Find Next greater element in Binary Search Tree

Given a binary search tree and a target value, the task is to find the next greater element of the target value in the binary search tree.

Examples:

Input:

               5
             /   \
           3      7
          / \     / \
         2   4 6   8

Target: 4
Output: 5
Explanation: The next greater element of 4 is 5

Input:

               4
              / \
            2    6
          / \      \
        1   3      8

Target: 6
Output: 8
Explanation: The next greater element of 6 is 8

Approach: To solve the problem follow the below idea:

Finding the next greater element in a binary search tree involves performing an in-order traversal of the tree to create a sorted list of its node values. Once we have the sorted list of node values, we can easily find the next greater element of a given node by iterating through the list starting from the target node’s value until we find a value greater than the node’s value.

Below are the steps for the above approach:

• Perform an in-order traversal of the binary search tree and store its node values in a vector.
• Find the target node’s value in the vector.
• Iterate through the vector starting from the target node’s value until we find a value greater than the target node’s value.
• If we find a value greater than the target node’s value, return it as the next greater element. If we reach the end of the vector without finding a greater value, return -1 to indicate that the next greater element does not exist.

Below is the code for the above approach:

C++

// C++ code for the above approach:
#include <bits/stdc++.h>
using namespace std;

// Definition for a binary
// search tree node.
struct TreeNode {
    int val;
    TreeNode* left;
    TreeNode* right;
    TreeNode(int x)
        : val(x), left(NULL), right(NULL)
    {
    }
};

void inorderTraversal(TreeNode* root, vector<int>& values)
{
    if (!root)
        return;
    inorderTraversal(root->left, values);
    values.push_back(root->val);
    inorderTraversal(root->right, values);
}

int getNextGreaterElement(TreeNode* root, int target)
{

    // To store the values of the binary
    // search tree
    vector<int> values;

    // Perform in-order traversal and
    // store values in the vector
    inorderTraversal(root, values);

    auto it

        // Find target value in the vector
        = find(values.begin(), values.end(), target);

    // If target value is not found, return
    // -1
    if (it == values.end())
        return -1;

    // Calculate the distance between the target
    // value and the beginning of the vector
    auto dist = distance(values.begin(), it);

    // Iterate over the vector starting
    // from the target value
    for (int i = dist + 1; i < values.size(); i++) {

        // If an element greater than the
        // target value is found, return it
        if (values[i] > target) {
            return values[i];
        }
    }

    // If next greater element is not found,
    // return -1
    return -1;
}

// Drivers code
int main()
{

    /*
     *           5
     *         /   \
     *        3     7
     *       / \   / \
     *      2   4 6   8
     */
    TreeNode* root = new TreeNode(5);
    root->left = new TreeNode(3);
    root->right = new TreeNode(7);
    root->left->left = new TreeNode(2);
    root->left->right = new TreeNode(4);
    root->right->left = new TreeNode(6);
    root->right->right = new TreeNode(8);

    int target = 4;
    int nextGreaterElement
        = getNextGreaterElement(root, target);

    // Function Call
    cout << "The next greater element of " << target
         << " is " << nextGreaterElement << endl;

    return 0;
}

Java

// Java code for the above approach:
import java.util.*;

// Definition for a binary
// search tree node.
class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;

    TreeNode(int x)
    {
        val = x;
        left = null;
        right = null;
    }
}

public class Main {

    static void inorderTraversal(TreeNode root,
                                 List<Integer> values)
    {
        if (root == null)
            return;
        inorderTraversal(root.left, values);
        values.add(root.val);
        inorderTraversal(root.right, values);
    }

    static int getNextGreaterElement(TreeNode root,
                                     int target)
    {

        // To store the values of the binary
        // search tree
        List<Integer> values = new ArrayList<>();

        // Perform in-order traversal and
        // store values in the list
        inorderTraversal(root, values);

        // Find target value in the list
        int dist = values.indexOf(target);

        // If target value is not found, return -1
        if (dist == -1)
            return -1;

        // Iterate over the list starting
        // from the target value
        for (int i = dist + 1; i < values.size(); i++) {

            // If an element greater than the
            // target value is found, return it
            if (values.get(i) > target) {
                return values.get(i);
            }
        }

        // If next greater element is not found,
        // return -1
        return -1;
    }

    // Drivers code
    public static void main(String[] args)
    {

        /*
         *           5
         *         /   \
         *        3     7
         *       / \   / \
         *      2   4 6   8
         */
        TreeNode root = new TreeNode(5);
        root.left = new TreeNode(3);
        root.right = new TreeNode(7);
        root.left.left = new TreeNode(2);
        root.left.right = new TreeNode(4);
        root.right.left = new TreeNode(6);
        root.right.right = new TreeNode(8);

        int target = 4;
        int nextGreaterElement
            = getNextGreaterElement(root, target);

        // Function Call
        System.out.println("The next greater element of "
                           + target + " is "
                           + nextGreaterElement);
    }
}
// This code is contributed by Prajwal Kandekar

Python3

# Definition for a binary search tree node
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

# Function to perform in-order traversal and store values in the vector
def inorderTraversal(root, values):
    if not root:
        return
    inorderTraversal(root.left, values)
    values.append(root.val)
    inorderTraversal(root.right, values)

# Function to get the next greater element of a target in the binary search tree
def getNextGreaterElement(root, target):
    # To store the values of the binary search tree
    values = []

    # Perform in-order traversal and store values in the vector
    inorderTraversal(root, values)

    # Find target value in the vector
    try:
        index = values.index(target)
    except ValueError:
        return -1

    # Iterate over the vector starting from the target value
    for i in range(index + 1, len(values)):
        # If an element greater than the target value is found, return it
        if values[i] > target:
            return values[i]

    # If next greater element is not found, return -1
    return -1

# Driver code
if __name__ == '__main__':
    # Construct the binary search tree
    """
             5
           /   \
          3     7
         / \   / \
        2   4 6   8
    """
    root = TreeNode(5)
    root.left = TreeNode(3)
    root.right = TreeNode(7)
    root.left.left = TreeNode(2)
    root.left.right = TreeNode(4)
    root.right.left = TreeNode(6)
    root.right.right = TreeNode(8)

    # Target element to find the next greater element of
    target = 4

    # Function call
    nextGreaterElement = getNextGreaterElement(root, target)

    # Print the result
    if nextGreaterElement == -1:
        print(f"The next greater element of {target} is not found.")
    else:
        print(f"The next greater element of {target} is {nextGreaterElement}.")

C#

// C# code for the above approach:

using System;
using System.Collections.Generic;

// Definition for a binary search tree node.
class TreeNode {
    public int val;
    public TreeNode left;
    public TreeNode right;

    public TreeNode(int x)
    {
        val = x;
        left = null;
        right = null;
    }
}

public class GFG {

    static void inorderTraversal(TreeNode root,
                                 List<int> values)
    {
        if (root == null)
            return;
        inorderTraversal(root.left, values);
        values.Add(root.val);
        inorderTraversal(root.right, values);
    }

    static int getNextGreaterElement(TreeNode root,
                                     int target)
    {
        // To store the values of the binary search tree
        List<int> values = new List<int>();

        // Perform in-order traversal and store values in
        // the list
        inorderTraversal(root, values);

        // Find target value in the list
        int dist = values.IndexOf(target);

        // If target value is not found, return -1
        if (dist == -1)
            return -1;

        // Iterate over the list starting from the target
        // value
        for (int i = dist + 1; i < values.Count; i++) {
            // If an element greater than the target value
            // is found, return it
            if (values[i] > target) {
                return values[i];
            }
        }

        // If next greater element is not found, return -1
        return -1;
    }

    static public void Main()
    {

        /*
         *           5
         *         /   \
         *        3     7
         *       / \   / \
         *      2   4 6   8
         */
        TreeNode root = new TreeNode(5);
        root.left = new TreeNode(3);
        root.right = new TreeNode(7);
        root.left.left = new TreeNode(2);
        root.left.right = new TreeNode(4);
        root.right.left = new TreeNode(6);
        root.right.right = new TreeNode(8);

        int target = 4;
        int nextGreaterElement
            = getNextGreaterElement(root, target);

        // Function Call
        Console.WriteLine("The next greater element of "
                          + target + " is "
                          + nextGreaterElement);
    }
}

// This code is contributed by lokesh.

Javascript

// Definition for a binary
// search tree node.
class TreeNode {
  constructor(val) {
    this.val = val;
    this.left = null;
    this.right = null;
  }
}

function inorderTraversal(root, values) {
  if (!root) return;
  inorderTraversal(root.left, values);
  values.push(root.val);
  inorderTraversal(root.right, values);
}

function getNextGreaterElement(root, target) {
  // To store the values of the binary
  // search tree
  const values = [];

  // Perform in-order traversal and
  // store values in the array
  inorderTraversal(root, values);

  // Find target value in the array
  const idx = values.indexOf(target);

  // If target value is not found, return -1
  if (idx === -1) return -1;

  // Iterate over the array starting from the
  // target value index
  for (let i = idx + 1; i < values.length; i++) {
    // If an element greater than the target
    // value is found, return it
    if (values[i] > target) {
      return values[i];
    }
  }

  // If next greater element is not found,
  // return -1
  return -1;
}

// Driver code
(function main() {
  /*
   *           5
   *         /   \
   *        3     7
   *       / \   / \
   *      2   4 6   8
   */
  const root = new TreeNode(5);
  root.left = new TreeNode(3);
  root.right = new TreeNode(7);
  root.left.left = new TreeNode(2);
  root.left.right = new TreeNode(4);
  root.right.left = new TreeNode(6);
  root.right.right = new TreeNode(8);

  const target = 4;
  const nextGreaterElement = getNextGreaterElement(root, target);

  // Function Call
  console.log(`The next greater element of ${target} is ${nextGreaterElement}`);
})();

Output

The next greater element of 4 is 5

Time Complexity: O(n) where n is the number of nodes in the binary search tree.
Auxiliary Space: O(n), to store the node values in a vector.

Approach 2: Recursive Approach

Implementation :

C++

#include <climits>
#include <iostream>
using namespace std;

struct Node {
    int val;
    Node* left;
    Node* right;

    Node(int value)
        : val(value)
        , left(nullptr)
        , right(nullptr)
    {
    }
};

int findNextGreater(Node* root, int target)
{
    int successor = INT_MAX;
    while (root) {
        if (root->val > target) {
            successor = min(successor, root->val);
            root = root->left;
        }
        else {
            root = root->right;
        }
    }
    return successor;
}

int main()
{
    Node* root = new Node(2);
    root->left = new Node(4);
    root->right = new Node(7);
    root->left->left = new Node(2);
    root->left->right = new Node(3);
    root->right->left = new Node(6);
    root->right->right = new Node(9);

    int target = 6;
    int nextGreater = findNextGreater(root, target);
    cout << "Next greater element after " << target
         << " is: " << nextGreater << endl;

    // Clean up the memory
    delete root->right->right;
    delete root->right->left;
    delete root->left->right;
    delete root->left->left;
    delete root->right;
    delete root->left;
    delete root;

    return 0;
}

Java

import java.io.*;
class Node {
    int val;
    Node left;
    Node right;
    Node(int value) {
        val = value;
        left = null;
        right = null;
    }
}
public class Main {
    public static int findNextGreater(Node root, int target) {
        int successor = Integer.MAX_VALUE;
        while (root != null) {
            if (root.val > target) {
                successor = Math.min(successor, root.val);
                root = root.left;
            } else {
                root = root.right;
            }
        }
        return successor;
    }
    public static void main(String[] args) {
        Node root = new Node(2);
        root.left = new Node(4);
        root.right = new Node(7);
        root.left.left = new Node(2);
        root.left.right = new Node(3);
        root.right.left = new Node(6);
        root.right.right = new Node(9);
        int target = 6;
        int nextGreater = findNextGreater(root, target);
        System.out.println("Next greater element after " + target + " is: " + nextGreater);
        root.right.right = null;
        root.right.left = null;
        root.left.right = null;
        root.left.left = null;
        root.right = null;
        root.left = null;
        root = null;
    }
}

Python

class Node:
    def __init__(self, value):
        self.val = value
        self.left = None
        self.right = None

def findNextGreater(root, target):
    successor = float('inf')
    while root:
        if root.val > target:
            successor = min(successor, root.val)
            root = root.left
        else:
            root = root.right
    return successor

if __name__ == "__main__":
    root = Node(2)
    root.left = Node(4)
    root.right = Node(7)
    root.left.left = Node(2)
    root.left.right = Node(3)
    root.right.left = Node(6)
    root.right.right = Node(9)

    target = 6
    nextGreater = findNextGreater(root, target)
    print("Next greater element after", target, "is:", nextGreater)

    root.right.right = None
    root.right.left = None
    root.left.right = None
    root.left.left = None
    root.right = None
    root.left = None
    root = None

C#

using System;

public class Node
{
    public int val;
    public Node left;
    public Node right;
    public Node(int value)
    {
        val = value;
        left = null;
        right = null;
    }
}
public class GFG
{
    public static int FindNextGreater(Node root, int target)
    {
        int successor = int.MaxValue;
        while (root != null)
        {
            if (root.val > target)
            {
                successor = Math.Min(successor, root.val);
                root = root.left;
            }
            else
            {
                root = root.right;
            }
        }
        return successor;
    }
    public static void Main()
    {
        Node root = new Node(2);
        root.left = new Node(4);
        root.right = new Node(7);
        root.left.left = new Node(2);
        root.left.right = new Node(3);
        root.right.left = new Node(6);
        root.right.right = new Node(9);
        int target = 6;
        int nextGreater = FindNextGreater(root, target);
        Console.WriteLine("Next greater element after " + target + " is: " + nextGreater);
        // Clean up the memory.
        root.right.right = null;
        root.right.left = null;
        root.left.right = null;
        root.left.left = null;
        root.right = null;
        root.left = null;
        root = null;
    }
}

Javascript

class Node {
    constructor(value) {
        this.val = value;
        this.left = null;
        this.right = null;
    }
}

function findNextGreater(root, target) {
    let successor = Number.MAX_SAFE_INTEGER;
    while (root) {
        if (root.val > target) {
            successor = Math.min(successor, root.val);
            root = root.left;
        } else {
            root = root.right;
        }
    }
    return successor;
}

// Driver code
let root = new Node(2);
root.left = new Node(4);
root.right = new Node(7);
root.left.left = new Node(2);
root.left.right = new Node(3);
root.right.left = new Node(6);
root.right.right = new Node(9);

let target = 6;
let nextGreater = findNextGreater(root, target);
// Clean up the memory
root.right.right = null;
root.right.left = null;
root.left.right = null;
root.left.left = null;
root.right = null;
root.left = null;
root = null;
console.log("Next greater element after " + target + " is: " + nextGreater);

Output

Next greater element after 6 is: 7