Binary Search Trees

Binary Search Trees are the first of many specialized trees

Binary search trees have the core property where left <= node < right thus allowing elements to be stored in sorted fashion easily

Runtime analysis

BSTs have the same runtime as Trees but if the tree is balanced, it implies that insertions of elements in sorted order can be done in $O(\log n)$ which is faster than what inserting into a sorted array can achieve

Core properties

1. left <= node < right

2. In-order traversal produces a sorted array

3. The maximum value exists on the rightmost leaf of the right sub-tree

4. The minimum value exists on the leftmost leaf of the left sub-tree

Techniques

Most of the techniques of a BST is the same as those Trees, however, there is a technique that only BSTs can achieve

Using in-order traversal

The core property of BSTs allow in-order traversal to become a sequential traversal of the elements in sorted order. Once a problem mentions that the tree is a BST, try thinking of how to exploit this property to solve the problem