Understanding the difference between a Binary Search Tree (BST) and a Binary Tree is essential when it comes to programming, as they are the two most commonly used data structures in computer science. To help you better understand how these trees work and why they are so important, let’s take a look at what sets them apart.
At their core, binary search trees and binary trees both use the same node data structure. A node is simply an object that holds data as well as pointers to other nodes. Nodes can be used to create a hierarchy, allowing items to be organized in an efficient manner.
BSTs and Binary Trees differ mainly in the comparisons and rules used for the insertion and retrieval of data. BSTs compare elements according to a certain order, usually numerical or lexicographical values, while Binary Trees do not make any such comparisons; instead, elements are just placed wherever space is available within the tree structure. This means that BSTs are more efficient than binary trees because elements can be quickly located by performing comparisons on their values.
Another way BSTs and binary trees differ is in terms of their height and balance factor. The height of a tree refers to the number of nodes between its root node (the topmost node) and its deepest leaf node (the bottommost node). A balanced tree has a height that remains roughly the same even after new elements are added or removed from it while an unbalanced tree has heights that vary significantly once items have been inserted or removed from it.
Comparison/Contrast between BSTs and Binary Trees
When looking at data structures, a comparison between BSTs and Binary Trees is a great way to understand the difference between the two. Choosing which structure to use for your project can be difficult, so it's important to understand their differences.
First, let's start by defining a Binary Tree and a BST. A Binary Tree is a type of data structure that follows a particular pattern: every node has at most two children, also known as 'left' and 'right'. A BST (Binary Search Tree) is a specific type of binary tree that follows an additional ordering restriction. In addition to the two-child rule, each node must have all elements in its left subtree less than itself and all elements in its right subtree greater than itself.
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The insertion/search differences between BSTs and Binary Trees are quite significant. To insert into or search through a binary tree we need to traverse through the entire tree using either breadth-first or depth-first searches. But with BSTs insertion/search becomes much more efficient since we can simply compare each element as we traverse down the tree and quickly return true if found or false if not found.
Another key difference is how balanced vs unbalanced trees play out in each type. Unbalanced trees can be easily created when inserting into binary trees but with BSTs the balance is always maintained since the additional ordering restrictions prevent any unbalance from occurring.
In terms of ordering restrictions for insertion, BSTs have stricter rules imposed on them than binary trees do; elements must be able to be compared in order for nodes to be placed properly within the tree. Source
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