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// A utility function to search a given key in BST
public Node search(Node root, int key)
{
    // Base Cases: root is null or key is present at root
    if (root==null || root.key==key)
        return root;

    // val is greater than root's key
    if (root.key > key)
        return search(root.left, key);

    // val is less than root's key
    return search(root.right, key);
}

Illustration to search 6 in below tree:
1. Start from root.
2. Compare the inserting element with root, if less than root, then recurse for left, else recurse for right.
3. If element to search is found anywhere, return true, else return false.
bstsearch


Insertion of a key
A new key is always inserted at leaf. We start searching a key from root till we hit a leaf node. Once a leaf node is found, the new node is added as a child of the leaf node.

         100                               100
        /   \        Insert 40            /    \
      20     500    --------->          20     500
     /  \                              /  \
    10   30                           10   30
                                              \
                                              40
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// Java program to demonstrate insert operation in binary search tree
class BinarySearchTree {

    /* Class containing left and right child of current node and key value*/
    class Node {
        int key;
        Node left, right;

        public Node(int item) {
            key = item;
            left = right = null;
        }
    }

    // Root of BST
    Node root;

    // Constructor
    BinarySearchTree() {
        root = null;
    }

    // This method mainly calls insertRec()
    void insert(int key) {
       root = insertRec(root, key);
    }

    /* A recursive function to insert a new key in BST */
    Node insertRec(Node root, int key) {

        /* If the tree is empty, return a new node */
        if (root == null) {
            root = new Node(key);
            return root;
        }

        /* Otherwise, recur down the tree */
        if (key < root.key)
            root.left = insertRec(root.left, key);
        else if (key > root.key)
            root.right = insertRec(root.right, key);

        /* return the (unchanged) node pointer */
        return root;
    }

    // This method mainly calls InorderRec()
    void inorder()  {
       inorderRec(root);
    }

    // A utility function to do inorder traversal of BST
    void inorderRec(Node root) {
        if (root != null) {
            inorderRec(root.left);
            System.out.println(root.key);
            inorderRec(root.right);
        }
    }

    // Driver Program to test above functions
    public static void main(String[] args) {
        BinarySearchTree tree = new BinarySearchTree();

        /* Let us create following BST
              50
           /     \
          30      70
         /  \    /  \
       20   40  60   80 */
        tree.insert(50);
        tree.insert(30);
        tree.insert(20);
        tree.insert(40);
        tree.insert(70);
        tree.insert(60);
        tree.insert(80);

        // print inorder traversal of the BST
        tree.inorder();
    }
}