Binary Search Tree with Insert and Delete Operations

Write a Python program to implement a Binary Search Tree (BST) with insert and delete operations. A Binary Search Tree is a node-based binary tree data structure that has the following properties: the left subtree contains only nodes with keys less than the node's key; the right subtree contains only nodes with keys greater than the node's key; and both left and right subtrees are also binary search trees.

Algorithm for BST class

1. Define a TreeNode class to represent nodes in the BST.
2. Implement insertion by traversing the tree to find the correct position.
3. Implement search by comparing values and traversing left or right accordingly.
4. Implement deletion handling three cases: no children, one child, two children.
5. Implement tree traversal methods using a recursive approach.

Example 1

Input: ["BST", "insert", "insert", "insert", "search", "delete", "search", "inorderTraversal"]
[[], [5], [3], [7], [3], [3], [3], []]
Output: [null, null, null, null, true, null, false, [5, 7]]
Explanation: 

bst = BST()
bst.insert(5)    // Insert 5
bst.insert(3)    // Insert 3
bst.insert(7)    // Insert 7
bst.search(3)    // Returns true as 3 exists
bst.delete(3)    // Delete 3
bst.search(3)    // Returns false as 3 is deleted
bst.inorderTraversal() // Returns [5, 7]

Example 2

Input: ["BST", "insert", "insert", "insert", "insert", "delete", "preorderTraversal"]
[[], [10], [5], [15], [3], [10], []]
Output: [null, null, null, null, null, null, [5, 3, 15]]
Explanation: 

bst = BST()
bst.insert(10)   // Insert 10
bst.insert(5)    // Insert 5
bst.insert(15)   // Insert 15
bst.insert(3)    // Insert 3
bst.delete(10)   // Delete 10, new root becomes 5
bst.preorderTraversal() // Returns [5, 3, 15]

Constraints

-10^9 ≤ val ≤ 10^9
At most 10^4 calls will be made to insert, delete, search, inorderTraversal, and preorderTraversal.
Each val is unique.
Time Complexity: O(h) for insert, delete, and search operations, where h is the height of the tree
Space Complexity: O(n) for the tree storage, O(h) for recursive operations