Second largest element in BST

Given a Binary Search Tree(BST), find the second largest element. 
Examples:

Input: Root of below BST
    10
   /
  5

Output:  5


Input: Root of below BST
        10
      /   \
    5      20
             \ 
              30 

Output:  20

Source: Microsoft Interview

The idea is similar to below post. 
K’th Largest Element in BST when modification to BST is not allowed
The second largest element is second last element in inorder traversal and second element in reverse inorder traversal. We traverse given Binary Search Tree in reverse inorder and keep track of counts of nodes visited. Once the count becomes 2, we print the node.
Below is the implementation of above idea. 

C++

// C++ program to find 2nd largest element in BST
#include<bits/stdc++.h>
using namespace std;

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

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

// A function to find 2nd largest element in a given tree.
void secondLargestUtil(Node *root, int &c)
{
    // Base cases, the second condition is important to
    // avoid unnecessary recursive calls
    if (root == NULL || c >= 2)
        return;

    // Follow reverse inorder traversal so that the
    // largest element is visited first
    secondLargestUtil(root->right, c);

    // Increment count of visited nodes
    c++;

    // If c becomes k now, then this is the 2nd largest
    if (c == 2)
    {
        cout << "2nd largest element is "
             << root->key << endl;
        return;
    }

    // Recur for left subtree
    secondLargestUtil(root->left, c);
}

// Function to find 2nd largest element
void secondLargest(Node *root)
{
    // Initialize count of nodes visited as 0
    int c = 0;

    // Note that c is passed by reference
    secondLargestUtil(root, c);
}

/* A utility function to insert a new node with given key in BST */
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->left  = insert(node->left, key);
    else if (key > node->key)
        node->right = insert(node->right, key);

    /* 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 */
    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);

    secondLargest(root);

    return 0;
}

Java

// Java code to find second largest element in BST

// A binary tree node
class Node {

    int data;
    Node left, right;

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

class BinarySearchTree {

    // Root of BST
    Node root;

    // Constructor
    BinarySearchTree()
    {
        root = null;
    }

    // function to insert new nodes
    public void insert(int data)
    {
        this.root = this.insertRec(this.root, data);
    }

    /* A utility function to insert a new node with given
    key in BST */
    Node insertRec(Node node, int data)
    {
        /* If the tree is empty, return a new node */
        if (node == null) {
            this.root = new Node(data);
            return this.root;
        }

        /* Otherwise, recur down the tree */
        if (data < node.data) {
            node.left = this.insertRec(node.left, data);
        } else {
            node.right = this.insertRec(node.right, data);
        }
        return node;
    }

    // class that stores the value of count
    public class count {
        int c = 0;
    }

    // Function to find 2nd largest element
    void secondLargestUtil(Node node, count C)
    {
        // Base cases, the second condition is important to
        // avoid unnecessary recursive calls
        if (node == null || C.c >= 2)
            return;

        // Follow reverse inorder traversal so that the
        // largest element is visited first
        this.secondLargestUtil(node.right, C);

         // Increment count of visited nodes
        C.c++;

        // If c becomes k now, then this is the 2nd largest
        if (C.c == 2) {
            System.out.print("2nd largest element is "+
                                              node.data);
            return;
        }

         // Recur for left subtree
        this.secondLargestUtil(node.left, C);
    }

    // Function to find 2nd largest element
    void secondLargest(Node node)
    {
        // object of class count
        count C = new count();
        this.secondLargestUtil(this.root, C);
    }

    // Driver function
    public static void main(String[] args)
    {
        BinarySearchTree tree = new BinarySearchTree();

        /* Let us create following BST
              50
           /     \
          30      70
         /  \    /  \
       20   40  60   80 */

        tree.insert(50);
        tree.insert(30);
        tree.insert(20);
        tree.insert(40);
        tree.insert(70);
        tree.insert(60);
        tree.insert(80);

        tree.secondLargest(tree.root);
    }
}

// This code is contributed by Kamal Rawal

Python3

# Python3 code to find second largest
# element in BST
class Node:

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

# A function to find 2nd largest
# element in a given tree.
def secondLargestUtil(root, c):

    # Base cases, the second condition
    # is important to avoid unnecessary
    # recursive calls
    if root == None or c[0] >= 2:
        return

    # Follow reverse inorder traversal so that
    # the largest element is visited first
    secondLargestUtil(root.right, c)

    # Increment count of visited nodes
    c[0] += 1

    # If c becomes k now, then this is
    # the 2nd largest
    if c[0] == 2:
        print("2nd largest element is",
                              root.key)
        return

    # Recur for left subtree
    secondLargestUtil(root.left, c)

# Function to find 2nd largest element
def secondLargest(root):

    # Initialize count of nodes
    # visited as 0
    c = [0]

    # Note that c is passed by reference
    secondLargestUtil(root, c)

# 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 Node(key)

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

    # 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)

    secondLargest(root)

# This code is contributed by PranchalK

C#

using System;

// C# code to find second largest element in BST

// A binary tree node
public class Node
{

    public int data;
    public Node left, right;

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

public class BinarySearchTree
{

    // Root of BST
    public Node root;

    // Constructor
  public BinarySearchTree()
    {
        root = null;
    }

    // function to insert new nodes
    public virtual void insert(int data)
    {
        this.root = this.insertRec(this.root, data);
    }

    /* A utility function to insert a new node with given
    key in BST */
    public virtual Node insertRec(Node node, int data)
    {
        /* If the tree is empty, return a new node */
        if (node == null)
        {
            this.root = new Node(data);
            return this.root;
        }

        /* Otherwise, recur down the tree */
        if (data < node.data)
        {
            node.left = this.insertRec(node.left, data);
        }
        else
        {
            node.right = this.insertRec(node.right, data);
        }
        return node;
    }

    // class that stores the value of count
    public class count
    {
        private readonly BinarySearchTree outerInstance;

        public count(BinarySearchTree outerInstance)
        {
            this.outerInstance = outerInstance;
        }

        public int c = 0;
    }

    // Function to find 2nd largest element
    public virtual void secondLargestUtil(Node node, count C)
    {
        // Base cases, the second condition is important to
        // avoid unnecessary recursive calls
        if (node == null || C.c >= 2)
        {
            return;
        }

        // Follow reverse inorder traversal so that the
        // largest element is visited first
        this.secondLargestUtil(node.right, C);

         // Increment count of visited nodes
        C.c++;

        // If c becomes k now, then this is the 2nd largest
        if (C.c == 2)
        {
            Console.Write("2nd largest element is " + node.data);
            return;
        }

         // Recur for left subtree
        this.secondLargestUtil(node.left, C);
    }

    // Function to find 2nd largest element
    public virtual void secondLargest(Node node)
    {
        // object of class count
        count C = new count(this);
        this.secondLargestUtil(this.root, C);
    }

    // Driver function
    public static void Main(string[] args)
    {
        BinarySearchTree tree = new BinarySearchTree();

        /* Let us create following BST
              50
           /     \
          30      70
         /  \    /  \
       20   40  60   80 */

        tree.insert(50);
        tree.insert(30);
        tree.insert(20);
        tree.insert(40);
        tree.insert(70);
        tree.insert(60);
        tree.insert(80);

        tree.secondLargest(tree.root);
    }
}

  // This code is contributed by Shrikant13

Javascript

<script>

// JavaScript code to find second largest
// element in BST

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



    // Root of BST
    var root = null;



    // function to insert new nodes
     function insert(data)
    {
        this.root = this.insertRec(this.root, data);
    }

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

        /* Otherwise, recur down the tree */
        if (data < node.data) {
            node.left = this.insertRec(node.left, data);
        } else {
            node.right = this.insertRec(node.right, data);
        }
        return node;
    }

    // class that stores the value of count
     class count {
     constructor(){
        this.c = 0;
        }
    }

    // Function to find 2nd largest element
    function secondLargestUtil(node,  C)
    {
        // Base cases, the second condition is important to
        // avoid unnecessary recursive calls
        if (node == null || C.c >= 2)
            return;

        // Follow reverse inorder traversal so that the
        // largest element is visited first
        this.secondLargestUtil(node.right, C);

         // Increment count of visited nodes
        C.c++;

        // If c becomes k now, then this is the 2nd largest
        if (C.c == 2) {
            document.write("2nd largest element is "+
                                              node.data);
            return;
        }

         // Recur for left subtree
        this.secondLargestUtil(node.left, C);
    }

    // Function to find 2nd largest element
    function secondLargest(node)
    {
        // object of class count
        var C = new count();
        this.secondLargestUtil(this.root, C);
    }

    // Driver function


        /* Let us create following BST
              50
           /     \
          30      70
         /  \    /  \
       20   40  60   80 */

        insert(50);
        insert(30);
        insert(20);
        insert(40);
        insert(70);
        insert(60);
        insert(80);

        secondLargest(root);

// This code contributed by aashish1995

</script>

Output:

2nd largest element is 70

Time complexity : O(h) where h is height of BST. 

Space Complexity: O(n) for call stack where n is total no of nodes in BST

This article is contributed by Ravi. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above