Binary Search Tree Complete Implementation

Binary Tree : A data struc­ture in which we have nodes con­tain­ing data and two ref­er­ences to other nodes, one on the left and one on the right.

Binary Tree con­sist of Nodes

Nodes are noth­ing but objects of a class and each node has data and a link to the left node and right node.
Usu­ally we call the start­ing node of a tree as root.
class Node{
    int data;
    Node left;
    Node right;    
    public Node(int data){
        this.data = data;
        left = null;
        right = null;
    }
}

 Left and right node of a Leaf node points to NULL so you will know that you have reached to the end of the tree.
Binary Tree Node
Binary Tree Node
Binary Search Tree:

Often we call it as BST, is a type of Binary tree which has a spe­cial property.

Nodes smaller than root goes to the left of the root and Nodes greater than root goes to the right of the root.

Binary Search Tree
Binary Search Tree
Oper­a­tions:

Insert(int n) : Add a node the tree with value n. Its O(lgn)

Find(int n) : Find a node the tree with value n. Its O(lgn)

Delete (int n) : Delete a node the tree with value n. Its O(lgn)

Dis­play(): Prints the entire tree in increas­ing order. O(n).

Detail Expla­na­tions for the Operations:

Find(int n):

Its very sim­ple oper­a­tion to perform.
start from the root and com­pare root.data with n
if root.data is greater than n that means we need to go to the left of the root.
if root.data is smaller than n that means we need to go to the right of the root.
if any point of time root.data is equal to the n then we have found the node, return true.
if we reach to the leaves (end of the tree) return false, we didn’t find the element
BST Find()
BST Find()
Insert(int n):

Very much sim­i­lar to find() operation.
To insert a node our first task is to find the place to insert the node.
Take cur­rent = root .
start from the cur­rent and com­pare root.data with n
if current.data is greater than n that means we need to go to the left of the root.
if current.data is smaller than n that means we need to go to the right of the root.
if any point of time cur­rent is null that means we have reached to the leaf node, insert your node here with the help of par­ent node. (See code)
BST Insert()
BST Insert()
Delete(int n):

Com­pli­cated than Find() and Insert() oper­a­tions. Here we have to deal with 3 cases.

Node to be deleted is a leaf node ( No Children).
Node to be deleted has only one child.
Node to be deleted has two childrens.
Node to be deleted is a leaf node ( No Children).

its a very sim­ple case, if a node to be deleted has no chil­dren then just tra­verse to that node, keep track of par­ent node and the side in which the node exist(left or right) and set parent.left = null or parent.right = null;

 

BST - Node to be deleted is a leaf node ( No Children).
BST — Node to be deleted is a leaf node ( No Children).
Node to be deleted has only one child.

its a slightly com­plex case. if a node to be deleted(deleteNode) has only one child then just tra­verse to that node, keep track of par­ent node and the side in which the node exist(left or right).
check which side child is null (since it has only one child).
Say node to be deleted has child on its left side . Then take the entire sub tree from the left side and add it to the par­ent and the side on which deleteN­ode exist, see step 1 and example.
BST - Node to be deleted has only one child.
BST — Node to be deleted has only one child.
Node to be deleted has two childrens.

Now this is quite exciting :)

You just can­not replace the deleteN­ode with any of its child, Why? Lets try out a example.

BST - Node to be deleted has 2 children - Example -1
BST — Node to be deleted has 2 chil­dren — Exam­ple –1
What to do now?????

Dont worry we have solu­tion for this :)

Find The Successor:

Suc­ces­sor is the node which will replace the deleted node. Now the ques­tion is to how to find it and where to find it.

Suc­ces­sor is the smaller node in the right sub tree of the node to be deleted.

BST - Node to be deleted has 2 children - Example -2
BST — Node to be deleted has 2 chil­dren — Exam­ple –2
Dis­play() : To know about how we are dis­play­ing nodes in increas­ing order, Click Here

Com­plete Example :

 

BST - Complete Example
BST — Com­plete Example
Com­plete Exam­ple Code:

public class BinarySearchTree {
    public static  Node root;
    public BinarySearchTree(){
        this.root = null;
    }
    
    public boolean find(int id){
        Node current = root;
        while(current!=null){
            if(current.data==id){
                return true;
            }else if(current.data>id){
                current = current.left;
            }else{
                current = current.right;
            }
        }
        return false;
    }
    public boolean delete(int id){
        Node parent = root;
        Node current = root;
        boolean isLeftChild = false;
        while(current.data!=id){
            parent = current;
            if(current.data>id){
                isLeftChild = true;
                current = current.left;
            }else{
                isLeftChild = false;
                current = current.right;
            }
            if(current ==null){
                return false;
            }
        }
        //if i am here that means we have found the node
        //Case 1: if node to be deleted has no children
        if(current.left==null && current.right==null){
            if(current==root){
                root = null;
            }
            if(isLeftChild ==true){
                parent.left = null;
            }else{
                parent.right = null;
            }
        }
        //Case 2 : if node to be deleted has only one child
        else if(current.right==null){
            if(current==root){
                root = current.left;
            }else if(isLeftChild){
                parent.left = current.left;
            }else{
                parent.right = current.left;
            }
        }
        else if(current.left==null){
            if(current==root){
                root = current.right;
            }else if(isLeftChild){
                parent.left = current.right;
            }else{
                parent.right = current.right;
            }
        }else if(current.left!=null && current.right!=null){
            
            //now we have found the minimum element in the right sub tree
            Node successor     = getSuccessor(current);
            if(current==root){
                root = successor;
            }else if(isLeftChild){
                parent.left = successor;
            }else{
                parent.right = successor;
            }            
            successor.left = current.left;
        }        
        return true;        
    }
    
    public Node getSuccessor(Node deleleNode){
        Node successsor =null;
        Node successsorParent =null;
        Node current = deleleNode.right;
        while(current!=null){
            successsorParent = successsor;
            successsor = current;
            current = current.left;
        }
        //check if successor has the right child, it cannot have left child for sure
        // if it does have the right child, add it to the left of successorParent.
//        successsorParent
        if(successsor!=deleleNode.right){
            successsorParent.left = successsor.right;
            successsor.right = deleleNode.right;
        }
        return successsor;
    }
    public void insert(int id){
        Node newNode = new Node(id);
        if(root==null){
            root = newNode;
            return;
        }
        Node current = root;
        Node parent = null;
        while(true){
            parent = current;
            if(id<current.data){                
                current = current.left;
                if(current==null){
                    parent.left = newNode;
                    return;
                }
            }else{
                current = current.right;
                if(current==null){
                    parent.right = newNode;
                    return;
                }
            }
        }
    }
    public void display(Node root){
        if(root!=null){
            display(root.left);
            System.out.print(" " + root.data);
            display(root.right);
        }
    }
    public static void main(String arg[]){
        BinarySearchTree b = new BinarySearchTree();
        b.insert(3);b.insert(8);
        b.insert(1);b.insert(4);b.insert(6);b.insert(2);b.insert(10);b.insert(9);
        b.insert(20);b.insert(25);b.insert(15);b.insert(16);
        System.out.println("Original Tree : ");
        b.display(b.root);        
        System.out.println("");
        System.out.println("Check whether Node with value 4 exists : " + b.find(4));
        System.out.println("Delete Node with no children (2) : " + b.delete(2));        
        b.display(root);
        System.out.println("\n Delete Node with one child (4) : " + b.delete(4));        
        b.display(root);
        System.out.println("\n Delete Node with Two children (10) : " + b.delete(10));        
        b.display(root);
    }
}

class Node{
    int data;
    Node left;
    Node right;    
    public Node(int data){
        this.data = data;
        left = null;
        right = null;
    }
}
view rawBinarySearchTree.java hosted with ❤ by GitHub
Output:
Original Tree :
1 2 3 4 6 8 9 10 15 16 20 25
Check whether Node with value 4 exists : true
Delete Node with no children (2) : true
1 3 4 6 8 9 10 15 16 20 25
Delete Node with one child (4) : true
1 3 6 8 9 10 15 16 20 25
Delete Node with Two children (10) : true
1 3 6 8 9 15 16 20 25