Difference between binary tree and binary search tree

Binary tree: Tree where each node has up to two leaves

  1
 / \
2   3

Binary search tree: Used for searching. A binary tree where the left child contains only nodes with values less than the parent node, and where the right child only contains nodes with values greater than or equal to the parent.

  2
 / \
1   3

Binary Tree is a specialized form of tree with two child (left child and right Child). It is simply representation of data in Tree structure

Binary Search Tree (BST) is a special type of Binary Tree that follows following condition:

1. left child node is smaller than its parent Node
2. right child node is greater than its parent Node

A binary tree is made of nodes, where each node contains a "left" pointer, a "right" pointer, and a data element. The "root" pointer points to the topmost node in the tree. The left and right pointers recursively point to smaller "subtrees" on either side. A null pointer represents a binary tree with no elements -- the empty tree. The formal recursive definition is: a binary tree is either empty (represented by a null pointer), or is made of a single node, where the left and right pointers (recursive definition ahead) each point to a binary tree.

A binary search tree (BST) or "ordered binary tree" is a type of binary tree where the nodes are arranged in order: for each node, all elements in its left subtree are less to the node (<), and all the elements in its right subtree are greater than the node (>).

    5
   / \
  3   6 
 / \   \
1   4   9    

The tree shown above is a binary search tree -- the "root" node is a 5, and its left subtree nodes (1, 3, 4) are < 5, and its right subtree nodes (6, 9) are > 5. Recursively, each of the subtrees must also obey the binary search tree constraint: in the (1, 3, 4) subtree, the 3 is the root, the 1 < 3 and 4 > 3.

Watch out for the exact wording in the problems -- a "binary search tree" is different from a "binary tree".

As everybody above has explained about the difference between binary tree and binary search tree, i am just adding how to test whether the given binary tree is binary search tree.

boolean b = new Sample().isBinarySearchTree(n1, Integer.MIN_VALUE, Integer.MAX_VALUE);
.......
.......
.......
public boolean isBinarySearchTree(TreeNode node, int min, int max)
{

    if(node == null)
    {
        return true;
    }

    boolean left = isBinarySearchTree(node.getLeft(), min, node.getValue());
    boolean right = isBinarySearchTree(node.getRight(), node.getValue(), max);

    return left && right && (node.getValue()<max) && (node.getValue()>=min);

}

Hope it will help you. Sorry if i am diverting from the topic as i felt it's worth mentioning this here.