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 stands for a data structure which is made up of nodes that can only have two children references.

Binary Search Tree (BST) on the other hand, is a special form of Binary Tree data structure where each node has a comparable value, and smaller valued children attached to left and larger valued children attached to the right.

Thus, all BST's are Binary Tree however only some Binary Tree's may be also BST. Notify that BST is a subset of Binary Tree.

So, Binary Tree is more of a general data-structure than Binary Search Tree. And also you have to notify that Binary Search Tree is a sorted tree whereas there is no such set of rules for generic Binary Tree.

Binary Tree

A Binary Tree which is not a BST;

         5
       /   \
      /     \
     9       2
    / \     / \
  15   17  19  21

Binary Search Tree (sorted Tree)

A Binary Search Tree which is also a Binary Tree;

         50
       /    \
      /      \
     25      75
    /  \    /  \
  20    30 70   80

Binary Search Tree Node property

Also notify that for any parent node in the BST;

• All the left nodes have smaller value than the value of the parent node. In the upper example, the nodes with values { 20, 25, 30 } which are all located on the left (left descendants) of 50, are smaller than 50.

• All the right nodes have greater value than the value of the parent node. In the upper example, the nodes with values { 70, 75, 80 } which are all located on the right (right descendants) of 50, are greater than 50.

There is no such a rule for Binary Tree Node. The only rule for Binary Tree Node is having two childrens so it self-explains itself that why called binary.