Binary Search Tree insert with Parent Pointer

We have discussed simple BST insert. How to insert in a tree where parent pointer needs to be maintained. Parent pointers are helpful to quickly find ancestors of a node, LCA of two nodes, successor of a node, etc.

In recursive calls of simple insertion, we return pointer of root of subtree created in a subtree. So the idea is to store this pointer for left and right subtrees. We set parent pointers of this returned pointers after the recursive calls. This makes sure that all parent pointers are set during insertion. Parent of root is set to NULL. We handle this by assigning parent as NULL by default to all newly allocated nodes. 

Implementation:

C++

// C++ program to demonstrate insert operation
// in binary search tree with parent pointer
#include<bits/stdc++.h>

struct Node
{
    int key;
    struct Node *left, *right, *parent;
};

// A utility function to create a new BST Node
struct Node *newNode(int item)
{
    struct Node *temp =  new Node;
    temp->key = item;
    temp->left = temp->right = NULL;
    temp->parent = NULL;
    return temp;
}

// A utility function to do inorder traversal of BST
void inorder(struct Node *root)
{
    if (root != NULL)
    {
        inorder(root->left);
        printf("Node : %d, ", root->key);
        if (root->parent == NULL)
          printf("Parent : NULL \n");
        else
          printf("Parent : %d \n", root->parent->key);
        inorder(root->right);
    }
}

/* A utility function to insert a new Node with
   given key in BST */
struct Node* insert(struct Node* node, int key)
{
    /* If the tree is empty, return a new Node */
    if (node == NULL) return newNode(key);

    /* Otherwise, recur down the tree */
    if (key < node->key)
    {
        Node *lchild = insert(node->left, key);
        node->left  = lchild;

        // Set parent of root of left subtree
        lchild->parent = node;
    }
    else if (key > node->key)
    {
        Node *rchild = insert(node->right, key);
        node->right  = rchild;

        // Set parent of root of right subtree
        rchild->parent = node;
    }

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

// Driver Program to test above functions
int main()
{
    /* Let us create following BST
              50
           /     \
          30      70
         /  \    /  \
       20   40  60   80 */
    struct Node *root = NULL;
    root = insert(root, 50);
    insert(root, 30);
    insert(root, 20);
    insert(root, 40);
    insert(root, 70);
    insert(root, 60);
    insert(root, 80);

    // print inorder traversal of the BST
    inorder(root);

    return 0;
}

Java

// Java program to demonstrate insert operation
// in binary search tree with parent pointer
class GfG {

static class Node
{
    int key;
    Node left, right, parent;
}

// A utility function to create a new BST Node
static Node newNode(int item)
{
    Node temp = new Node();
    temp.key = item;
    temp.left = null;
    temp.right = null;
    temp.parent = null;
    return temp;
}

// A utility function to do inorder traversal of BST
static void inorder(Node root)
{
    if (root != null)
    {
        inorder(root.left);
        System.out.print("Node : "+ root.key + " , ");
        if (root.parent == null)
        System.out.println("Parent : NULL");
        else
        System.out.println("Parent : " + root.parent.key);
        inorder(root.right);
    }
}

/* A utility function to insert a new Node with
given key in BST */
static Node insert(Node node, int key)
{
    /* If the tree is empty, return a new Node */
    if (node == null) return newNode(key);

    /* Otherwise, recur down the tree */
    if (key < node.key)
    {
        Node lchild = insert(node.left, key);
        node.left = lchild;

        // Set parent of root of left subtree
        lchild.parent = node;
    }
    else if (key > node.key)
    {
        Node rchild = insert(node.right, key);
        node.right = rchild;

        // Set parent of root of right subtree
        rchild.parent = node;
    }

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

// Driver Program to test above functions
public static void main(String[] args)
{
    /* Let us create following BST
            50
        /     \
        30     70
        / \ / \
    20 40 60 80 */
    Node root = null;
    root = insert(root, 50);
    insert(root, 30);
    insert(root, 20);
    insert(root, 40);
    insert(root, 70);
    insert(root, 60);
    insert(root, 80);

    // print iNorder traversal of the BST
    inorder(root);
}
}

Python3

# Python3 program to demonstrate insert operation
# in binary search tree with parent pointer

# A utility function to create a new BST Node
class newNode:
    def __init__(self, item):
        self.key = item
        self.left = self.right = None
        self.parent = None

# A utility function to do inorder
# traversal of BST
def inorder(root):
    if root != None:
        inorder(root.left)
        print("Node :", root.key, ", ", end = "")
        if root.parent == None:
            print("Parent : NULL")
        else:
            print("Parent : ", root.parent.key)
        inorder(root.right)

# A utility function to insert a new
# Node with given key in BST
def insert(node, key):

    # If the tree is empty, return a new Node
    if node == None:
        return newNode(key)

    # Otherwise, recur down the tree
    if key < node.key:
        lchild = insert(node.left, key)
        node.left = lchild

        # Set parent of root of left subtree
        lchild.parent = node
    elif key > node.key:
        rchild = insert(node.right, key)
        node.right = rchild

        # Set parent of root of right subtree
        rchild.parent = node

    # return the (unchanged) Node pointer
    return node

# Driver Code
if __name__ == '__main__':

    # Let us create following BST
    #         50
    #     /     \
    #     30     70
    #     / \ / \
    # 20 40 60 80
    root = None
    root = insert(root, 50)
    insert(root, 30)
    insert(root, 20)
    insert(root, 40)
    insert(root, 70)
    insert(root, 60)
    insert(root, 80)

    # print iNorder traversal of the BST
    inorder(root)

# This code is contributed by PranchalK

C#

// C# program to demonstrate insert operation
// in binary search tree with parent pointer
using System;

class GfG
{
    class Node
    {
        public int key;
        public Node left, right, parent;
    }

    // A utility function to create a new BST Node
    static Node newNode(int item)
    {
        Node temp = new Node();
        temp.key = item;
        temp.left = null;
        temp.right = null;
        temp.parent = null;
        return temp;
    }

    // A utility function to do
    // inorder traversal of BST
    static void inorder(Node root)
    {
        if (root != null)
        {
            inorder(root.left);
            Console.Write("Node : "+ root.key + " , ");
            if (root.parent == null)
            Console.WriteLine("Parent : NULL");
            else
            Console.WriteLine("Parent : " +
                                root.parent.key);
            inorder(root.right);
        }
    }

    /* A utility function to insert a new Node with
    given key in BST */
    static Node insert(Node node, int key)
    {
        /* If the tree is empty, return a new Node */
        if (node == null) return newNode(key);

        /* Otherwise, recur down the tree */
        if (key < node.key)
        {
            Node lchild = insert(node.left, key);
            node.left = lchild;

            // Set parent of root of left subtree
            lchild.parent = node;
        }
        else if (key > node.key)
        {
            Node rchild = insert(node.right, key);
            node.right = rchild;

            // Set parent of root of right subtree
            rchild.parent = node;
        }

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

    // Driver code
    public static void Main(String[] args)
    {
        /* Let us create following BST
                50
            / \
            30 70
            / \ / \
        20 40 60 80 */
        Node root = null;
        root = insert(root, 50);
        insert(root, 30);
        insert(root, 20);
        insert(root, 40);
        insert(root, 70);
        insert(root, 60);
        insert(root, 80);

        // print iNorder traversal of the BST
        inorder(root);
    }
}

// This code is contributed 29AjayKumar

Javascript

<script>
// javascript program to demonstrate insert operation
// in binary search tree with parent pointer

     class Node {
            constructor() {
                this.key = 0;
                this.left = null;
                this.right = null;
                this.parent = null;
            }
        }


// A utility function to create a new BST Node
function newNode(item)
{
    var temp = new Node();
    temp.key = item;
    temp.left = null;
    temp.right = null;
    temp.parent = null;
    return temp;
}

// A utility function to do inorder traversal of BST
function inorder(root)
{
    if (root != null)
    {
        inorder(root.left);
        document.write("Node : "+ root.key + " , ");
        if (root.parent == null)
        document.write("Parent : NULL<br/>");
        else
        document.write("Parent : " + root.parent.key+"<br/>");
        inorder(root.right);
    }
}

/* A utility function to insert a new Node with
given key in BST */
function insert(node , key)
{
    /* If the tree is empty, return a new Node */
    if (node == null) return newNode(key);

    /* Otherwise, recur down the tree */
    if (key < node.key)
    {
        var lchild = insert(node.left, key);
        node.left = lchild;

        // Set parent of root of left subtree
        lchild.parent = node;
    }
    else if (key > node.key)
    {
        var rchild = insert(node.right, key);
        node.right = rchild;

        // Set parent of root of right subtree
        rchild.parent = node;
    }

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

// Driver Program to test above functions

    /* Let us create following BST
            50
        /     \
        30     70
        / \ / \
    20 40 60 80 */
    var root = null;
    root = insert(root, 50);
    insert(root, 30);
    insert(root, 20);
    insert(root, 40);
    insert(root, 70);
    insert(root, 60);
    insert(root, 80);

    // print iNorder traversal of the BST
    inorder(root);

// This code contributed by umadevi9616
</script>

Output

Node : 20, Parent : 30 
Node : 30, Parent : 50 
Node : 40, Parent : 30 
Node : 50, Parent : NULL 
Node : 60, Parent : 70 
Node : 70, Parent : 50 
Node : 80, Parent : 70 

Time Complexity: The time complexity of insertion in a binary search tree (BST) depends on the height of the tree. In the worst-case scenario, the height of the tree can be equal to the number of nodes in the tree, which leads to a time complexity of O(n). However, if the tree is balanced, the height is equal to log n, where n is the number of nodes in the tree. Therefore, the time complexity of the insert operation in a balanced BST is O(log n).

Space Complexity: The space complexity of the insert operation in a BST is O(h), where h is the height of the tree. In the worst-case scenario, the height of the tree is equal to the number of nodes in the tree, leading to a space complexity of O(n). However, if the tree is balanced, the height is equal to log n, leading to a space complexity of O(log n).

Exercise:
How to maintain parent pointer during deletion.

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