Floor in Binary Search Tree (BST)

Given a Binary Search Tree and a number x, find floor of x in the given BST.

Input : x = 14 and root of below tree
            10
           /  \
          5    15
              /  \
            12    30
Output : 12

Input : x = 15 and root of below tree
            10
           /  \
          5    15
              /  \
            12    30
Output : 15

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

A simple solution is to traverse the tree using (Inorder or Preorder or Postorder) and keep track of closest smaller or same element. Time complexity of this solution is O(n) where n is total number of Nodes in BST.

We can efficiently find closest smaller or same element in O(h) time where h is height of BST. Algorithm to find the floor of a key in a binary search tree (BST):

1 Start at the root Node.
2 If root->data == key, 
     floor of the key is equal 
     to the root.
3 Else if root->data > key, then 
     floor of the key must lie in the
     left subtree.
4 Else floor may lie in the right subtree 
  but only if there is a value lesser than 
  or equal to the key.If not, then root is
  the key.

For finding ciel of BST you can refer to this article.

C++

// CPP code to find floor of a key in BST 
#include <bits/stdc++.h> 
using namespace std; 
  
/*Structure of each Node in the tree*/
struct Node { 
    int data; 
    Node *left, *right; 
}; 
  
/*This function is used to create and 
initialises new Nodes*/
Node* newNode(int key) 
{ 
    Node* temp = new Node; 
    temp->left = temp->right = NULL; 
    temp->data = key; 
    return temp; 
} 
  
/* This function is used to insert 
 new values in BST*/
Node* insert(Node* root, int key) 
{ 
    if (!root) 
        return newNode(key); 
    if (key < root->data) 
        root->left = insert(root->left, key); 
    else
        root->right = insert(root->right, key); 
    return root; 
} 
  
/*This function is used to find floor of a key*/
int floor(Node* root, int key) 
{ 
    if (!root) 
        return INT_MAX; 
  
    /* If root->data is equal to key */
    if (root->data == key) 
        return root->data; 
  
    /* If root->data is greater than the key */
    if (root->data > key) 
        return floor(root->left, key); 
  
    /* Else, the floor may lie in right subtree 
      or may be equal to the root*/
    int floorValue = floor(root->right, key); 
    return (floorValue <= key) ? floorValue : root->data; 
} 
  
int main() 
{ 
    /* Let us create following BST 
              7 
            /    \ 
           5      10 
         /  \    /  \ 
        3    6   8   12 */
    Node* root = NULL; 
    root = insert(root, 7); 
    insert(root, 10); 
    insert(root, 5); 
    insert(root, 3); 
    insert(root, 6); 
    insert(root, 8); 
    insert(root, 12); 
    cout << floor(root, 9) << endl; 
    return 0; 
} 

Java

// Java code to find floor of a key in BST 
class GfG { 
  
    /*Structure of each Node in the tree*/
    static class Node { 
        int data; 
        Node left, right; 
    } 
  
    /*This function is used to create and  
initialises new Nodes*/
    static Node newNode(int key) 
    { 
        Node temp = new Node(); 
        temp.left = null; 
        temp.right = null; 
        temp.data = key; 
        return temp; 
    } 
  
    /* This function is used to insert  
new values in BST*/
    static Node insert(Node root, int key) 
    { 
        if (root == null) 
            return newNode(key); 
        if (key < root.data) 
            root.left = insert(root.left, key); 
        else
            root.right = insert(root.right, key); 
        return root; 
    } 
  
    /*This function is used to find floor of a key*/
    static int floor(Node root, int key) 
    { 
        if (root == null) 
            return Integer.MAX_VALUE; 
  
        /* If root->data is equal to key */
        if (root.data == key) 
            return root.data; 
  
        /* If root->data is greater than the key */
        if (root.data > key) 
            return floor(root.left, key); 
  
        /* Else, the floor may lie in right subtree  
    or may be equal to the root*/
        int floorValue = floor(root.right, key); 
        return (floorValue <= key) ? floorValue : root.data; 
    } 
  
    public static void main(String[] args) 
    { 
        /* Let us create following BST  
            7  
            / \  
        5     10  
        / \ / \  
        3 6 8 12 */
        Node root = null; 
        root = insert(root, 7); 
        insert(root, 10); 
        insert(root, 5); 
        insert(root, 3); 
        insert(root, 6); 
        insert(root, 8); 
        insert(root, 12); 
        System.out.println(floor(root, 9)); 
    } 
} 

Python3

# Python3 code to find floor of a key in BST 
INT_MAX = 2147483647
  
# Binary Tree Node  
""" A utility function to create a 
new BST node """
class newNode:  
  
    # Construct to create a newNode  
    def __init__(self, data):  
        self.data = data 
        self.left = None
        self.right = None
  
""" This function is used to insert  
new values in BST"""
def insert(root, key):  
  
    if (not root): 
        return newNode(key)  
    if (key < root.data):  
        root.left = insert(root.left, key)  
    else: 
        root.right = insert(root.right, key)  
    return root  
  
"""This function is used to find floor of a key"""
def floor(root, key) : 
  
    if (not root):  
        return INT_MAX  
  
    """ If root.data is equal to key """
    if (root.data == key) : 
        return root.data  
  
    """ If root.data is greater than the key """
    if (root.data > key) : 
        return floor(root.left, key)  
  
    """ Else, the floor may lie in right subtree  
    or may be equal to the root"""
    floorValue = floor(root.right, key)  
    return floorValue if (floorValue <= key) else root.data  
  
# Driver Code  
if __name__ == '__main__': 
  
    """ Let us create following BST  
            7  
            / \  
        5     10  
        / \ / \  
        3 6 8 12 """
    root = None
    root = insert(root, 7)  
    insert(root, 10)  
    insert(root, 5)  
    insert(root, 3)  
    insert(root, 6)  
    insert(root, 8)  
    insert(root, 12)  
    print(floor(root, 9)) 
  
# This code is contributed by 
# Shubham Singh(SHUBHAMSINGH10) 

C#

// C# code to find floor of a key in BST 
using System; 
  
class GfG { 
  
    /*Structure of each Node in the tree*/
    public class Node { 
        public int data; 
        public Node left, right; 
    } 
  
    /*This function is used to create and  
initialises new Nodes*/
    static Node newNode(int key) 
    { 
        Node temp = new Node(); 
        temp.left = null; 
        temp.right = null; 
        temp.data = key; 
        return temp; 
    } 
  
    /* This function is used to insert  
new values in BST*/
    static Node insert(Node root, int key) 
    { 
        if (root == null) 
            return newNode(key); 
        if (key < root.data) 
            root.left = insert(root.left, key); 
        else
            root.right = insert(root.right, key); 
        return root; 
    } 
  
    /*This function is used to find floor of a key*/
    static int floor(Node root, int key) 
    { 
        if (root == null) 
            return int.MaxValue; 
  
        /* If root->data is equal to key */
        if (root.data == key) 
            return root.data; 
  
        /* If root->data is greater than the key */
        if (root.data > key) 
            return floor(root.left, key); 
  
        /* Else, the floor may lie in right subtree  
    or may be equal to the root*/
        int floorValue = floor(root.right, key); 
        return (floorValue <= key) ? floorValue : root.data; 
    } 
  
    // Driver code 
    public static void Main(String[] args) 
    { 
        /* Let us create following BST  
            7  
            / \  
        5     10  
        / \ / \  
        3 6 8 12 */
        Node root = null; 
        root = insert(root, 7); 
        insert(root, 10); 
        insert(root, 5); 
        insert(root, 3); 
        insert(root, 6); 
        insert(root, 8); 
        insert(root, 12); 
        Console.WriteLine(floor(root, 9)); 
    } 
} 
  
// This code has been contributed by 29AjayKumar 

Output:

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Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

C++

Java

Python3

C#

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