A binary tree is a data structure that is commonly used in computer science and programming. It is a tree-like structure that is made up of nodes, with each node having a maximum of two children. In this article, we will be discussing the implementation of a binary tree in C++ and its various applications.
The basic structure of a binary tree is a node, which is made up of an element and two pointers. The first pointer points to the left child of the node, and the second pointer points to the right child of the node. If a node does not have a left or right child, the pointer is set to NULL. The root node is the topmost node in the tree, and it does not have a parent.
The basic operations that can be performed on a binary tree are insertion, deletion, and search. Insertion is the process of adding a new node to the tree. The new node is placed in the correct location in the tree based on its value. Deletion is the process of removing a node from the tree. The node is removed based on its value, and the tree is restructured to maintain its balance. Search is the process of finding a specific node in the tree based on its value.
In C++, a binary tree can be implemented using a class or a struct. A class is a user-defined data type that can have its own methods and properties. A struct is a data type that can have its own properties but does not have any methods. In this article, we will be implementing a binary tree using a class.
The following is an example of a binary tree class in C++:
class BinaryTree { private: struct Node { int data;
Node* left; Node* right; };
Node* root; public: BinaryTree(); void insert(int); void deleteNode(int); Node* search(int); };
The class has a private struct called Node, which contains the data, left pointer, and right pointer for each node in the tree. The class also has a private pointer called root, which points to the root node of the tree. The class has three public methods, insert, deleteNode, and search, which are used to perform the basic operations on the tree.
The constructor for the class initializes the root pointer to NULL, indicating that the tree is empty.
BinaryTree::BinaryTree() { root = NULL; }
The insert method is used to add a new node to the tree. The method takes an integer as a parameter, which is the value of the new node. The method starts by creating a new node and setting its data to the value passed as a parameter. The left and right pointers of the new node are set to NULL. The method then checks if the tree is empty, and if it is, the new node is set as the root. If the tree is not empty, the method starts at the root and compares the value of the new node to the value of the current node. If the new value is less than the current value, the method moves to the left child, and if the value is greater, it moves to the right child. The process is repeated until a leaf node is reached, and the new node is inserted as the left or right child of the leaf node.
