree data structure in which each parent node can have at most two children. The two children are generally referred to as the left child and the right child. A binary tree is represented by a pointer to the topmost node, commonly known as the "root" of the tree. If the tree is empty, then the value of the root is NULL. Each node of a binary tree consists of three parts: a data item, a pointer to the left child, and a pointer to the right child.
There are different types of binary trees, including:
- Full Binary Tree: A full binary tree is a special type of binary tree in which every parent node/internal node has either two or no children.
- Perfect Binary Tree: A perfect binary tree is a type of binary tree in which every internal node has exactly two child nodes, and all the leaf nodes are at the same level.
- Complete Binary Tree: A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible.
- Skewed Binary Tree: A skewed binary tree is a pathological/degenerate tree in which the tree is either dominated by the left nodes or the right nodes.
- Balanced Binary Tree: A balanced binary tree is a type of binary tree in which the difference between the height of the left and right subtrees of any node is not more than one.
Binary trees can be used in various applications, such as hashing, routing data for network traffic, data compression, preparing binary heaps, and binary search trees. Basic operations on binary trees include inserting an element, removing an element, searching for an element, and traversing the tree. Auxiliary operations include finding the height of the tree, finding the level of a node of the tree, and finding the size of the entire tree.
