Floor in Binary Search Tree (BST)

Last Updated : 22 Oct, 2025

Given a Binary Search Tree and a number x, we have to find the floor of x in the given BST, where floor means the greatest value node of the BST which is smaller than or equal to x. if x is smaller than the smallest node of BST then return -1.

Examples:

Input:

floor-in-binary-search-tree-bst-1


Output: 55
Explanantion:

floor-in-binary-search-tree-bst-2
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Table of Content

[Expected Approach - 1] Using Recursion - O(h) Time and O(h) Space

The idea is to find the floor in a BST by traversing recursively: if the node’s value is greater than the key, move left; if it is less than or equal to the key, record it and move right.

Follow the given steps to solve the problem:

  • Start at the root node.
  • If root->data == x, the floor of x is equal to the root.
  • Else if root->data > x, the floor must lie in the left subtree.
  • Otherwise, search in the right subtree for a value less than or equal to x, but if not found, the root itself is the floor.
C++ 
// C++ implementation to find floor of given 
// number x in BST
#include <iostream>
using namespace std;

class Node {
public:
    int data;
    Node *left;
    Node *right;    
  
    Node(int x) {
        data = x;
        left = nullptr;
        right = nullptr;
    }
};

// This function is used to find floor 
// of given number x
int floor(Node* root, int x) {
  
   // Base case: return -1 if no floor found
   if (root == nullptr) {
        return -1; 
    }

    // If the root's data is equal to x, 
    // we've found the floor
    if (root->data == x) {
        return root->data;
    }

    // If root's data is greater than x, 
    // search in the left subtree
    if (root->data > x) {
        return floor(root->left, x);
    }

    // Else, search in the right subtree 
    // and compare with current root
    int floorValue = floor(root->right, x);

    // If the right subtree returns 
    //a valid floor, return that
    // Otherwise, return the current root's data
    return (floorValue <= x && floorValue != -1)
                              ? floorValue : root->data;
}

int main() {
  
    // Representation of the given tree
    //       10
    //       / \
    //      5  15
    //         / \
    //        12 30 
    Node* root = new Node(10);
    root->left = new Node(5);
    root->right = new Node(15);
    root->right->left = new Node(12);
    root->right->right = new Node(30);

    int x = 14;
    cout << floor(root, x) << endl;
    return 0;
}
C 
// C implementation to find floor of given 
// number x in BST
#include <stdio.h>
#include <stdlib.h>

struct Node {
    int data;
    struct Node* left;
    struct Node* right;    
};

// This function is used to find floor 
// of given number x
int floor(struct Node* root, int x) {

    // Base case: return -1 if no floor found
    if (root == NULL) {
        return -1; 
    }

    // If the root's data is equal to x, 
    // we've found the floor
    if (root->data == x) {
        return root->data;
    }

    // If root's data is greater than x, 
    // search in the left subtree
    if (root->data > x) {
        return floor(root->left, x);
    }

    // Else, search in the right subtree 
    // and compare with current root
    int floorValue = floor(root->right, x);

    // If the right subtree returns 
    // a valid floor, return that
    // Otherwise, return the current root's data
    return (floorValue <= x && floorValue != -1)
                                ? floorValue : root->data;
}

struct Node* createNode(int x) {
    struct Node* newNode 
      = (struct Node*)malloc(sizeof(struct Node));
    newNode->data = x;
    newNode->left = NULL;
    newNode->right = NULL;
    return newNode;
}

int main() {

    // Representation of the given tree
    //       10
    //       / \
    //      5  15
    //         / \
    //        12 30 
    struct Node* root = createNode(10);
    root->left = createNode(5);
    root->right = createNode(15);
    root->right->left = createNode(12);
    root->right->right = createNode(30);

    int x = 14;
    printf("%d\n", floor(root, x));

    return 0;
}
Java 
// Java implementation to find floor of given 
// number x in BST

class Node {
    int data;
    Node left, right;

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

// This function is used to find floor 
// of given number x
class GfG {

    static int floor(Node root, int x) {

        // Base case: return -1 if no floor found
        if (root == null) {
            return -1;
        }

        // If the root's data is equal to x, 
        // we've found the floor
        if (root.data == x) {
            return root.data;
        }

        // If root's data is greater than x, 
        // search in the left subtree
        if (root.data > x) {
            return floor(root.left, x);
        }

        // Else, search in the right subtree 
        // and compare with current root
        int floorValue = floor(root.right, x);

        // If the right subtree returns a valid floor,
        // return that, otherwise return the current root's data
        return (floorValue <= x && floorValue != -1)
                                ? floorValue : root.data;
    }

    public static void main(String[] args) {

        // Representation of the given tree
        //       10
        //       / \
        //      5  15
        //         / \
        //        12 30 
        Node root = new Node(10);
        root.left = new Node(5);
        root.right = new Node(15);
        root.right.left = new Node(12);
        root.right.right = new Node(30);

        int x = 14;
        System.out.println(floor(root, x));
    }
}
Python 
# Python implementation to find floor of given 
# number x in BST
class Node:
    def __init__(self, x):
        self.data = x
        self.left = None
        self.right = None

# This function is used to find floor 
# of given number x
def find_floor(root, x):

    # Base case: return -1 if no floor found
    if root is None:
        return -1

    # If the root's data is equal to x, 
    # we've found the floor
    if root.data == x:
        return root.data

    # If root's data is greater than x, 
    # search in the left subtree
    if root.data > x:
        return find_floor(root.left, x)

    # Else, search in the right subtree 
    # and compare with current root
    floor_value = find_floor(root.right, x)

    # If the right subtree returns a valid floor,
    # return that, otherwise return the current root's data
    return floor_value if floor_value <= x \
                   and floor_value != -1 else root.data


if __name__ == "__main__":

    # Representation of the given tree
    #       10
    #       / \
    #      5  15
    #         / \
    #        12 30 
    root = Node(10)
    root.left = Node(5)
    root.right = Node(15)
    root.right.left = Node(12)
    root.right.right = Node(30)

    x = 14
    print(find_floor(root, x))
C# 
// C# implementation to find floor of given 
// number x in BST
using System;

class Node {
    public int data;
    public Node left, right;

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

// This function is used to find floor 
// of given number x
class GfG {
    static int FindFloor(Node root, int x) {

        // Base case: return -1 if no floor found
        if (root == null) {
            return -1;
        }

        // If the root's data is equal to x, 
        // we've found the floor
        if (root.data == x) {
            return root.data;
        }

        // If root's data is greater than x, 
        // search in the left subtree
        if (root.data > x) {
            return FindFloor(root.left, x);
        }

        // Else, search in the right subtree 
        // and compare with current root
        int floorValue = FindFloor(root.right, x);

        // If the right subtree returns a valid floor,
        // return that, otherwise return the current root's data
        return (floorValue <= x && floorValue != -1)
                                ? floorValue : root.data;
    }

    static void Main(string[] args) {

        // Representation of the given tree
        //       10
        //       / \
        //      5  15
        //         / \
        //        12 30 
        Node root = new Node(10);
        root.left = new Node(5);
        root.right = new Node(15);
        root.right.left = new Node(12);
        root.right.right = new Node(30);

        int x = 14;
        Console.WriteLine(FindFloor(root, x));
    }
}
JavaScript 
// JavaScript implementation to find floor of given 
// number x in BST
class Node {
    constructor(x) {
        this.data = x;
        this.left = null;
        this.right = null;
    }
}

// This function is used to find floor 
// of given number x
function findFloor(root, x) {

    // Base case: return -1 if no floor found
    if (root === null) {
        return -1;
    }

    // If the root's data is equal to x, 
    // we've found the floor
    if (root.data === x) {
        return root.data;
    }

    // If root's data is greater than x, 
    // search in the left subtree
    if (root.data > x) {
        return findFloor(root.left, x);
    }

    // Else, search in the right subtree 
    // and compare with current root
    let floorValue = findFloor(root.right, x);

    // If the right subtree returns a valid floor,
    // return that, otherwise return the current root's data
    return (floorValue <= x && floorValue !== -1)
                                ? floorValue : root.data;
}
// Driver Code
// Representation of the given tree
//       10
//       / \
//      5  15
//         / \
//        12 30 
let root = new Node(10);
root.left = new Node(5);
root.right = new Node(15);
root.right.left = new Node(12);
root.right.right = new Node(30);

let x = 14;
console.log(findFloor(root, x));

Output
12

[Expected Approach - 2] Iterative Solution- O(h) Time and O(1) Space

The idea is to iteratively traverse the BST to find the greatest value smaller than or equal to x. If the current node's data is greater than x, move left. If it's smaller, update the floor value and move right. This process continues until the closest floor value is found.

Below is the implementation of the above approach:

C++ 
// C++ implementation to find floor of given 
// number x in BST
#include <iostream>
using namespace std;

class Node {
public:
    int data;
    Node *left;
    Node *right;    
  
    Node(int x) {
        data = x;
        left = nullptr;
        right = nullptr;
    }
};

// This function is used to find floor 
// of given number x
int floor(Node* root, int x) {
  
    // Initialize variable to store the floor value
    int floorValue = -1;

    while (root != nullptr) {
      
        // If the root's data is equal to x, 
        // we've found the floor
        if (root->data == x) {
            return root->data;
        }

        // If root's data is greater than x, 
        // search in the left subtree
        if (root->data > x) {
            root = root->left;
        } 
        else {
          
            // Update floorValue and move to the 
            // right subtree
            floorValue = root->data;
            root = root->right;
        }
    }

    return floorValue;
}

int main() {
  
    // Representation of the given tree
    //       10
    //       / \
    //      5  15
    //         / \
    //        12 30 
    Node* root = new Node(10);
    root->left = new Node(5);
    root->right = new Node(15);
    root->right->left = new Node(12);
    root->right->right = new Node(30);

    int x = 14;
    cout << floor(root, x) << endl;
    return 0;
}
C 
// C implementation to find floor of given 
// number x in BST
#include <stdio.h>
#include <stdlib.h>

struct Node {
    int data;
    struct Node *left;
    struct Node *right;    
};

// This function is used to find floor 
// of given number x
int floor(struct Node* root, int x) {
  
    // Initialize variable to store the floor value
    int floorValue = -1;

    while (root != NULL) {
      
        // If the root's data is equal to x, 
        // we've found the floor
        if (root->data == x) {
            return root->data;
        }

        // If root's data is greater than x, 
        // search in the left subtree
        if (root->data > x) {
            root = root->left;
        } 
        else {
          
            // Update floorValue and move to the 
            // right subtree
            floorValue = root->data;
            root = root->right;
        }
    }

    // Return the floor value found
    return floorValue;
}

struct Node* createNode(int x) {
    struct Node* newNode
             = (struct Node*)malloc(sizeof(struct Node));
    newNode->data = x;
    newNode->left = NULL;
    newNode->right = NULL;
    return newNode;
}
int main() {
  
    // Representation of the given tree
    //       10
    //       / \
    //      5  15
    //         / \
    //        12 30 
    struct Node* root = createNode(10);
    root->left = createNode(5);
    root->right = createNode(15);
    root->right->left = createNode(12);
    root->right->right = createNode(30);

    int x = 14;
    printf("%d\n", floor(root, x));
    return 0;
}
Java 
// Java implementation to find floor of given 
// number x in BST
class Node {
    int data;
    Node left;
    Node right;    

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

class GfG {
  
    // This function is used to find floor 
    // of given number x
    static int floor(Node root, int x) {

        // Initialize variable to store the floor value
        int floorValue = -1;

        while (root != null) {

            // If the root's data is equal to x, 
            // we've found the floor
            if (root.data == x) {
                return root.data;
            }

            // If root's data is greater than x, 
            // search in the left subtree
            if (root.data > x) {
                root = root.left;
            } 
            else {

                // Update floorValue and move to the 
                // right subtree
                floorValue = root.data;
                root = root.right;
            }
        }

        // Return the floor value found
        return floorValue;
    }

    public static void main(String[] args) {
  
        // Representation of the given tree
        //       10
        //       / \
        //      5  15
        //         / \
        //        12 30 
        Node root = new Node(10);
        root.left = new Node(5);
        root.right = new Node(15);
        root.right.left = new Node(12);
        root.right.right = new Node(30);

        int x = 14;
        System.out.println(floor(root, x));
    }
}
Python 
# Python implementation to find floor of given 
# number x in BST
class Node:
    def __init__(self, x):
        self.data = x
        self.left = None
        self.right = None

# This function is used to find floor 
# of given number x
def floor(root, x):
  
    # Initialize variable to store the floor value
    floor_value = -1

    while root is not None:
      
        # If the root's data is equal to x, 
        # we've found the floor
        if root.data == x:
            return root.data

        # If root's data is greater than x, 
        # search in the left subtree
        if root.data > x:
            root = root.left
        else:
          
            # Update floor_value and move to the 
            # right subtree
            floor_value = root.data
            root = root.right

    return floor_value

if __name__ == "__main__":
  
    # Representation of the given tree
    #       10
    #       / \
    #      5  15
    #         / \
    #        12 30 
    root = Node(10)
    root.left = Node(5)
    root.right = Node(15)
    root.right.left = Node(12)
    root.right.right = Node(30)

    x = 14
    print(floor(root, x))
C# 
// C# implementation to find floor of given 
// number x in BST
using System;

class Node {
    public int data;
    public Node left;
    public Node right;    

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

// This function is used to find floor 
// of given number x
class GfG {
    static int Floor(Node root, int x) {
  
        // Initialize variable to store the floor value
        int floorValue = -1;

        while (root != null) {
      
            // If the root's data is equal to x, 
            // we've found the floor
            if (root.data == x) {
                return root.data;
            }

            // If root's data is greater than x, 
            // search in the left subtree
            if (root.data > x) {
                root = root.left;
            } 
            else {
              
                // Update floorValue and move to the 
                // right subtree
                floorValue = root.data;
                root = root.right;
            }
        }

        // Return the floor value found
        return floorValue;
    }

    static void Main() {
  
        // Representation of the given tree
        //       10
        //       / \
        //      5  15
        //         / \
        //        12 30 
        Node root = new Node(10);
        root.left = new Node(5);
        root.right = new Node(15);
        root.right.left = new Node(12);
        root.right.right = new Node(30);

        int x = 14;
        Console.WriteLine(Floor(root, x));
    }
}
JavaScript 
// JavaScript implementation to find floor of given 
// number x in BST
class Node {
    constructor(x) {
        this.data = x;
        this.left = null;
        this.right = null;
    }
}

// This function is used to find floor 
// of given number x
function floor(root, x) {
  
    // Initialize variable to store the floor value
    let floorValue = -1;

    while (root !== null) {
      
        // If the root's data is equal to x, 
        // we've found the floor
        if (root.data === x) {
            return root.data;
        }

        // If root's data is greater than x, 
        // search in the left subtree
        if (root.data > x) {
            root = root.left;
        } 
        else {
        
            // Update floorValue and move to the 
            // right subtree
            floorValue = root.data;
            root = root.right;
        }
    }

    return floorValue;
}
// Driver Code
// Representation of the given tree
//       10
//       / \
//      5  15
//         / \
//        12 30 
const root = new Node(10);
root.left = new Node(5);
root.right = new Node(15);
root.right.left = new Node(12);
root.right.right = new Node(30);

const x = 14;
console.log(floor(root, x));

Output
12
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