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
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 ceil of BST you can refer to this article.
C++
// C++ 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 andinitializes 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 BSTclass GfG { /*Structure of each Node in the tree*/ static class Node { int data; Node left, right; } /*This function is used to create andinitializes 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 insertnew 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 BSTINT_MAX = 2147483647# Binary Tree Node""" A utility function to create anew 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 insertnew 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 Codeif __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 BSTusing 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 andinitializes 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 insertnew 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 |
Javascript
<script>// Javascript code to find floor of a key in BSTclass Node{ constructor() { this.data=0; this.left=this.right=null; }}/*This function is used to create andinitializes new Nodes*/function newNode(key){ let temp = new Node(); temp.left = null; temp.right = null; temp.data = key; return temp;}/* This function is used to insertnew values in BST*/function insert(root,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*/function floor(root,key){ if (root == null) return Number.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*/ let floorValue = floor(root.right, key); return (floorValue <= key) ? floorValue : root.data;}/* Let us create following BST 7 / \ 5 10 / \ / \ 3 6 8 12 */let root = null;root = insert(root, 7);insert(root, 10);insert(root, 5);insert(root, 3);insert(root, 6);insert(root, 8);insert(root, 12);document.write(floor(root, 9));// This code is contributed by rag2127</script> |
Output:
8
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