A binary tree is a tree data structure in which each node has at most two children, referred to as the left child and the right child.

Characteristics

  • Each node contains a value.
  • A node can have a maximum of two children.
  • The left child is always smaller than the parent node.
  • The right child is always greater than or equal to the parent node.

Types of Binary Trees

  • Binary Search Tree (BST): In a BST, for each node, all the elements in the left subtree are smaller than the node, and all the elements in the right subtree are larger than the node.
  • Balanced Binary Tree: A binary tree is balanced if for each node, the height difference between its left and right subtrees is at most 1.
  • Full Binary Tree: A binary tree is full if every node has either 0 or 2 children.
  • Complete Binary Tree: A binary tree is complete if all levels are fully filled, except possibly the last level, which is filled from left to right.

Operations

  • Insertion: Insert a new node in the binary tree while maintaining its properties.
  • Deletion: Delete a node from the binary tree while maintaining its properties.
  • Traversal: Visit all nodes in the binary tree in a specific order.

Insertion

The insertion process involves:

  1. Starting at the root node.
  2. Comparing the value to be inserted with the current node.
  3. If the value is less than the current node, move to the left child.
  4. If the value is greater than or equal to the current node, move to the right child.
  5. Repeat steps 3 and 4 until a null node is reached.
  6. Insert the new node at this position.

Insertion in a Binary Tree

For more information on binary trees, you can read our comprehensive guide on Binary Tree Operations.

Conclusion

The binary tree is a fundamental data structure in computer science with various applications. It is essential to understand its characteristics, types, and operations to implement more complex algorithms.

For further reading on data structures, explore our Data Structures section.