Difference between binary tree and binary search tree

Question

Can anyone please explain the difference between binary tree and binary search tree with an example?

Answer 1

Binary tree

Binary tree can be anything which has 2 child and 1 parent. It can be implemented as linked list or array, or with your custom API. Once you start to add more specific rules into it, it becomes more specialized tree. Most common known implementation is that, add smaller nodes on left and larger ones on right.

For example, a labeled binary tree of size 9 and height 3, with a root node whose value is 2. Tree is unbalanced and not sorted. https://en.wikipedia.org/wiki/Binary_tree

For example, in the tree on the left, A has the 6 children {B,C,D,E,F,G}. It can be converted into the binary tree on the right.

Binary Search

Binary Search is technique/algorithm which is used to find specific item on node chain. Binary search works on sorted arrays.

Binary search compares the target value to the middle element of the array; if they are unequal, the half in which the target cannot lie is eliminated and the search continues on the remaining half until it is successful or the remaining half is empty. https://en.wikipedia.org/wiki/Binary_search_algorithm

A tree representing binary search. The array being searched here is [20, 30, 40, 50, 90, 100], and the target value is 40.

Binary search tree

This is one of the implementations of binary tree. This is specialized for searching.

Binary search tree and B-tree data structures are based on binary search.

Binary search trees (BST), sometimes called ordered or sorted binary trees, are a particular type of container: data structures that store "items" (such as numbers, names etc.) in memory. https://en.wikipedia.org/wiki/Binary_search_tree

A binary search tree of size 9 and depth 3, with 8 at the root. The leaves are not drawn.

And finally great schema for performance comparison of well-known data-structures and algorithms applied:

Image taken from Algorithms (4th Edition)