Implementation of Binary Search Tree in Javascript

In this article, we would be implementing the Binary Search Tree data structure in Javascript. A tree is a a collection of node connected by some edges. A tree is a non linear data structure. A Binary Search tree is a binary tree in which nodes which have lesser value are stored on the left while the nodes with higher value are stored at the right.
Now lets see an example of of an Binary Search Tree node:

As in the above code snippet we define a node class having three property data, left and right, Left and right are pointers to the left and right node in a Binary Search Tree. Data is initialized with data which is passed when object for this node is created and left and right is set to null.

Now lets see an example of an Binary Search Tree class.

The above example shows a framework of a Binary Search tree class, which contains a private variable root which holds the root of a tree, it is initialized to null.
Now lets implement each of this function:

1. insert(data) – It inserts a new node in a tree with a value data

   // helper method which creates a new node to  // be inserted and calls insertNode insert(data) {     // Creating a node and initailising      // with data      var newNode = new Node(data);                            // root is null then node will     // be added to the tree and made root.     if(this.root === null)         this.root = newNode;     else            // find the correct position in the          // tree and add the node         this.insertNode(this.root, newNode); }    // Method to insert a node in a tree // it moves over the tree to find the location // to insert a node with a given data  insertNode(node, newNode) {     // if the data is less than the node     // data move left of the tree      if(newNode.data < node.data)     {         // if left is null insert node here         if(node.left === null)             node.left = newNode;         else                // if left is not null recurr until              // null is found             this.insertNode(node.left, newNode);      }        // if the data is more than the node     // data move right of the tree      else     {         // if right is null insert node here         if(node.right === null)             node.right = newNode;         else                // if right is not null recurr until              // null is found             this.insertNode(node.right,newNode);     } }

   In the above code we have two methods insert(data) and insertNode(node, newNode). Lets understand them one by one:-

   
   
   
   • insert(data) – It creates a new node with a value data, if the tree is empty it add this node to tree and make it a root, otherwise it calls insert(node, data).
   • insert(node, data) – It compares the given data with the data of current node and moves left or right accordingly and recur until it finds a correct node with a null value where new node can be added.
2. remove(data) – This function removes a node with a given data.

   // helper method that calls the  // removeNode with a given data remove(data) {     // root is re-initialized with     // root of a modified tree.     this.root = this.removeNode(this.root, data); }    // Method to remove node with a  // given data // it recurrs over the tree to find the // data and removes it removeNode(node, key) {                // if the root is null then tree is      // empty     if(node === null)         return null;        // if data to be delete is less than      // roots data then move to left subtree     else if(key < node.data)     {         node.left = this.removeNode(node.left, key);         return node;     }        // if data to be delete is greater than      // roots data then move to right subtree     else if(key > node.data)     {         node.right = this.removeNode(node.right, key);         return node;     }        // if data is similar to the root's data      // then delete this node     else     {          // deleting node with no children         if(node.left === null && node.right === null)         {             node = null;             return node;         }            // deleting node with one children         if(node.left === null)         {             node = node.right;             return node;         }                    else if(node.right === null)         {             node = node.left;             return node;         }            // Deleting node with two children         // minumum node of the rigt subtree         // is stored in aux         var aux = this.findMinNode(node.right);         node.data = aux.data;            node.right = this.removeNode(node.right, aux.data);         return node;     }    }

   In the above code we have two method remove(data) and removeNode(node, data), let understand them one by one:

   • remove(data) – It is helper methods which calls removeNode by passing root node and given data and updates the root of the tree with the value returned by the function
   • removeNode(node, data) – It searches for a node with a given data and then perform certain steps to delete it.

   While deleting a node from the tree their are three different scenarios as follows:-

   • Deleting the leaf node – As leaf node do not have any children hence they can be easily removed and null is returned to the parent node
   • Deleting a node with one child – If a node have a left child then we update the pointer of the parent node to the left child of the node to be deleted and similarly if a node have a right child then we update the pointer of the parent node to the right child of the node to be deleted
   • Deleting a node with two children – In order to delete a node with two children we find the node with minimum value in its right subtree and replace this node with the minimum valued node and remove the minimum valued node from the tree

   In the above code we have used findMinNode(node), it is defined in a helper method section.
   Recommendation: Binary Search Tree | Set 2 (Delete) It contains a detail explaination and a video tutorial for deleting a node from binary search tree.

Tree Traversal

Now Lets understand different ways of traversing a Binary Search Tree.

1. inorder(node) – It performs inorder traversal of a tree starting from a given node
   Algorithm for inorder:

   Traverse the left subtree i.e perform inorder on left subtree
   Visit the root
   Traverse the right subtree i.e perform inorder on right subtree
   

   // Performs inorder traversal of a tree inorder(node) {     if(node !== null)     {         this.inorder(node.left);         console.log(node.data);         this.inorder(node.right);     } }

2. preorder(node) – It performs preorder traversal of a tree starting from a given node.
   Algorithm for preoder:

   Visit the root
   Traverse the left subtree i.e perform inorder on left subtree
   Traverse the right subtree i.e perform inorder on right subtree
   

   // Performs preorder traversal of a tree     preorder(node) {     if(node != null)     {         console.log(node.data);         this.preorder(node.left);         this.preorder(node.right);     } }

3. postorder(node) – It performs postorder traversal of a tree starting from a given node.
   Algorithm for postorder:

   Traverse the left subtree i.e perform inorder on left subtree
   Traverse the right subtree i.e perform inorder on right subtree
   Visit the root
   

   // Performs postorder traversal of a tree postorder(node) {     if(node != null)     {         this.postorder(node.left);         this.postorder(node.right);         console.log(node.data);     } }

Helper Methods

Lets declare some helper method which are useful while working with Binary Search Tree.

1. findMinNode(node) – It searches for a node with a minimum value starting from node.

   //  finds the minimum node in tree // searching starts from given node findMinNode(node) {     // if left of a node is null     // then it must be minimum node     if(node.left === null)         return node;     else         return this.findMinNode(node.left); }

   As seen in the above method we start from a node and keeping moving to the left subtree until we find a node whose left child is null, once we find such node we return it.

2. getRootNode() – It returns the root node of a tree.

   // returns root of the tree getRootNode() {     return this.root; }

3. search(data) – It searches the node with a value data in the entire tree.

   // search for a node with given data search(node, data) {    // if trees is empty return null     if(node === null)         return null;        // if data is less than node's data     // move left     else if(data < node.data)         return this.search(node.left, data);        // if data is less than node's data     // move left     else if(data > node.data)         return this.search(node.right, data);        // if data is equal to the node data      // return node     else         return node; }

Note : Different helper method can be declared in the BinarySearchTree class as per the requirement.
Implementation
Now lets use the BinarySearchTree class and its different methods described above.

For more on binary trees please refer to the following article: Binary tree Data Structure

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.