There are numerous applications we need to find floor (ceil) value of a key in a binary search tree or sorted array. For example, consider designing memory management system in which free nodes are arranged in BST. Find best fit for the input request.
Ceil Value Node: Node with smallest data larger than or equal to key value.
Imagine we are moving down the tree, and assume we are root node. The comparison yields three possibilities,
A) Root data is equal to key. We are done, root data is ceil value.
B) Root data < key value, certainly the ceil value can’t be in left subtree. Proceed to search on right subtree as reduced problem instance.
C) Root data > key value, the ceil value may be in left subtree. We may find a node with is larger data than key value in left subtree, if not the root itself will be ceil node.
Here is the code for ceil value.
C++
// Program to find ceil of a given value in BST #include <bits/stdc++.h> using namespace std; /* A binary tree node has key, left child and right child */class node { public: int key; node* left; node* right; }; /* Helper function that allocates a new node with the given key and NULL left and right pointers.*/node* newNode(int key) { node* Node = new node(); Node->key = key; Node->left = NULL; Node->right = NULL; return (Node); } // Function to find ceil of a given input in BST. If input is more // than the max key in BST, return -1 int Ceil(node* root, int input) { // Base case if (root == NULL) return -1; // We found equal key if (root->key == input) return root->key; // If root's key is smaller, ceil must be in right subtree if (root->key < input) return Ceil(root->right, input); // Else, either left subtree or root has the ceil value int ceil = Ceil(root->left, input); return (ceil >= input) ? ceil : root->key; } // Driver program to test above function int main() { node* root = newNode(8); root->left = newNode(4); root->right = newNode(12); root->left->left = newNode(2); root->left->right = newNode(6); root->right->left = newNode(10); root->right->right = newNode(14); for (int i = 0; i < 16; i++) cout << i << " " << Ceil(root, i) << endl; return 0; } // This code is contributed by rathbhupendra |
C
// Program to find ceil of a given value in BST #include <stdio.h> #include <stdlib.h> /* A binary tree node has key, left child and right child */struct node { int key; struct node* left; struct node* right; }; /* Helper function that allocates a new node with the given key and NULL left and right pointers.*/struct node* newNode(int key) { struct node* node = (struct node*)malloc(sizeof(struct node)); node->key = key; node->left = NULL; node->right = NULL; return (node); } // Function to find ceil of a given input in BST. If input is more // than the max key in BST, return -1 int Ceil(struct node* root, int input) { // Base case if (root == NULL) return -1; // We found equal key if (root->key == input) return root->key; // If root's key is smaller, ceil must be in right subtree if (root->key < input) return Ceil(root->right, input); // Else, either left subtree or root has the ceil value int ceil = Ceil(root->left, input); return (ceil >= input) ? ceil : root->key; } // Driver program to test above function int main() { struct node* root = newNode(8); root->left = newNode(4); root->right = newNode(12); root->left->left = newNode(2); root->left->right = newNode(6); root->right->left = newNode(10); root->right->right = newNode(14); for (int i = 0; i < 16; i++) printf("%d %d
", i, Ceil(root, i)); return 0; } |
Java
// Java program to find ceil of a given value in BST class Node { int data; Node left, right; Node(int d) { data = d; left = right = null; } } class BinaryTree { Node root; // Function to find ceil of a given input in BST. // If input is more than the max key in BST, // return -1 int Ceil(Node node, int input) { // Base case if (node == null) { return -1; } // We found equal key if (node.data == input) { return node.data; } // If root's key is smaller, // ceil must be in right subtree if (node.data < input) { return Ceil(node.right, input); } // Else, either left subtree or root // has the ceil value int ceil = Ceil(node.left, input); return (ceil >= input) ? ceil : node.data; } // Driver Code public static void main(String[] args) { BinaryTree tree = new BinaryTree(); tree.root = new Node(8); tree.root.left = new Node(4); tree.root.right = new Node(12); tree.root.left.left = new Node(2); tree.root.left.right = new Node(6); tree.root.right.left = new Node(10); tree.root.right.right = new Node(14); for (int i = 0; i < 16; i++) { System.out.println(i + " " + tree.Ceil(tree.root, i)); } } } // This code has been contributed by Mayank Jaiswal |
Python
# Python program to find ceil of a given value in BST # A Binary tree node class Node: # Constructor to create a new node def __init__(self, data): self.key = data self.left = None self.right = None # Function to find ceil of a given input in BST. If input # is more than the max key in BST, return -1 def ceil(root, inp): # Base Case if root == None: return -1 # We found equal key if root.key == inp : return root.key # If root's key is smaller, ceil must be in right subtree if root.key < inp: return ceil(root.right, inp) # Else, either left subtre or root has the ceil value val = ceil(root.left, inp) return val if val >= inp else root.key # Driver program to test above function root = Node(8) root.left = Node(4) root.right = Node(12) root.left.left = Node(2) root.left.right = Node(6) root.right.left = Node(10) root.right.right = Node(14) for i in range(16): print "% d % d" %(i, ceil(root, i)) # This code is contributed by Nikhil Kumar Singh(nickzuck_007) |
C#
using System; // C# program to find ceil of a given value in BST public class Node { public int data; public Node left, right; public Node(int d) { data = d; left = right = null; } } public class BinaryTree { public static Node root; // Function to find ceil of a given input in BST. If input is more // than the max key in BST, return -1 public virtual int Ceil(Node node, int input) { // Base case if (node == null) { return -1; } // We found equal key if (node.data == input) { return node.data; } // If root's key is smaller, ceil must be in right subtree if (node.data < input) { return Ceil(node.right, input); } // Else, either left subtree or root has the ceil value int ceil = Ceil(node.left, input); return (ceil >= input) ? ceil : node.data; } // Driver program to test the above functions public static void Main(string[] args) { BinaryTree tree = new BinaryTree(); BinaryTree.root = new Node(8); BinaryTree.root.left = new Node(4); BinaryTree.root.right = new Node(12); BinaryTree.root.left.left = new Node(2); BinaryTree.root.left.right = new Node(6); BinaryTree.root.right.left = new Node(10); BinaryTree.root.right.right = new Node(14); for (int i = 0; i < 16; i++) { Console.WriteLine(i + " " + tree.Ceil(root, i)); } } } // This code is contributed by Shrikant13 |
Output:
0 2 1 2 2 2 3 4 4 4 5 6 6 6 7 8 8 8 9 10 10 10 11 12 12 12 13 14 14 14 15 -1
Exercise:
1. Modify above code to find floor value of input key in a binary search tree.
2. Write neat algorithm to find floor and ceil values in a sorted array. Ensure to handle all possible boundary conditions.
— Venki. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
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