### Binary Search Tree (BST)

A **Binary Search Tree (BST)** is a hierarchical data structure used for efficient searching, insertion, and deletion operations. In a binary search tree, each node contains a key value and has at most two children: a left child and a right child. The key property of a binary search tree is that for every node, all values in its left subtree are less than its key value, and all values in its right subtree are greater than its key value. This ordering property allows for fast searching, as it enables the use of a binary search algorithm to locate elements within the tree. Binary search trees are widely used in various applications due to their simplicity and efficiency in organizing and accessing data

In the below **PDF** we discuss about **Binary Search Tree** in detail in simple language, Hope this will help in better understanding.

#### Operations on Binary Search Tree:

**Search:**Searching for a specific key within the BST. The search operation starts from the root node and compares the target key with the current node’s key. If the target key is equal to the current node’s key, the search is successful. If the target key is less than the current node’s key, the search continues in the left subtree; otherwise, it continues in the right subtree. This process repeats recursively until the target key is found or the search reaches a leaf node.**Insertion:**Adding a new key-value pair to the BST while maintaining the binary search tree property. The insertion operation begins at the root node and follows a similar process to the search operation to find the appropriate position for the new key. Once the correct position is determined, a new node containing the key-value pair is inserted into the tree as a leaf node.**Deletion:**Removing a key-value pair from the BST while preserving the binary search tree property. The deletion operation involves three cases:If the node to be deleted has no children, it is removed from the tree.

If the node has one child, the child node replaces the deleted node.

If the node has two children, it is replaced by its successor (the smallest key in its right subtree), and then the successor node is recursively deleted.**Inorder Traversal:**Visiting nodes in non-decreasing order of their keys. In a BST, inorder traversal results in visiting nodes in sorted order.**Preorder Traversal:**Visiting the root node, followed by recursively traversing the left subtree and then the right subtree.**Postorder Traversal:**Traversing the left subtree recursively, followed by traversing the right subtree recursively, and finally visiting the root node.**Minimum and Maximum:**Finding the node with the minimum (leftmost) or maximum (rightmost) key in the BST. These operations involve traversing the tree to the leftmost or rightmost node, respectively, from the root.

#### Benefits of Binary Search Tree:

**Fast Search:**With logarithmic time complexity for searching in balanced trees, BSTs offer rapid retrieval of data.**Dynamic Structure:**BSTs can dynamically adjust their structure as elements are inserted or deleted, making them ideal for scenarios where data is frequently changing.**Space Efficiency:**Unlike other data structures like arrays, BSTs don’t require contiguous memory allocation, allowing for efficient memory usage.**Versatility:**BSTs find applications in diverse fields ranging from databases and compilers to network routing algorithms and more, showcasing their versatility and utility.

**Conclusion:**

In conclusion, Binary Search Trees stand as a testament to the elegance and efficiency of data structures. Their simple yet powerful design facilitates rapid searching, insertion, and deletion operations, making them indispensable in various domains of computer science. By understanding the principles underlying BSTs and leveraging their capabilities, developers and engineers can unlock a world of possibilities in algorithm design and optimization.

#### Related Question

A Binary Search Tree (BST) is a data structure used for organizing elements in a sorted manner. Each node in a BST has at most two children, and for each node, all elements in its left subtree are less than the node’s value, while all elements in its right subtree are greater than the node’s value.

Unlike other trees, such as general trees or binary trees, a Binary Search Tree follows a specific ordering property where elements are arranged such that for any given node, all elements to its left are lesser, and all elements to its right are greater.

The main operations performed on a Binary Search Tree include insertion, deletion, searching, traversal (in-order, pre-order, post-order), and finding minimum and maximum elements.

Searching in a Binary Search Tree is efficient and is done recursively or iteratively. It involves comparing the target value with the current node’s value and traversing left or right based on the comparison until the target is found or the end of the tree is reached.

The time complexity of searching in a Binary Search Tree is O(h), where h is the height of the tree. In a balanced BST, the height is logarithmic with respect to the number of nodes, resulting in an average time complexity of O(log n), where n is the number of nodes. However, in the worst case, when the tree is unbalanced, the time complexity can degrade to O(n).

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