Remove BST keys outside the given range

Given a Binary Search Tree (BST) and a range [min, max], remove all keys which are outside the given range. The modified tree should also be BST. 

Examples:

Input : 

Output:

Explanation: all keys outside the range [-10, 13] are removed and the modified tree is BST.

The idea is

Fix the tree in a Post-order fashion. When we visit a node, we make sure that its left and right sub-trees are already fixed. 

While traversing the tree there are two possible cases for every node. 

1. Node’s key is outside the given range. This case has two sub-cases. 
   1. Node’s key is smaller than the min value. 
   2. Node’s key is greater than the max value. 
2. Node’s key is in range.

We don’t need to do anything for case 2. In case 1, we need to remove the node and change the root of the subtree rooted with this node. 

• In case 1 part 1, we simply remove the root and return the right sub-tree as a new root. 
• In case 1 part 2, we remove the root and return the left sub-tree as a new root.

Below is the implementation of the above approach. 

C++

// A C++ program to remove BST keys
// outside the given range

#include<bits/stdc++.h>
using namespace std;

// A BST node has key, and left and right pointers
struct node
{
    int key;
    struct node *left;
    struct node *right;
};

// Removes all nodes having value outside the
// given range and returns the root of modified tree
node* removeOutsideRange(node *root, int min, int max)
{
   // Base Case
   if (root == NULL)
      return NULL;

   // First fix the left and right subtrees of root
   root->left =  removeOutsideRange(root->left, min, max);
   root->right =  removeOutsideRange(root->right, min, max);

   // Now fix the root.  There are 2 possible cases
   // for root 1.a) Root's key is smaller than min
   // value (root is not in range)
   if (root->key < min)
   {
       node *rChild = root->right;
       delete root;
       return rChild;
   }
   // 1.b) Root's key is greater than max value
   // (root is not in range)
   if (root->key > max)
   {
       node *lChild = root->left;
       delete root;
       return lChild;
   }
   // 2. Root is in range
   return root;
}

// A utility function to create a new BST
// node with key as given num
node* newNode(int num)
{
    node* temp = new node;
    temp->key = num;
    temp->left = temp->right = NULL;
    return temp;
}

// A utility function to insert a given key to BST
node* insert(node* root, int key)
{
    if (root == NULL)
       return newNode(key);
    if (root->key > key)
       root->left = insert(root->left, key);
    else
       root->right = insert(root->right, key);
    return root;
}

// Utility function to traverse the binary
// tree after conversion
void inorderTraversal(node* root)
{
    if (root)
    {
        inorderTraversal( root->left );
        cout << root->key << " ";
        inorderTraversal( root->right );
    }
}

// Driver program to test above functions
int main()
{
    node* root = NULL;
    root = insert(root, 6);
    root = insert(root, -13);
    root = insert(root, 14);
    root = insert(root, -8);
    root = insert(root, 15);
    root = insert(root, 13);
    root = insert(root, 7);

    cout << "Inorder traversal of the given tree is: ";
    inorderTraversal(root);

    root = removeOutsideRange(root, -10, 13);

    cout << "\nInorder traversal of the modified tree is: ";
    inorderTraversal(root);

    return 0;
}

Java

// A Java program to remove BST
// keys outside the given range

import java.math.BigDecimal;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;

class GFG
{
    // Removes all nodes having value
    // outside the given range and
    // returns the root of modified tree
    private static Node removeOutsideRange(Node root,
                                           int min, int max)
    {
        // BASE CASE
        if(root == null)
        {
            return null;
        }

        // FIRST FIX THE LEFT AND
        // RIGHT SUBTREE OF ROOT
        root.left = removeOutsideRange(root.left,
                                       min, max);
        root.right = removeOutsideRange(root.right,
                                        min, max);

        // NOW FIX THE ROOT. THERE ARE
        // TWO POSSIBLE CASES FOR THE ROOT
        // 1. a) Root's key is smaller than
        // min value(root is not in range)
        if(root.key < min)
        {
            Node rchild = root.right;
            root = null;
            return rchild;
        }

        // 1. b) Root's key is greater than
        // max value (Root is not in range)
        if(root.key > max)
        {
            Node lchild = root.left;
            root = null;
            return lchild;
        }

        // 2. Root in range
        return root;
    }

    public static Node newNode(int num)
    {
        Node temp = new Node();
        temp.key = num;
        temp.left = null;
        temp.right = null;
        return temp;
    }

    public static Node insert(Node root,
                              int key)
    {
        if(root == null)
        {
            return newNode(key);
        }
        if(root.key > key)
        {
            root.left = insert(root.left, key);
        }
        else
        {
            root.right = insert(root.right, key);
        }
        return root;
    }

    private static void inorderTraversal(Node root)
    {
        if(root != null)
        {
            inorderTraversal(root.left);
            System.out.print(root.key + " ");
            inorderTraversal(root.right);
        }
    }

    // Driver code
    public static void main(String[] args)
    {
        Node root = null;
        root = insert(root, 6);
        root = insert(root, -13);
        root = insert(root, 14);
        root = insert(root, -8);
        root = insert(root, 15);
        root = insert(root, 13);
        root = insert(root, 7);

        System.out.print("Inorder Traversal of " +
                           "the given tree is: ");
        inorderTraversal(root);

        root = removeOutsideRange(root, -10, 13);

        System.out.print("\nInorder traversal of " +
                           "the modified tree: ");
        inorderTraversal(root);
    }
}

class Node
{
    int key;
    Node left;
    Node right;
}

// This code is contributed by Divya

Python3

# Python3 program to remove BST keys
# outside the given range

# A BST node has key, and left and right
# pointers. A utility function to create
# a new BST node with key as given num
class newNode:

    # Constructor to create a new node
    def __init__(self, data):
        self.key = data
        self.left = None
        self.right = None

# Removes all nodes having value outside
# the given range and returns the root
# of modified tree
def removeOutsideRange(root, Min, Max):

    # Base Case
    if root == None:
        return None

    # First fix the left and right
    # subtrees of root
    root.left = removeOutsideRange(root.left,
                                   Min, Max)
    root.right = removeOutsideRange(root.right,
                                    Min, Max)

    # Now fix the root. There are 2
    # possible cases for root
    # 1.a) Root's key is smaller than
    #      min value (root is not in range)
    if root.key < Min:
        rChild = root.right
        return rChild

    # 1.b) Root's key is greater than max
    #      value (root is not in range)
    if root.key > Max:
        lChild = root.left
        return lChild

    # 2. Root is in range
    return root


# A utility function to insert a given
# key to BST
def insert(root, key):
    if root == None:
        return newNode(key)
    if root.key > key:
        root.left = insert(root.left, key)
    else:
        root.right = insert(root.right, key)
    return root

# Utility function to traverse the binary
# tree after conversion
def inorderTraversal(root):
    if root:
        inorderTraversal( root.left)
        print(root.key, end = " ")
        inorderTraversal( root.right)

# Driver Code
if __name__ == '__main__':
    root = None
    root = insert(root, 6)
    root = insert(root, -13)
    root = insert(root, 14)
    root = insert(root, -8)
    root = insert(root, 15)
    root = insert(root, 13)
    root = insert(root, 7)

    print("Inorder traversal of the given tree is:",
                                          end = " ")
    inorderTraversal(root)

    root = removeOutsideRange(root, -10, 13)
    print()
    print("Inorder traversal of the modified tree is:",
                                             end = " ")
    inorderTraversal(root)

# This code is contributed by PranchalK

C#

// A C# program to remove BST
// keys outside the given range

using System;

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

public class GFG
{
    // Removes all nodes having value
    // outside the given range and
    // returns the root of modified tree
    private static Node removeOutsideRange(Node root,
                                        int min, int max)
    {
        // BASE CASE
        if(root == null)
        {
            return null;
        }

        // FIRST FIX THE LEFT AND
        // RIGHT SUBTREE OF ROOT
        root.left = removeOutsideRange(root.left,
                                    min, max);
        root.right = removeOutsideRange(root.right,
                                        min, max);

        // NOW FIX THE ROOT. THERE ARE
        // TWO POSSIBLE CASES FOR THE ROOT
        // 1. a) Root's key is smaller than
        // min value(root is not in range)
        if(root.key < min)
        {
            Node rchild = root.right;
            root = null;
            return rchild;
        }

        // 1. b) Root's key is greater than
        // max value (Root is not in range)
        if(root.key > max)
        {
            Node lchild = root.left;
            root = null;
            return lchild;
        }

        // 2. Root in range
        return root;
    }

    public static Node newNode(int num)
    {
        Node temp = new Node();
        temp.key = num;
        temp.left = null;
        temp.right = null;
        return temp;
    }

    public static Node insert(Node root,
                            int key)
    {
        if(root == null)
        {
            return newNode(key);
        }
        if(root.key > key)
        {
            root.left = insert(root.left, key);
        }
        else
        {
            root.right = insert(root.right, key);
        }
        return root;
    }

    private static void inorderTraversal(Node root)
    {
        if(root != null)
        {
            inorderTraversal(root.left);
            Console.Write(root.key + " ");
            inorderTraversal(root.right);
        }
    }

    // Driver code
    public static void Main(String[] args)
    {
        Node root = null;
        root = insert(root, 6);
        root = insert(root, -13);
        root = insert(root, 14);
        root = insert(root, -8);
        root = insert(root, 15);
        root = insert(root, 13);
        root = insert(root, 7);

        Console.Write("Inorder Traversal of " +
                        "the given tree is: ");
        inorderTraversal(root);

        root = removeOutsideRange(root, -10, 13);

        Console.Write("\nInorder traversal of " +
                        "the modified tree: ");
        inorderTraversal(root);
    }
}

// This code has been contributed
// by PrinciRaj1992

Javascript

<script>

// A JavaScript program to remove BST
// keys outside the given range


class Node {
    constructor() {
        this.key = 0;
        this.left = null;
        this.right = null;
    }
}
// Removes all nodes having value
    // outside the given range and
    // returns the root of modified tree
     function removeOutsideRange(root , min , max) {
        // BASE CASE
        if (root == null) {
            return null;
        }

        // FIRST FIX THE LEFT AND
        // RIGHT SUBTREE OF ROOT
        root.left =
        removeOutsideRange(root.left, min, max);
        root.right =
        removeOutsideRange(root.right, min, max);

        // NOW FIX THE ROOT. THERE ARE
        // TWO POSSIBLE CASES FOR THE ROOT
        // 1. a) Root's key is smaller than
        // min value(root is not in range)
        if (root.key < min) {
    var rchild = root.right;
            root = null;
            return rchild;
        }

        // 1. b) Root's key is greater than
        // max value (Root is not in range)
        if (root.key > max) {
    var lchild = root.left;
            root = null;
            return lchild;
        }

        // 2. Root in range
        return root;
    }

    function newNode(num) {
var temp = new Node();
        temp.key = num;
        temp.left = null;
        temp.right = null;
        return temp;
    }

    function insert(root , key) {
        if (root == null) {
            return newNode(key);
        }
        if (root.key > key) {
            root.left = insert(root.left, key);
        } else {
            root.right = insert(root.right, key);
        }
        return root;
    }

     function inorderTraversal(root) {
        if (root != null) {
            inorderTraversal(root.left);
            document.write(root.key + " ");
            inorderTraversal(root.right);
        }
    }

    // Driver code

var root = null;
        root = insert(root, 6);
        root = insert(root, -13);
        root = insert(root, 14);
        root = insert(root, -8);
        root = insert(root, 15);
        root = insert(root, 13);
        root = insert(root, 7);

        document.write("Inorder Traversal of " +
        "the given tree is: ");
        inorderTraversal(root);

        root = removeOutsideRange(root, -10, 13);

        document.write("<br/>Inorder traversal of " +
        "the modified tree: ");
        inorderTraversal(root);

// This code is contributed by todaysgaurav

</script>

Output

Inorder traversal of the given tree is: -13 -8 6 7 13 14 15 
Inorder traversal of the modified tree is: -8 6 7 13 

Time Complexity: O(N)
Auxiliary Space: O(1)