A Binary Search Tree (BST) is a type of binary tree data structure that follows a set of specific rules. It is composed of nodes where each node contains a value and has at most two child nodes: a left child and a right child. These child nodes are arranged in a way that satisfies the following criteria:
1. The value in the left child node is always less than the value in its parent node, whereas the value in the right child node is always greater than or equal to the value in its parent node.
2. Both the left and right subtrees of any given node must also be BSTs. This recursive property allows for efficient search, insertion, and deletion operations in the binary search tree.
This special organization enables efficient searching within the binary search tree. When a value is compared during a search operation, if the value matches the value of the current node, the search is successful. If the value is smaller, the search resumes in the left subtree. Conversely, if the value is greater, the search continues in the right subtree.
BSTs are particularly useful for quickly finding or inserting elements in an ordered collection. Their balanced forms, such as AVL trees or Red-Black trees, maintain optimal time complexity for both searching and inserting elements, limiting the tree's height to logarithmic proportions.
In summary, a BST is a binary tree structure that arranges its nodes in a specific order, providing efficient search, insertion, and deletion operations, primarily applied in data retrieval tasks and ordered collections.
