Inorder Successor in Binary Search Tree

In Binary Tree, Inorder successor of a node is the next node in Inorder traversal of the Binary Tree. Inorder Successor is NULL for the last node in Inorder traversal. 

In Binary Search Tree, Inorder Successor of an input node can also be defined as the node with the smallest key greater than the key of the input node. So, it is sometimes important to find next node in sorted order.

In the above diagram, inorder successor of 8 is 10, inorder successor of 10 is 12 and inorder successor of 14 is 20.

Method 1 (Uses Parent Pointer) 

In this method, we assume that every node has a parent pointer. 
The Algorithm is divided into two cases on the basis of the right subtree of the input node being empty or not.

Input: node, root // node is the node whose Inorder successor is needed. 

Output: succ // succ is Inorder successor of node.

1. If right subtree of node is not NULL, then succ lies in right subtree. Do the following. 
   Go to right subtree and return the node with minimum key value in the right subtree.
2. If right subtree of node is NULL, then succ is one of the ancestors. Do the following. 
   Travel up using the parent pointer until you see a node which is left child of its parent. The parent of such a node is the succ.

Implementation:

Note that the function to find InOrder Successor is highlighted (with gray background) in below code.  

C++

#include <iostream>
using namespace std;

/* A binary tree node has data,
   the pointer to left child
   and a pointer to right child */
struct node {
    int data;
    struct node* left;
    struct node* right;
    struct node* parent;
};

struct node* minValue(struct node* node);

struct node* inOrderSuccessor(
    struct node* root,
    struct node* n)
{
    // step 1 of the above algorithm
    if (n->right != NULL)
        return minValue(n->right);

    // step 2 of the above algorithm
    struct node* p = n->parent;
    while (p != NULL && n == p->right) {
        n = p;
        p = p->parent;
    }
    return p;
}

/* Given a non-empty binary search tree,
    return the minimum data
    value found in that tree. Note that
    the entire tree does not need
    to be searched. */
struct node* minValue(struct node* node)
{
    struct node* current = node;

    /* loop down to find the leftmost leaf */
    while (current->left != NULL) {
        current = current->left;
    }
    return current;
}

/* Helper function that allocates a new
    node with the given data and
    NULL left and right pointers. */
struct node* newNode(int data)
{
    struct node* node = (struct node*)
        malloc(sizeof(
            struct node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    node->parent = NULL;

    return (node);
}

/* Give a binary search tree and
   a number, inserts a new node with
    the given number in the correct
    place in the tree. Returns the new
    root pointer which the caller should
    then use (the standard trick to
    avoid using reference parameters). */
struct node* insert(struct node* node,
                    int data)
{
    /* 1. If the tree is empty, return a new,
      single node */
    if (node == NULL)
        return (newNode(data));
    else {
        struct node* temp;

        /* 2. Otherwise, recur down the tree */
        if (data <= node->data) {
            temp = insert(node->left, data);
            node->left = temp;
            temp->parent = node;
        }
        else {
            temp = insert(node->right, data);
            node->right = temp;
            temp->parent = node;
        }

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

/* Driver program to test above functions*/
int main()
{
    struct node *root = NULL, *temp, *succ, *min;

    // creating the tree given in the above diagram
    root = insert(root, 20);
    root = insert(root, 8);
    root = insert(root, 22);
    root = insert(root, 4);
    root = insert(root, 12);
    root = insert(root, 10);
    root = insert(root, 14);
    temp = root->left->right->right;

    succ = inOrderSuccessor(root, temp);
    if (succ != NULL)
        cout << "\n Inorder Successor of " << temp->data<< " is "<< succ->data;
    else
        cout <<"\n Inorder Successor doesn't exit";

    getchar();
    return 0;
}

// this code is contributed by shivanisinghss2110

C

#include <stdio.h>
#include <stdlib.h>

/* A binary tree node has data,
   the pointer to left child
   and a pointer to right child */
struct node {
    int data;
    struct node* left;
    struct node* right;
    struct node* parent;
};

struct node* minValue(struct node* node);

struct node* inOrderSuccessor(
    struct node* root,
    struct node* n)
{
    // step 1 of the above algorithm
    if (n->right != NULL)
        return minValue(n->right);

    // step 2 of the above algorithm
    struct node* p = n->parent;
    while (p != NULL && n == p->right) {
        n = p;
        p = p->parent;
    }
    return p;
}

/* Given a non-empty binary search tree,
    return the minimum data
    value found in that tree. Note that
    the entire tree does not need
    to be searched. */
struct node* minValue(struct node* node)
{
    struct node* current = node;

    /* loop down to find the leftmost leaf */
    while (current->left != NULL) {
        current = current->left;
    }
    return current;
}

/* Helper function that allocates a new
    node with the given data and
    NULL left and right pointers. */
struct node* newNode(int data)
{
    struct node* node = (struct node*)
        malloc(sizeof(
            struct node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    node->parent = NULL;

    return (node);
}

/* Give a binary search tree and
   a number, inserts a new node with
    the given number in the correct
    place in the tree. Returns the new
    root pointer which the caller should
    then use (the standard trick to
    avoid using reference parameters). */
struct node* insert(struct node* node,
                    int data)
{
    /* 1. If the tree is empty, return a new,
      single node */
    if (node == NULL)
        return (newNode(data));
    else {
        struct node* temp;

        /* 2. Otherwise, recur down the tree */
        if (data <= node->data) {
            temp = insert(node->left, data);
            node->left = temp;
            temp->parent = node;
        }
        else {
            temp = insert(node->right, data);
            node->right = temp;
            temp->parent = node;
        }

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

/* Driver program to test above functions*/
int main()
{
    struct node *root = NULL, *temp, *succ, *min;

    // creating the tree given in the above diagram
    root = insert(root, 20);
    root = insert(root, 8);
    root = insert(root, 22);
    root = insert(root, 4);
    root = insert(root, 12);
    root = insert(root, 10);
    root = insert(root, 14);
    temp = root->left->right->right;

    succ = inOrderSuccessor(root, temp);
    if (succ != NULL)
        printf(
            "\n Inorder Successor of %d is %d ",
            temp->data, succ->data);
    else
        printf("\n Inorder Successor doesn't exit");

    getchar();
    return 0;
}

Java

// Java program to find minimum
// value node in Binary Search Tree

// A binary tree node
class Node {

    int data;
    Node left, right, parent;

    Node(int d)
    {
        data = d;
        left = right = parent = null;
    }
}

class BinaryTree {

    static Node head;

    /* Given a binary search tree and a number,
     inserts a new node with the given number in
     the correct place in the tree. Returns the new
     root pointer which the caller should then use
     (the standard trick to avoid using reference
     parameters). */
    Node insert(Node node, int data)
    {

        /* 1. If the tree is empty, return a new,
         single node */
        if (node == null) {
            return (new Node(data));
        }
        else {

            Node temp = null;

            /* 2. Otherwise, recur down the tree */
            if (data <= node.data) {
                temp = insert(node.left, data);
                node.left = temp;
                temp.parent = node;
            }
            else {
                temp = insert(node.right, data);
                node.right = temp;
                temp.parent = node;
            }

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

    Node inOrderSuccessor(Node root, Node n)
    {

        // step 1 of the above algorithm
        if (n.right != null) {
            return minValue(n.right);
        }

        // step 2 of the above algorithm
        Node p = n.parent;
        while (p != null && n == p.right) {
            n = p;
            p = p.parent;
        }
        return p;
    }

    /* Given a non-empty binary search
       tree, return the minimum data
       value found in that tree. Note that
       the entire tree does not need
       to be searched. */
    Node minValue(Node node)
    {
        Node current = node;

        /* loop down to find the leftmost leaf */
        while (current.left != null) {
            current = current.left;
        }
        return current;
    }

    // Driver program to test above functions
    public static void main(String[] args)
    {
        BinaryTree tree = new BinaryTree();
        Node root = null, temp = null, suc = null, min = null;
        root = tree.insert(root, 20);
        root = tree.insert(root, 8);
        root = tree.insert(root, 22);
        root = tree.insert(root, 4);
        root = tree.insert(root, 12);
        root = tree.insert(root, 10);
        root = tree.insert(root, 14);
        temp = root.left.right.right;
        suc = tree.inOrderSuccessor(root, temp);
        if (suc != null) {
            System.out.println(
                "Inorder successor of "
                + temp.data + " is " + suc.data);
        }
        else {
            System.out.println(
                "Inorder successor does not exist");
        }
    }
}

// This code has been contributed by Mayank Jaiswal

Python3

# Python program to find the inorder successor in a BST

# A binary tree node
class Node:

    # Constructor to create a new node
    def __init__(self, key):
        self.data = key
        self.left = None
        self.right = None

def inOrderSuccessor(n):

    # Step 1 of the above algorithm
    if n.right is not None:
        return minValue(n.right)

    # Step 2 of the above algorithm
    p = n.parent
    while( p is not None):
        if n != p.right :
            break
        n = p
        p = p.parent
    return p

# Given a non-empty binary search tree, return the
# minimum data value found in that tree. Note that the
# entire tree doesn't need to be searched
def minValue(node):
    current = node

    # loop down to find the leftmost leaf
    while(current is not None):
        if current.left is None:
            break
        current = current.left

    return current


# Given a binary search tree and a number, inserts a
# new node with the given number in the correct place
# in the tree. Returns the new root pointer which the
# caller should then use( the standard trick to avoid
# using reference parameters)
def insert( node, data):

    # 1) If tree is empty then return a new singly node
    if node is None:
        return Node(data)
    else:

        # 2) Otherwise, recur down the tree
        if data <= node.data:
            temp = insert(node.left, data)
            node.left = temp
            temp.parent = node
        else:
            temp = insert(node.right, data)
            node.right = temp
            temp.parent = node

        # return  the unchanged node pointer
        return node


# Driver program to test above function

root = None

# Creating the tree given in the above diagram
root = insert(root, 20)
root = insert(root, 8);
root = insert(root, 22);
root = insert(root, 4);
root = insert(root, 12);
root = insert(root, 10);
root = insert(root, 14);
temp = root.left.right.right

succ = inOrderSuccessor(temp)
if succ is not None:
    print ("\nInorder Successor of % d is % d "%(temp.data, succ.data))
else:
    print ("\nInorder Successor doesn't exist")

# This code is contributed by Nikhil Kumar Singh(nickzuck_007)

C#

// C# program to find minimum
// value node in Binary Search Tree
using System;

// A binary tree node
public
  class Node
  {
    public
      int data;
    public
      Node left, right, parent;
    public
      Node(int d)
    {
      data = d;
      left = right = parent = null;
    }
  }

public class BinaryTree
{
  static Node head;

  /* Given a binary search tree and a number,
     inserts a new node with the given number in
     the correct place in the tree. Returns the new
     root pointer which the caller should then use
     (the standard trick to avoid using reference
     parameters). */
  Node insert(Node node, int data)
  {

    /* 1. If the tree is empty, return a new,
         single node */
    if (node == null)
    {
      return (new Node(data));
    }
    else
    {

      Node temp = null;

      /* 2. Otherwise, recur down the tree */
      if (data <= node.data)
      {
        temp = insert(node.left, data);
        node.left = temp;
        temp.parent = node;
      }
      else
      {
        temp = insert(node.right, data);
        node.right = temp;
        temp.parent = node;
      }

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

  Node inOrderSuccessor(Node root, Node n)
  {

    // step 1 of the above algorithm
    if (n.right != null)
    {
      return minValue(n.right);
    }

    // step 2 of the above algorithm
    Node p = n.parent;
    while (p != null && n == p.right)
    {
      n = p;
      p = p.parent;
    }
    return p;
  }

  /* Given a non-empty binary search
       tree, return the minimum data
       value found in that tree. Note that
       the entire tree does not need
       to be searched. */
  Node minValue(Node node)
  {
    Node current = node;

    /* loop down to find the leftmost leaf */
    while (current.left != null)
    {
      current = current.left;
    }
    return current;
  }

  // Driver program to test above functions
  public static void Main(String[] args)
  {
    BinaryTree tree = new BinaryTree();
    Node root = null, temp = null, suc = null, min = null;
    root = tree.insert(root, 20);
    root = tree.insert(root, 8);
    root = tree.insert(root, 22);
    root = tree.insert(root, 4);
    root = tree.insert(root, 12);
    root = tree.insert(root, 10);
    root = tree.insert(root, 14);
    temp = root.left.right.right;
    suc = tree.inOrderSuccessor(root, temp);
    if (suc != null) {
      Console.WriteLine(
        "Inorder successor of "
        + temp.data + " is " + suc.data);
    }
    else {
      Console.WriteLine(
        "Inorder successor does not exist");
    }
  }
}

// This code is contributed by aashish1995

Javascript

<script>

// JavaScript program to find minimum
// value node in Binary Search Tree

// A binary tree node
class Node {
    constructor(val) {
        this.data = val;
        this.left = null;
        this.right = null;
        this.parent = null;
    }
}


    var head;

    /*
     * Given a binary search tree and a number,
     inserts a new node with the given
     * number in the correct place in the tree.
     Returns the new root pointer which
     * the caller should then use
     (the standard trick to afunction using reference
     * parameters).
     */
    function insert(node , data) {

        /*
         * 1. If the tree is empty,
         return a new, single node
         */
        if (node == null) {
            return (new Node(data));
        } else {

            var temp = null;

            /* 2. Otherwise, recur down the tree */
            if (data <= node.data) {
                temp = insert(node.left, data);
                node.left = temp;
                temp.parent = node;
            } else {
                temp = insert(node.right, data);
                node.right = temp;
                temp.parent = node;
            }

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

    function inOrderSuccessor(root,  n) {

        // step 1 of the above algorithm
        if (n.right != null) {
            return minValue(n.right);
        }

        // step 2 of the above algorithm
        var p = n.parent;
        while (p != null && n == p.right) {
            n = p;
            p = p.parent;
        }
        return p;
    }

    /*
     * Given a non-empty binary search tree,
     return the minimum data value found in
     * that tree. Note that the entire tree
     does not need to be searched.
     */
    function minValue(node) {
        var current = node;

        /* loop down to find the leftmost leaf */
        while (current.left != null) {
            current = current.left;
        }
        return current;
    }

    // Driver program to test above functions

        var root = null, temp = null,
        suc = null, min = null;
        root = insert(root, 20);
        root = insert(root, 8);
        root = insert(root, 22);
        root = insert(root, 4);
        root = insert(root, 12);
        root = insert(root, 10);
        root = insert(root, 14);
        temp = root.left.right.right;
        suc = inOrderSuccessor(root, temp);
        if (suc != null) {
            document.write("Inorder successor of " +
            temp.data + " is " + suc.data);
        } else {
            document.write(
            "Inorder successor does not exist"
            );
        }

// This code contributed by gauravrajput1

</script>

Output

 Inorder Successor of 14 is 20

Complexity Analysis:

• Time Complexity:
• O(h), where h is the height of the tree. 
  As in the second case(suppose skewed tree) we have to travel all the way towards the root.
• Auxiliary Space: O(1). 
  Due to no use of any data structure for storing values.

Method 2 (Search from root) 
Parent pointer is NOT needed in this algorithm. The Algorithm is divided into two cases on the basis of right subtree of the input node being empty or not.

Input: node, root // node is the node whose Inorder successor is needed. 

Output: succ // succ is Inorder successor of node.

1. If right subtree of node is not NULL, then succ lies in right subtree. Do the following. 
   Go to right subtree and return the node with minimum key value in the right subtree.
2. If right subtree of node is NULL, then start from the root and use search-like technique. Do the following. 
   Travel down the tree, if a node’s data is greater than root’s data then go right side, otherwise, go to left side.

Below is the implementation of the above approach:

C++

// C++ program for above approach
#include <iostream>
using namespace std;

/* A binary tree node has data,
   the pointer to left child
   and a pointer to right child */
struct node
{
    int data;
    struct node* left;
    struct node* right;
    struct node* parent;
};

struct node* minValue(struct node* node);

struct node* inOrderSuccessor(struct node* root,
                              struct node* n)
{

    // Step 1 of the above algorithm
    if (n->right != NULL)
        return minValue(n->right);

    struct node* succ = NULL;

    // Start from root and search for
    // successor down the tree
    while (root->data != n->data)
    {
        if (n->data < root->data)
        {
            succ = root;
            root = root->left;
        }
        else
            root = root->right;

    }

    return succ;
}

// Given a non-empty binary search tree,
// return the minimum data value found
// in that tree. Note that the entire
// tree does not need to be searched.
struct node* minValue(struct node* node)
{
    struct node* current = node;

    // Loop down to find the leftmost leaf
    while (current->left != NULL)
    {
        current = current->left;
    }
    return current;
}

// Helper function that allocates a new
// node with the given data and NULL left
// and right pointers.
struct node* newNode(int data)
{
    struct node* node = (struct node*)
    malloc(sizeof(struct node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    node->parent = NULL;

    return (node);
}

// Give a binary search tree and a
// number, inserts a new node with
// the given number in the correct
// place in the tree. Returns the new
// root pointer which the caller should
// then use (the standard trick to
// avoid using reference parameters).
struct node* insert(struct node* node,
                    int data)
{

    /* 1. If the tree is empty, return a new,
       single node */
    if (node == NULL)
        return (newNode(data));
    else
    {
        struct node* temp;

        /* 2. Otherwise, recur down the tree */
        if (data <= node->data)
        {
            temp = insert(node->left, data);
            node->left = temp;
            temp->parent = node;
        }
        else
        {
            temp = insert(node->right, data);
            node->right = temp;
            temp->parent = node;
        }

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

// Driver code
int main()
{
    struct node *root = NULL, *temp, *succ, *min;

    // Creating the tree given in the above diagram
    root = insert(root, 20);
    root = insert(root, 8);
    root = insert(root, 22);
    root = insert(root, 4);
    root = insert(root, 12);
    root = insert(root, 10);
    root = insert(root, 14);
    temp = root->left->right->right;

    // Function Call
    succ = inOrderSuccessor(root, temp);
    if (succ != NULL)
        cout << "\n Inorder Successor of "
             << temp->data << " is "<< succ->data;
    else
        cout <<"\n Inorder Successor doesn't exit";

    getchar();
    return 0;
}

// This code is contributed by shivanisinghss2110

C

// C program for above approach
#include <stdio.h>
#include <stdlib.h>

/* A binary tree node has data,
   the pointer to left child
   and a pointer to right child */
struct node
{
    int data;
    struct node* left;
    struct node* right;
    struct node* parent;
};

struct node* minValue(struct node* node);

struct node* inOrderSuccessor(
    struct node* root,
    struct node* n)
{

    // step 1 of the above algorithm
    if (n->right != NULL)
        return minValue(n->right);

    struct node* succ = NULL;

    // Start from root and search for
    // successor down the tree
    while (root != NULL)
    {
        if (n->data < root->data)
        {
            succ = root;
            root = root->left;
        }
        else if (n->data > root->data)
            root = root->right;
        else
            break;
    }

    return succ;
}

/* Given a non-empty binary search tree,
    return the minimum data
    value found in that tree. Note that
    the entire tree does not need
    to be searched. */
struct node* minValue(struct node* node)
{
    struct node* current = node;

    /* loop down to find the leftmost leaf */
    while (current->left != NULL)
    {
        current = current->left;
    }
    return current;
}

/* Helper function that allocates a new
    node with the given data and
    NULL left and right pointers. */
struct node* newNode(int data)
{
    struct node* node = (struct node*)
        malloc(sizeof(
            struct node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    node->parent = NULL;

    return (node);
}

/* Give a binary search tree and
   a number, inserts a new node with
    the given number in the correct
    place in the tree. Returns the new
    root pointer which the caller should
    then use (the standard trick to
    avoid using reference parameters). */
struct node* insert(struct node* node,
                    int data)
{
    /* 1. If the tree is empty, return a new,
      single node */
    if (node == NULL)
        return (newNode(data));
    else
    {
        struct node* temp;

        /* 2. Otherwise, recur down the tree */
        if (data <= node->data)
        {
            temp = insert(node->left, data);
            node->left = temp;
            temp->parent = node;
        }
        else
        {
            temp = insert(node->right, data);
            node->right = temp;
            temp->parent = node;
        }

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

/* Driver program to test above functions*/
int main()
{
    struct node *root = NULL, *temp, *succ, *min;

    // creating the tree given in the above diagram
    root = insert(root, 20);
    root = insert(root, 8);
    root = insert(root, 22);
    root = insert(root, 4);
    root = insert(root, 12);
    root = insert(root, 10);
    root = insert(root, 14);
    temp = root->left->right->right;

    // Function Call
    succ = inOrderSuccessor(root, temp);
    if (succ != NULL)
        printf(
            "\n Inorder Successor of %d is %d ",
            temp->data, succ->data);
    else
        printf("\n Inorder Successor doesn't exit");

    getchar();
    return 0;
}

// Thanks to R.Srinivasan for suggesting this method.

Java

// Java program for above approach
class GFG
{

/* A binary tree node has data,
   the pointer to left child
   and a pointer to right child */
static class node
{
    int data;
    node left;
    node right;
    node parent;
};

static node inOrderSuccessor(
    node root,
    node n)
{

    // step 1 of the above algorithm
    if (n.right != null)
        return minValue(n.right);

    node succ = null;

    // Start from root and search for
    // successor down the tree
    while (root != null)
    {
        if (n.data < root.data)
        {
            succ = root;
            root = root.left;
        }
        else if (n.data > root.data)
            root = root.right;
        else
            break;
    }
    return succ;
}

/* Given a non-empty binary search tree,
    return the minimum data
    value found in that tree. Note that
    the entire tree does not need
    to be searched. */
static node minValue(node node)
{
    node current = node;

    /* loop down to find the leftmost leaf */
    while (current.left != null)
    {
        current = current.left;
    }
    return current;
}

/* Helper function that allocates a new
    node with the given data and
    null left and right pointers. */
static node newNode(int data)
{
    node node = new node();
    node.data = data;
    node.left = null;
    node.right = null;
    node.parent = null;

    return (node);
}

/* Give a binary search tree and
   a number, inserts a new node with
    the given number in the correct
    place in the tree. Returns the new
    root pointer which the caller should
    then use (the standard trick to
    astatic void using reference parameters). */
static  node insert(node node,
                    int data)
{

    /* 1. If the tree is empty, return a new,
      single node */
    if (node == null)
        return (newNode(data));
    else
    {
        node temp;

        /* 2. Otherwise, recur down the tree */
        if (data <= node.data)
        {
            temp = insert(node.left, data);
            node.left = temp;
            temp.parent = node;
        }
        else
        {
            temp = insert(node.right, data);
            node.right = temp;
            temp.parent = node;
        }

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

/* Driver program to test above functions*/
public static void main(String[] args)
{
    node root = null, temp, succ, min;

    // creating the tree given in the above diagram
    root = insert(root, 20);
    root = insert(root, 8);
    root = insert(root, 22);
    root = insert(root, 4);
    root = insert(root, 12);
    root = insert(root, 10);
    root = insert(root, 14);
    temp = root.left.right.right;

    // Function Call
    succ = inOrderSuccessor(root, temp);
    if (succ != null)
        System.out.printf(
            "\n Inorder Successor of %d is %d ",
            temp.data, succ.data);
    else
        System.out.printf("\n Inorder Successor doesn't exit");
}
}

// This code is contributed by gauravrajput1

Python3

# Python program to find
# the inorder successor in a BST

# A binary tree node
class Node:

    # Constructor to create a new node
    def __init__(self, key):
        self.data = key
        self.left = None
        self.right = None

def inOrderSuccessor(root, n):

    # Step 1 of the above algorithm
    if n.right is not None:
        return minValue(n.right)

    # Step 2 of the above algorithm
    succ=Node(None)


    while( root):
        if(root.data<n.data):
            root=root.right
        elif(root.data>n.data):
            succ=root
            root=root.left
        else:
            break
    return succ

# Given a non-empty binary search tree,
# return the minimum data value
# found in that tree. Note that the
# entire tree doesn't need to be searched
def minValue(node):
    current = node

    # loop down to find the leftmost leaf
    while(current is not None):
        if current.left is None:
            break
        current = current.left

    return current


# Given a binary search tree
# and a number, inserts a
# new node with the given
# number in the correct place
# in the tree. Returns the
# new root pointer which the
# caller should then use
# (the standard trick to avoid
# using reference parameters)
def insert( node, data):

    # 1) If tree is empty
    # then return a new singly node
    if node is None:
        return Node(data)
    else:

        # 2) Otherwise, recur down the tree
        if data <= node.data:
            temp = insert(node.left, data)
            node.left = temp
            temp.parent = node
        else:
            temp = insert(node.right, data)
            node.right = temp
            temp.parent = node

        # return  the unchanged node pointer
        return node


# Driver program to test above function
if __name__ == "__main__":
  root = None

  # Creating the tree given in the above diagram
  root = insert(root, 20)
  root = insert(root, 8);
  root = insert(root, 22);
  root = insert(root, 4);
  root = insert(root, 12);
  root = insert(root, 10);
  root = insert(root, 14);
  temp = root.left.right

  succ = inOrderSuccessor( root, temp)
  if succ is not None:
      print("Inorder Successor of" ,
               temp.data ,"is" ,succ.data)
  else:
      print("InInorder Successor doesn't exist")

C#

// C# program for above approach
using System;

public class GFG
{

  /* A binary tree node has data,
   the pointer to left child
   and a pointer to right child */
  public
    class node
    {
      public
        int data;
      public
        node left;
      public
        node right;
      public
        node parent;
    };

  static node inOrderSuccessor(
    node root,
    node n)
  {

    // step 1 of the above algorithm
    if (n.right != null)
      return minValue(n.right);

    node succ = null;

    // Start from root and search for
    // successor down the tree
    while (root != null)
    {
      if (n.data < root.data)
      {
        succ = root;
        root = root.left;
      }
      else if (n.data > root.data)
        root = root.right;
      else
        break;
    }
    return succ;
  }

  /* Given a non-empty binary search tree,
    return the minimum data
    value found in that tree. Note that
    the entire tree does not need
    to be searched. */
  static node minValue(node node)
  {
    node current = node;

    /* loop down to find the leftmost leaf */
    while (current.left != null)
    {
      current = current.left;
    }
    return current;
  }

  /* Helper function that allocates a new
    node with the given data and
    null left and right pointers. */
  static node newNode(int data)
  {
    node node = new node();
    node.data = data;
    node.left = null;
    node.right = null;
    node.parent = null;

    return (node);
  }

  /* Give a binary search tree and
   a number, inserts a new node with
    the given number in the correct
    place in the tree. Returns the new
    root pointer which the caller should
    then use (the standard trick to
    astatic void using reference parameters). */
  static  node insert(node node,
                      int data)
  {

    /* 1. If the tree is empty, return a new,
      single node */
    if (node == null)
      return (newNode(data));
    else
    {
      node temp;

      /* 2. Otherwise, recur down the tree */
      if (data <= node.data)
      {
        temp = insert(node.left, data);
        node.left = temp;
        temp.parent = node;
      }
      else
      {
        temp = insert(node.right, data);
        node.right = temp;
        temp.parent = node;
      }

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

  /* Driver program to test above functions*/
  public static void Main(String[] args)
  {
    node root = null, temp, succ;

    // creating the tree given in the above diagram
    root = insert(root, 20);
    root = insert(root, 8);
    root = insert(root, 22);
    root = insert(root, 4);
    root = insert(root, 12);
    root = insert(root, 10);
    root = insert(root, 14);
    temp = root.left.right.right;

    // Function Call
    succ = inOrderSuccessor(root, temp);
    if (succ != null)
      Console.Write(
      "\n Inorder Successor of {0} is {1} ",
      temp.data, succ.data);
    else
      Console.Write("\n Inorder Successor doesn't exit");
  }
}

// This code is contributed by gauravrajput1

Javascript

<script>

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

function inOrderSuccessor(root,n)
{
    // step 1 of the above algorithm
    if (n.right != null)
        return minValue(n.right);

    let succ = null;

    // Start from root and search for
    // successor down the tree
    while (root != null)
    {
        if (n.data < root.data)
        {
            succ = root;
            root = root.left;
        }
        else if (n.data > root.data)
            root = root.right;
        else
            break;
    }
    return succ;
}

function minValue(node)
{
    let current = node;

    /* loop down to find the leftmost leaf */
    while (current.left != null)
    {
        current = current.left;
    }
    return current;
}


function insert(node,data)
{
    /* 1. If the tree is empty, return a new,
      single node */
    if (node == null)
        return (new Node(data));
    else
    {
        let temp;

        /* 2. Otherwise, recur down the tree */
        if (data <= node.data)
        {
            temp = insert(node.left, data);
            node.left = temp;
            temp.parent = node;
        }
        else
        {
            temp = insert(node.right, data);
            node.right = temp;
            temp.parent = node;
        }

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

let root = null, temp, succ, min;

// creating the tree given in the above diagram
root = insert(root, 20);
root = insert(root, 8);
root = insert(root, 22);
root = insert(root, 4);
root = insert(root, 12);
root = insert(root, 10);
root = insert(root, 14);
temp = root.left.right.right;

// Function Call
succ = inOrderSuccessor(root, temp);
if (succ != null)
    document.write(
"<br> Inorder Successor of "+temp.data+"  is "+
 succ.data);
else
    document.write("<br> Inorder Successor doesn't exit");

// This code is contributed by unknown2108

</script>

Output

 Inorder Successor of 14 is 20

Complexity Analysis:

• Time Complexity: O(h), where h is the height of the tree. 
  In the worst case as explained above we travel the whole height of the tree
• Auxiliary Space: O(1). 
  Due to no use of any data structure for storing values.

Method 3 (Inorder traversal) An inorder transversal of BST produces a sorted sequence. Therefore, we perform an inorder traversal. The first encountered node with value greater than the node is the inorder successor. 

Input: node, root // node is the node whose ignorer successor is needed.

Output: succ // succ is Inorder successor of node.

Below is the implementation of the above approach:

C++

// C++ program for above approach
#include <iostream>
using namespace std;

/* A binary tree node has data,
   the pointer to left child
   and a pointer to right child */
struct node
{
    int data;
    struct node* left;
    struct node* right;
    struct node* parent;
};
struct node* newNode(int data);

void inOrderTraversal(struct node* root,
                              struct node* n,
                              struct node* succ)
{
    if(root==nullptr) { return; }

    inOrderTraversal(root->left, n, succ);
    if(root->data>n->data && !succ->left) { succ->left = root; return; }
    inOrderTraversal(root->right, n, succ);
}

struct node* inOrderSuccessor(struct node* root,
                              struct node* n)
{
    struct node* succ = newNode(0);
    inOrderTraversal(root, n, succ);
    return succ->left;
}

// Helper function that allocates a new
// node with the given data and NULL left
// and right pointers.
struct node* newNode(int data)
{
    struct node* node = (struct node*)
    malloc(sizeof(struct node));
    node->data = data;
    node->left = NULL;
    node->right = NULL;
    node->parent = NULL;

    return (node);
}

// Give a binary search tree and a
// number, inserts a new node with
// the given number in the correct
// place in the tree. Returns the new
// root pointer which the caller should
// then use (the standard trick to
// avoid using reference parameters).
struct node* insert(struct node* node,
                    int data)
{

    /* 1. If the tree is empty, return a new,
       single node */
    if (node == NULL)
        return (newNode(data));
    else
    {
        struct node* temp;

        /* 2. Otherwise, recur down the tree */
        if (data <= node->data)
        {
            temp = insert(node->left, data);
            node->left = temp;
            temp->parent = node;
        }
        else
        {
            temp = insert(node->right, data);
            node->right = temp;
            temp->parent = node;
        }

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

// Driver code
int main()
{
    struct node *root = NULL, *temp, *succ, *min;

    // Creating the tree given in the above diagram
    root = insert(root, 20);
    root = insert(root, 8);
    root = insert(root, 22);
    root = insert(root, 4);
    root = insert(root, 12);
    root = insert(root, 10);
    root = insert(root, 14);
    temp = root->left->right->right;

    // Function Call
    succ = inOrderSuccessor(root, temp);
    if (succ != NULL)
        cout << "\n Inorder Successor of "
             << temp->data << " is "<< succ->data;
    else
        cout <<"\n Inorder Successor doesn't exist";

    //getchar();
    return 0;
}

// This code is contributed by jaisw7

Java

// Java program for above approach
import java.util.*;

class GFG {

  /*
     * A binary tree node has data, the pointer to left child and a pointer to right
     * child
     */
  static class node {
    int data;
    node left;
    node right;
    node parent;
  };
  static void inOrderTraversal(node root) {
    if (root == null) {
      return;
    }

    inOrderTraversal(root.left);
    System.out.print(root.data);
    inOrderTraversal(root.right);
  }
  static void inOrderTraversal(node root, node n, node succ) {
    if (root == null) {
      return;
    }

    inOrderTraversal(root.left, n, succ);
    if (root.data > n.data && succ.left == null) {
      succ.left = root;
      return;
    }
    inOrderTraversal(root.right, n, succ);
  }

  static node inOrderSuccessor(node root, node n) {
    node succ = newNode(0);
    inOrderTraversal(root, n, succ);
    return succ.left;
  }

  // Helper function that allocates a new
  // node with the given data and null left
  // and right pointers.
  static node newNode(int data) {
    node node = new node();

    node.data = data;
    node.left = null;
    node.right = null;
    node.parent = null;

    return (node);
  }

  // Give a binary search tree and a
  // number, inserts a new node with
  // the given number in the correct
  // place in the tree. Returns the new
  // root pointer which the caller should
  // then use (the standard trick to
  // astatic void using reference parameters).
  static node insert(node node, int data) {

    /*
         * 1. If the tree is empty, return a new, single node
         */
    if (node == null)
      return (newNode(data));
    else {
      node temp;

      /* 2. Otherwise, recur down the tree */
      if (data <= node.data) {
        temp = insert(node.left, data);
        node.left = temp;
        temp.parent = node;
      } else {
        temp = insert(node.right, data);
        node.right = temp;
        temp.parent = node;
      }

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

  // Driver code
  public static void main(String[] args) {
    node root = null, temp, succ, min;

    // Creating the tree given in the above diagram
    root = insert(root, 20);
    root = insert(root, 8);
    root = insert(root, 22);
    root = insert(root, 4);
    root = insert(root, 12);
    root = insert(root, 10);
    root = insert(root, 14);
    temp = root.left.right.right;

    // Function Call
    succ = inOrderSuccessor(root, temp);
    if (succ != null)
      System.out.print("\n Inorder Successor of " + temp.data + " is " + succ.data);
    else
      System.out.print("\n Inorder Successor doesn't exist");

  }
}

// This code is contributed by Rajput-Ji

Python3

# Python program for above approach

''' A binary tree node has data,
   the pointer to left child
   and a pointer to right child '''
class Node :
    def __init__(self,data):
        self.data = data
        self.left = None
        self.right = None
        self.parent = None

def inOrderTraversal(root, n, succ):
    if(root == None): return
    inOrderTraversal(root.left, n, succ)
    if(root.data > n.data and not succ.left):
        succ.left = root
        return
    inOrderTraversal(root.right, n, succ)

def inOrderSuccessor(root, n):
    succ = Node(0)
    inOrderTraversal(root, n, succ)
    return succ.left

# Give a binary search tree and a
# number, inserts a new node with
# the given number in the correct
# place in the tree. Returns the new
# root pointer which the caller should
# then use (the standard trick to
# avoid using reference parameters).
def insert(node, data):
    #  1. If the tree is empty, return a new,
    #    single node
    if (node == None):
        return Node(data)
    else:
    #  2. Otherwise, recur down the tree
        if (data <= node.data):
            temp = insert(node.left, data)
            node.left = temp
            temp.parent = node
        else:
            temp = insert(node.right, data)
            node.right = temp
            temp.parent = node

        # Return the (unchanged) node pointer
        return node

# Driver code
root = None

# Creating the tree given in the above diagram
root = insert(root, 20)
root = insert(root, 8)
root = insert(root, 22)
root = insert(root, 4)
root = insert(root, 12)
root = insert(root, 10)
root = insert(root, 14)
temp = root.left.right.right

# Function Call
succ = inOrderSuccessor(root, temp)
if (succ != None): print("Inorder Successor of",temp.data,"is",succ.data)
else: print("Inorder Successor doesn't exist")

C#

// C# program for above approach
using System;
using System.Collections.Generic;

public class GFG {

  /*
     * A binary tree node has data, the pointer to left child and a pointer to right
     * child
     */
 public  class node {
   public  int data;
   public  node left;
   public  node right;
   public  node parent;
  };
  static void inOrderTraversal(node root) {
    if (root == null) {
      return;
    }

    inOrderTraversal(root.left);
    Console.Write(root.data);
    inOrderTraversal(root.right);
  }
  static void inOrderTraversal(node root, node n, node succ) {
    if (root == null) {
      return;
    }

    inOrderTraversal(root.left, n, succ);
    if (root.data > n.data && succ.left == null) {
      succ.left = root;
      return;
    }
    inOrderTraversal(root.right, n, succ);
  }

  static node inOrderSuccessor(node root, node n) {
    node succ = newNode(0);
    inOrderTraversal(root, n, succ);
    return succ.left;
  }

  // Helper function that allocates a new
  // node with the given data and null left
  // and right pointers.
  static node newNode(int data) {
    node node = new node();

    node.data = data;
    node.left = null;
    node.right = null;
    node.parent = null;

    return (node);
  }

  // Give a binary search tree and a
  // number, inserts a new node with
  // the given number in the correct
  // place in the tree. Returns the new
  // root pointer which the caller should
  // then use (the standard trick to
  // astatic void using reference parameters).
  static node insert(node node, int data) {

    /*
         * 1. If the tree is empty, return a new, single node
         */
    if (node == null)
      return (newNode(data));
    else {
      node temp;

      /* 2. Otherwise, recur down the tree */
      if (data <= node.data) {
        temp = insert(node.left, data);
        node.left = temp;
        temp.parent = node;
      } else {
        temp = insert(node.right, data);
        node.right = temp;
        temp.parent = node;
      }

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

  // Driver code
  public static void Main(String[] args) {
    node root = null, temp, succ, min;

    // Creating the tree given in the above diagram
    root = insert(root, 20);
    root = insert(root, 8);
    root = insert(root, 22);
    root = insert(root, 4);
    root = insert(root, 12);
    root = insert(root, 10);
    root = insert(root, 14);
    temp = root.left.right.right;

    // Function Call
    succ = inOrderSuccessor(root, temp);
    if (succ != null)
      Console.Write("\n Inorder Successor of " + temp.data + " is " + succ.data);
    else
      Console.Write("\n Inorder Successor doesn't exist");

  }
}

// This code contributed by Rajput-Ji

Javascript

<script>
// javascript program for above approach

    /*
     * A binary tree node has data, the pointer to left child and a pointer to right
     * child
     */
     class Node {
         constructor(){
        this.data = 0;
        this.left = null;
        this.right = null;
        this.parent = null;
    }
    }

    function inOrderTraversal( root) {
        if (root == null) {
            return;
        }

        inOrderTraversal(root.left);
        document.write(root.data);
        inOrderTraversal(root.right);
    }

    function inOrderTraversal( root,  n,  succ) {
        if (root == null) {
            return;
        }

        inOrderTraversal(root.left, n, succ);
        if (root.data > n.data && succ.left == null) {
            succ.left = root;
            return;
        }
        inOrderTraversal(root.right, n, succ);
    }

     function inOrderSuccessor( root,  n) {
        var succ = newNode(0);
        inOrderTraversal(root, n, succ);
        return succ.left;
    }

    // Helper function that allocates a new
    // node with the given data and null left
    // and right pointers.
     function newNode(data) {
        var node = new Node();

        node.data = data;
        node.left = null;
        node.right = null;
        node.parent = null;

        return (node);
    }

    // Give a binary search tree and a
    // number, inserts a new node with
    // the given number in the correct
    // place in the tree. Returns the new
    // root pointer which the caller should
    // then use (the standard trick to
    // afunction using reference parameters).
     function insert( node , data) {

        /*
         * 1. If the tree is empty, return a new, single node
         */
        if (node == null)
            return (newNode(data));
        else {
            var temp;

            /* 2. Otherwise, recur down the tree */
            if (data <= node.data) {
                temp = insert(node.left, data);
                node.left = temp;
                temp.parent = node;
            } else {
                temp = insert(node.right, data);
                node.right = temp;
                temp.parent = node;
            }

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

    // Driver code

        var root = null, temp, succ, min;

        // Creating the tree given in the above diagram
        root = insert(root, 20);
        root = insert(root, 8);
        root = insert(root, 22);
        root = insert(root, 4);
        root = insert(root, 12);
        root = insert(root, 10);
        root = insert(root, 14);
        temp = root.left.right.right;

        // Function Call
        succ = inOrderSuccessor(root, temp);
        if (succ != null)
            document.write("\n Inorder Successor of " + temp.data +
            " is " + succ.data);
        else
            document.write("\n Inorder Successor doesn't exist");

// This code contributed by Rajput-Ji
</script>

Output

 Inorder Successor of 14 is 20

Complexity Analysis:

• Time Complexity: O(h), where h is the height of the tree. In the worst case as explained above we travel the whole height of the tree.
• Auxiliary Space: O(h) because of the recursion stack.

Method 4 (Inorder traversal iterative) this method is inspired from the method 3 but with iterative and easy to understand approach.

Input: node, root // node is the node whose inorder successor is needed.
Output: succ // succ is Inorder successor of node.

Below is the implementation of the above approach:

C++

// C++ program for above approach

#include <bits/stdc++.h>
using namespace std;
/*
 * A binary tree node has data, the pointer to left child
 * and a pointer to right child
 */
struct node {
  int data;
  struct node* left;
  struct node* right;
  struct node* parent;
};
struct node* newNode(int data);

void inOrderTraversal(struct node* root)
{
  if (root == NULL) {
    return;
  }
  inOrderTraversal(root->left);
  cout << root->data;
  inOrderTraversal(root->right);
}

struct node* inOrderSuccessor(struct node* root, int key)
{
  stack<node*> _stack;
  while (root != NULL || !_stack.empty()) {
    while (root != NULL) {
      _stack.push(root);
      root = root->left;
    }
    root = _stack.top();
    _stack.pop();
    if (root->data > key)
      return root;
    root = root->right;
  }
  return NULL;
}

// Helper function that allocates a new
// node with the given data and NULL left
// and right pointers.
struct node* newNode(int data)
{
  struct node* node
    = (struct node*)malloc(sizeof(struct node));
  node->data = data;
  node->left = NULL;
  node->right = NULL;
  node->parent = NULL;

  return (node);
}

// Give a binary search tree and a
// number, inserts a new node with
// the given number in the correct
// place in the tree. Returns the new
// root pointer which the caller should
// then use (the standard trick to
// avoid using reference parameters).
struct node* insert(struct node* node, int data)
{

  /* 1. If the tree is empty, return a new,
       single node */
  if (node == NULL)
    return (newNode(data));
  else {
    struct node* temp;

    /* 2. Otherwise, recur down the tree */
    if (data <= node->data) {
      temp = insert(node->left, data);
      node->left = temp;
      temp->parent = node;
    }
    else {
      temp = insert(node->right, data);
      node->right = temp;
      temp->parent = node;
    }

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

// Driver code
int main()
{
  struct node *root = NULL, *temp, *succ, *min;

  // Creating the tree given in the above diagram
  root = insert(root, 20);
  root = insert(root, 8);
  root = insert(root, 22);
  root = insert(root, 4);
  root = insert(root, 12);
  root = insert(root, 10);
  root = insert(root, 14);
  temp = root->left->right->right;

  // Function Call
  succ = inOrderSuccessor(root, temp->data);
  if (succ != NULL)
    cout << "\n Inorder Successor of " << temp->data
    << " is " << succ->data;
  else
    cout << "\n Inorder Successor doesn't exist";

  return 0;
}

// This code is contributed by Abhijeet Kumar(abhijeet19403)

Java

// Java program for above approach
import java.util.*;

class GFG {

    /*
     * A binary tree node has data, the pointer to left
     * child and a pointer to right child
     */
    static class node {
        int data;
        node left;
        node right;
        node parent;
    };
    static void inOrderTraversal(node root)
    {
        if (root == null) {
            return;
        }

        inOrderTraversal(root.left);
        System.out.print(root.data);
        inOrderTraversal(root.right);
    }

    public static node inOrderSuccessor(node root, int key)
    {
        Deque<node> stack = new ArrayDeque<>();
        while (root != null || !stack.isEmpty()) {
            while (root != null) {
                stack.push(root);
                root = root.left;
            }
            root = stack.pop();
            if (root.data > key)
                return root;
            root = root.right;
        }
        return null;
    }

    // Helper function that allocates a new
    // node with the given data and null left
    // and right pointers.
    static node newNode(int data)
    {
        node node = new node();

        node.data = data;
        node.left = null;
        node.right = null;
        node.parent = null;

        return (node);
    }

    // Give a binary search tree and a
    // number, inserts a new node with
    // the given number in the correct
    // place in the tree. Returns the new
    // root pointer which the caller should
    // then use (the standard trick to
    // astatic void using reference parameters).
    static node insert(node node, int data)
    {

        /*
         * 1. If the tree is empty, return a new, single
         * node
         */
        if (node == null)
            return (newNode(data));
        else {
            node temp;

            /* 2. Otherwise, recur down the tree */
            if (data <= node.data) {
                temp = insert(node.left, data);
                node.left = temp;
                temp.parent = node;
            }
            else {
                temp = insert(node.right, data);
                node.right = temp;
                temp.parent = node;
            }

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

    // Driver code
    public static void main(String[] args)
    {
        node root = null, temp, succ, min;

        // Creating the tree given in the above diagram
        root = insert(root, 20);
        root = insert(root, 8);
        root = insert(root, 22);
        root = insert(root, 4);
        root = insert(root, 12);
        root = insert(root, 10);
        root = insert(root, 14);
        temp = root.left.right.right;

        // Function Call
        succ = inOrderSuccessor(root, temp.data);
        if (succ != null)
            System.out.print("\n Inorder Successor of "
                             + temp.data + " is "
                             + succ.data);
        else
            System.out.print(
                "\n Inorder Successor doesn't exist");
    }
}

// This code is contributed by Nitin Dhamija

Python3

# Python program for above approach

# A binary tree node has data, the pointer to left
# child and a pointer to right child

class Node:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None
        self.parent = None

def inOrderTraversal(root):
    if not root:
        return
    inOrderTraversal(root.left)
    print(root.data, end=' ')
    inOrderTraversal(root.right)

def inOrderSuccessor(root, key):
    _stack = []
    while root or _stack:
        while root:
            _stack.append(root)
            root = root.left
        root = _stack.pop()
        if root.data > key:
            return root
        root = root.right
    return None

    # Helper function that allocates a new
    # node with the given data and null left
    # and right pointers.
def newNode(data):
    return Node(data)

    # Give a binary search tree and a
    # number, inserts a new node with
    # the given number in the correct
    # place in the tree. Returns the new
    # root pointer which the caller should
    # then use (the standard trick to
    # astatic void using reference parameters).


def insert(node, data):
    if not node:
        return newNode(data)
    else:
        if data <= node.data:
            temp = insert(node.left, data)
            node.left = temp
            temp.parent = node
        else:
            temp = insert(node.right, data)
            node.right = temp
            temp.parent = node
        return node

if __name__ == "__main__":
    root = None
    root = insert(root, 20)
    root = insert(root, 8)
    root = insert(root, 22)
    root = insert(root, 4)
    root = insert(root, 12)
    root = insert(root, 10)
    root = insert(root, 14)
    temp = root.left.right.right
    succ = inOrderSuccessor(root, temp.data)
    if succ:
        print("\n Inorder Successor of",temp.data,"is",succ.data)
    else:
        print("\n Inorder Successor doesn't exist")

C#

// C# implementation of the approach
using System;
using System.Collections;
using System.Collections.Generic;

class GFG {

    /*
     * A binary tree node has data, the pointer to left
     * child and a pointer to right child
     */
    public class node {
        public int data;
        public node left;
        public node right;
        public node parent;
    };
    static void inOrderTraversal(node root)
    {
        if (root == null) {
            return;
        }

        inOrderTraversal(root.left);
        Console.Write(root.data);
        inOrderTraversal(root.right);
    }

    public static node inOrderSuccessor(node root, int key)
    {
        Stack<node> stack = new Stack<node>();
        while (root != null || stack.Count != 0) {
            while (root != null) {
                stack.Push(root);
                root = root.left;
            }
            root = stack.Pop();
            if (root.data > key)
                return root;
            root = root.right;
        }
        return null;
    }

    // Helper function that allocates a new
    // node with the given data and null left
    // and right pointers.
    static node newNode(int data)
    {
        node node = new node();

        node.data = data;
        node.left = null;
        node.right = null;
        node.parent = null;

        return (node);
    }

    // Give a binary search tree and a
    // number, inserts a new node with
    // the given number in the correct
    // place in the tree. Returns the new
    // root pointer which the caller should
    // then use (the standard trick to
    // astatic void using reference parameters).
    static node insert(node node, int data)
    {

        /*
         * 1. If the tree is empty, return a new, single
         * node
         */
        if (node == null)
            return (newNode(data));
        else {
            node temp;

            /* 2. Otherwise, recur down the tree */
            if (data <= node.data) {
                temp = insert(node.left, data);
                node.left = temp;
                temp.parent = node;
            }
            else {
                temp = insert(node.right, data);
                node.right = temp;
                temp.parent = node;
            }

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

    // Driver code
    public static void Main(string[] args)
    {
        node root = null, temp, succ, min;

        // Creating the tree given in the above diagram
        root = insert(root, 20);
        root = insert(root, 8);
        root = insert(root, 22);
        root = insert(root, 4);
        root = insert(root, 12);
        root = insert(root, 10);
        root = insert(root, 14);
        temp = root.left.right.right;

        // Function Call
        succ = inOrderSuccessor(root, temp.data);
        if (succ != null)
            Console.Write("\n Inorder Successor of "
                          + temp.data + " is " + succ.data);
        else
            Console.Write(
                "\n Inorder Successor doesn't exist");
    }
}

// This code is contributed by karandeep1234

Javascript

// Javascript program for above approach

/*
 * A binary tree node has data, the pointer to left child
 * and a pointer to right child
 */
class Node {
         constructor(){
        this.data = 0;
        this.left = null;
        this.right = null;
        this.parent = null;
    }
    }

function inOrderTraversal( root) {
        if (root == null) {
            return;
        }

        inOrderTraversal(root.left);
        document.write(root.data);
        inOrderTraversal(root.right);
    }

function inOrderSuccessor( root,  key)
{
  let _stack=[];
  while (root != null || _stack.length!=0) {
    while (root != null) {
      _stack.push(root);
      root = root.left;
    }
    root = _stack[_stack.length-1];
    _stack.pop();
    if (root.data > key.data)
      return root;
    root = root.right;
  }
  return null;
}

// Helper function that allocates a new
// node with the given data and NULL left
// and right pointers.
function newNode(data) {
        var node = new Node();

        node.data = data;
        node.left = null;
        node.right = null;
        node.parent = null;

        return (node);
    }

// Give a binary search tree and a
// number, inserts a new node with
// the given number in the correct
// place in the tree. Returns the new
// root pointer which the caller should
// then use (the standard trick to
// avoid using reference parameters).
function insert( node,  data)
{
  /* 1. If the tree is empty, return a new,
       single node */
  if (node == null)
    return (newNode(data));
  else {
    let temp;

    /* 2. Otherwise, recur down the tree */
    if (data <= node.data) {
      temp = insert(node.left, data);
      node.left = temp;
      temp.parent = node;
    }
    else {
      temp = insert(node.right, data);
      node.right = temp;
      temp.parent = node;
    }

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

// Driver code

        var root = null, temp, succ, min;

        // Creating the tree given in the above diagram
        root = insert(root, 20);
        root = insert(root, 8);
        root = insert(root, 22);
        root = insert(root, 4);
        root = insert(root, 12);
        root = insert(root, 10);
        root = insert(root, 14);
        temp = root.left.right.right;
        console.log(temp.data);

        // Function Call
        succ = inOrderSuccessor(root, temp);
        if (succ != null)
            console.log("\n Inorder Successor of " + temp.data +
            " is " + succ.data);
        else
            console.log("\n Inorder Successor doesn't exist");

            // This code is contributed by garg28harsh.

Output

 Inorder Successor of 14 is 20

Complexity Analysis:

• Time Complexity: O(h), where h is the height of the tree. In the worst case as explained above we travel the whole height of the tree
• Auxiliary Space: O(1). Due to no use of any data structure for storing values.