Smallest number in BST which is greater than or equal to N ( Iterative Approach)

Given a Binary Search Tree and a number N, the task is to find the smallest number in the binary search tree that is greater than or equal to N. 

Examples:

Input: N = 5   
              8
            /   \
           7     10
         /      /   \
        2      9     13

Output: 7
As 7 is the smallest number in BST which is greater than N = 5.

Input: N = 10 
           8
         /   \
        5    11
      /  \
     2    7
      \
       3

Output: 11
As 11 is the smallest number in BST which is greater than N = 10.

A recursive solution for this problem has been already been discussed in this post. Below is an iterative approach for the problem:

Using Morris Traversal the above problem can be solved in constant space. Find the inorder successor of the target. Keep two pointers, one pointing to the current node and one for storing the answer. 

Below is the implementation of the above approach:  

C++

// C++ code to find the smallest value greater
// than or equal to N
#include <bits/stdc++.h>
using namespace std;

struct Node {
    int key;
    Node *left, *right;
};

// To create new BST Node
Node* newNode(int item)
{
    Node* temp = new Node;
    temp->key = item;
    temp->left = temp->right = NULL;
    return temp;
}

// To insert a new node in BST
Node* insert(Node* node, int key)
{
    // if tree is empty return new node
    if (node == NULL)
        return newNode(key);

    // if key is less than or greater than
    // node value then recur down the tree
    if (key < node->key)
        node->left = insert(node->left, key);
    else if (key > node->key)
        node->right = insert(node->right, key);

    // return the (unchanged) node pointer
    return node;
}

// Returns smallest value greater than or
// equal to key.
int findFloor(Node* root, int key)
{
    Node *curr = root, *ans = NULL;

    // traverse in the tree
    while (curr) {

        // if the node is smaller than N,
        // move right.
        if (curr->key > key) {
            ans = curr;
            curr = curr->left;
        }


        // if it is equal to N, then it will be
        // the answer
        else if (curr->key == key) {
            ans = curr;
            break;
        }

        else // move to the right of the tree
            curr = curr->right;
    }

    if (ans != NULL)
       return ans->key;

    return -1;
}

// Driver code
int main()
{
    int N = 13;

    Node* root = insert(root, 19);
    insert(root, 2);
    insert(root, 1);
    insert(root, 3);
    insert(root, 12);
    insert(root, 9);
    insert(root, 21);
    insert(root, 25);

    printf("%d", findFloor(root, 15));

    return 0;
}

Java

// Java code to find the smallest value greater
// than or equal to N
class GFG
{
    static class Node
    {
        int key;
        Node left, right;
    };

    // To create new BST Node
    static Node newNode(int item)
    {
        Node temp = new Node();
        temp.key = item;
        temp.left = temp.right = null;
        return temp;
    }

    // To insert a new node in BST
    static Node insert(Node node, int key)
    {
        // if tree is empty return new node
        if (node == null)
        {
            return newNode(key);
        }

        // if key is less than or greater than
        // node value then recur down the tree
        if (key < node.key)
        {
            node.left = insert(node.left, key);
        }
        else if (key > node.key)
        {
            node.right = insert(node.right, key);
        }

        // return the (unchanged) node pointer
        return node;
    }

    // Returns smallest value greater than or
    // equal to key.
    static int findFloor(Node root, int key)
    {
        Node curr = root, ans = null;

        // traverse in the tree
        while (curr != null)
        {

            // if the node is smaller than N,
            // move right.
            if (curr.key > key)
            {
                ans = curr;
                curr = curr.left;
            }

            // if it is equal to N, then it will be
            // the answer
            else if (curr.key == key)
            {
                ans = curr;
                break;
            }
            else // move to the right of the tree
            {
                curr = curr.right;
            }
        }

        if (ans != null)
        {
            return ans.key;
        }
        return -1;
    }

    // Driver code
    public static void main(String[] args)
    {
        int N = 13;

        Node root = new Node();
        insert(root, 19);
        insert(root, 2);
        insert(root, 1);
        insert(root, 3);
        insert(root, 12);
        insert(root, 9);
        insert(root, 21);
        insert(root, 25);

        System.out.printf("%d", findFloor(root, 15));
    }
}

// This code is contributed by Rajput-Ji

Python3

# Python3 code to find the smallest
# value greater than or equal to N
class Node:

    def __init__(self, key):

        self.key = key
        self.left = None
        self.right = None

# To insert a new node in BST
def insert(node: Node, key: int) -> Node:

    # If tree is empty return new node
    if (node is None):
        return Node(key)

    # If key is less than or greater than
    # node value then recur down the tree
    if (key < node.key):
        node.left = insert(node.left, key)
    elif (key > node.key):
        node.right = insert(node.right, key)

    # Return the (unchanged) node pointer
    return node

# Returns smallest value greater than or
# equal to key.
def findFloor(root: Node, key: int) -> int:

    curr = root
    ans = None

    # Traverse in the tree
    while (curr):

        # If the node is smaller than N,
        # move right.
        if (curr.key > key):
            ans = curr
            curr = curr.left

        # If it is equal to N, then
        # it will be the answer
        elif (curr.key == key):
            ans = curr
            break

        else:  # Move to the right of the tree
            curr = curr.right

    if (ans != None):
        return ans.key

    return -1

# Driver code
if __name__ == "__main__":

    N = 13

    root = None
    root = insert(root, 19)
    insert(root, 2)
    insert(root, 1)
    insert(root, 3)
    insert(root, 12)
    insert(root, 9)
    insert(root, 21)
    insert(root, 25)

    print(findFloor(root, 15))

# This code is contributed by sanjeev2552

C#

// C# code to find the smallest value greater
// than or equal to N
using System;
using System.Collections.Generic;

class GFG
{
    class Node
    {
        public int key;
        public Node left, right;
    };

    // To create new BST Node
    static Node newNode(int item)
    {
        Node temp = new Node();
        temp.key = item;
        temp.left = temp.right = null;
        return temp;
    }

    // To insert a new node in BST
    static Node insert(Node node, int key)
    {
        // if tree is empty return new node
        if (node == null)
        {
            return newNode(key);
        }

        // if key is less than or greater than
        // node value then recur down the tree
        if (key < node.key)
        {
            node.left = insert(node.left, key);
        }
        else if (key > node.key)
        {
            node.right = insert(node.right, key);
        }

        // return the (unchanged) node pointer
        return node;
    }

    // Returns smallest value greater than or
    // equal to key.
    static int findFloor(Node root, int key)
    {
        Node curr = root, ans = null;

        // traverse in the tree
        while (curr != null)
        {

            // if the node is smaller than N,
            // move right.
            if (curr.key > key)
            {
                ans = curr;
                curr = curr.left;
            }

            // if it is equal to N, then it will be
            // the answer
            else if (curr.key == key)
            {
                ans = curr;
                break;
            }
            else // move to the right of the tree
            {
                curr = curr.right;
            }
        }

        if (ans != null)
        {
            return ans.key;
        }
        return -1;
    }

    // Driver code
    public static void Main(String[] args)
    {

        Node root = new Node();
        insert(root, 19);
        insert(root, 2);
        insert(root, 1);
        insert(root, 3);
        insert(root, 12);
        insert(root, 9);
        insert(root, 21);
        insert(root, 25);

        Console.Write("{0}", findFloor(root, 15));
    }
}

// This code is contributed by Rajput-Ji

Javascript

<script>

// Javascript code to find the smallest
// value greater than or equal to N
class Node
{
    constructor()
    {
        this.key = 0;
        this.left = null;
        this.right = null;
    }
};

// To create new BST Node
function newNode(item)
{
    var temp = new Node();
    temp.key = item;
    temp.left = temp.right = null;
    return temp;
}

// To insert a new node in BST
function insert(node, key)
{

    // If tree is empty return new node
    if (node == null)
    {
        return newNode(key);
    }

    // If key is less than or greater than
    // node value then recur down the tree
    if (key < node.key)
    {
        node.left = insert(node.left, key);
    }
    else if (key > node.key)
    {
        node.right = insert(node.right, key);
    }

    // Return the (unchanged) node pointer
    return node;
}

// Returns smallest value greater than or
// equal to key.
function findFloor(root, key)
{
    var curr = root, ans = null;

    // Traverse in the tree
    while (curr != null)
    {

        // If the node is smaller than N,
        // move right.
        if (curr.key > key)
        {
            ans = curr;
            curr = curr.left;
        }

        // If it is equal to N, then it will be
        // the answer
        else if (curr.key == key)
        {
            ans = curr;
            break;
        }

        // Move to the right of the tree
        else
        {
            curr = curr.right;
        }
    }
    if (ans != null)
    {
        return ans.key;
    }
    return -1;
}

// Driver code
var root = new Node();
insert(root, 19);
insert(root, 2);
insert(root, 1);
insert(root, 3);
insert(root, 12);
insert(root, 9);
insert(root, 21);
insert(root, 25);

document.write(findFloor(root, 15));

// This code is contributed by rutvik_56

</script>

Output

19

Complexity  Analysis:

• Time complexity: O(N) 
• Auxiliary Space: O(1)