Binary Tree Data Structure

• A binary tree is a hierarchical data structure where each node has at most two children, referred to as the left child and the right child

Structure Definition

• A structure can be defined to represent each node in the binary tree
• The structure contains a data field to store the value of the node, and two pointers, left and right, pointing to the left and right child nodes respectively

Node Creation

• A function, createNode(), can be defined to create a new node in the binary tree
• It takes the data value as input and allocates memory for the new node
• The data field of the node is initialized with the given value, and both the left and right pointers are set to NULL, indicating that the new node has no children initially

Insertion

• To insert a new node into the binary tree, a function, insertNode(), can be used
• If the tree is empty (the root is NULL), the new node becomes the root
• Otherwise, the function traverses the tree to find the appropriate position for the new node
• A common approach is to use a level-order traversal, where nodes are added level by level from left to right
• The function maintains a queue of nodes to visit
• It starts by enqueuing the root node
• While the queue is not empty, the function dequeues a node and checks if its left or right child is empty
• If the left child is empty, the new node is added as the left child
• If the right child is empty, the new node is added as the right child
• If both children are occupied, the function enqueues the left and right children for further exploration

Traversal

• Tree traversal is the process of visiting each node in the tree exactly once
• There are two main types of tree traversal: depth-first traversal and breadth-first traversal

Depth-First Traversal

• In depth-first traversal, the algorithm explores as far as possible along each branch before backtracking
• There are three types of depth-first traversal: in-order, pre-order, and post-order

In-Order Traversal

• In in-order traversal, the algorithm visits the left subtree, then the root, and finally the right subtree
• This is typically done recursively

Pre-Order Traversal

• In pre-order traversal, the algorithm visits the root, then the left subtree, and finally the right subtree
• This is typically done recursively

Post-Order Traversal

• In post-order traversal, the algorithm visits the left subtree, then the right subtree, and finally the root
• This is typically done recursively

Breadth-First Traversal

• In breadth-first traversal, the algorithm visits all the nodes at the current level before moving to the next level
• This is also known as level-order traversal
• This is typically done using a queue

Deletion

• Deleting a node from a binary tree involves several cases
• If the node to be deleted is a leaf node (has no children), it can simply be removed
• If the node has only one child, it can be replaced by its child
• If the node has two children, its inorder successor (the smallest node in its right subtree) can be found, its data can be copied to the node to be deleted, and then the inorder successor can be deleted

Search

• Searching for a node with a specific value in a binary tree involves traversing the tree and comparing the value of each node with the target value
• Depending on the structure of the tree, different search strategies can be employed
• In a binary search tree, where the value of each node is greater than or equal to the value of any node in its left subtree and less than or equal to the value of any node in its right subtree, a binary search-like approach can be used to efficiently locate the node
• Otherwise, a general tree traversal algorithm can be used to visit each node in the tree until the target node is found or the entire tree has been traversed

Example Code Snippet

• A basic example of constructing a binary tree node in C:

    struct Node {
    int data;
    struct Node* left;
    struct Node* right;
    };

    struct Node* createNode(int data){
    struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
    newNode->data = data;
    newNode->left = NULL;
    newNode->right = NULL;
    return newNode;
    }

• This code defines the structure for a node and a function to create new nodes.