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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-NodeBinary 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-TreeOper­a­tions:

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-FindInsert(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-InsertDelete(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.1Node to be deleted has only one child.

  1. 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).
  2. check which side child is null (since it has only one child).
  3. 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.1-1024x647Node 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-1-1024x518What 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-2-1024x615Dis­play() : To know about how we are dis­play­ing nodes in increas­ing order, Click Here

Com­plete Example :

 

Complete-ExampleCom­plete Exam­ple Code:

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

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  • Garima

    Very Easy to under­stand!!
    Gud Explantion 🙂

    • Sumit Jain

      Thanks Garima 🙂

  • Damaris Perez

    Hello, I don’t think this works if you want to get a suc­ces­sor for a node that has no right children.

    • tuto­ri­al­hori­zon

      That will be the case when node has only one child , 2nd case in dele­tion. In that it will not find the successor.

      • Damaris Perez

        But won’t the suc­ces­sor then become the right most child of the left?

      • Damaris Perez

        But I do see it, now. That it’s in the delete method. Thank you for your quick reply. 🙂

        • tuto­ri­al­hori­zon

          Can u give one exam­ple, it will be easy to understand.

          • Damaris Perez

            Oh, no. I under­stand it now. I was just con­fused because I was look­ing for every­thing in get­Suc­ces­sor(). So, I thought if the node to be deleted had no right chil­dren, then the right most child of the left branch became the suc­ces­sor, but that is all done in delete(), so I under­stand every­thing, now. Thank you.

          • tuto­ri­al­hori­zon

            Glad that its clear now. let me know if you find issues in other posts.

  • siva

    for insert, we tra­verse ele­ments until cur­rent not equal to null. so i changed con­di­tion for while loop current!=null instead or true. the loop goes infi­nite times. but why? can any­one help

  • Komal Shipe

    What will hap­pen if you add two nodes of same value?

  • Rotem Uzan

    Hi,
    I have a ques­tion, in the Delete() method, why we can’t just use the insert method and run it on the chil­dren of the deleted node ?
    it is because of the dif­fer­ent order we will receive ?
    Thanks !

  • Prashant Bisht

    I dont under­stand what is the sig­nif­i­cance of parent=current in insert .I think it will work with­out this line also.