Count of nodes in a binary tree having their nodes in range [L, R]

Given a Binary Tree consisting of N nodes and two positive integers L and R, the task is to find the count of nodes having their value in the range [L, R].

Examples:

Input: Tree in the image below, L = 4, R = 15

Output: 2
Explanation: The nodes in the given Tree that lies in the range [4, 15] are {5, 10}.

Input: Tree in the image below, L = 8, R = 20

Output: 4

Approach: The given problem can be solved by performing any Tree Traversal and maintaining the count of nodes having their values in the range [L, R]. This article uses a DFS traversal.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Class for node of the Tree
class Node {
public:
    int val;
    Node *left, *right;
};

// Function to create a new Binary node
Node* newNode(int item)
{
    Node* temp = new Node();
    temp->val = item;
    temp->left = temp->right = NULL;

    // Return the newly created node
    return temp;
}

// Function to find the count of
// nodes in the given tree with
// their value in the range [1, N]
int countRange(Node* root, int low,
               int high, int count)
{
    int val = 0;

    // If root exists
    if (root != NULL) {

        val += root->val >= low
                       && root->val <= high
                   ? 1
                   : 0;
    }

    // Otherwise return
    else {
        return 0;
    }

    // Add count of current node,
    // count in left subtree, and
    // count in the right subtree
    count = val
            + countRange(root->left,
                         low, high, count)
            + countRange(root->right,
                         low, high, count);

    // Return Answer
    return count;
}

// Driver Code
int main()
{
    Node* root = NULL;
    root = newNode(20);
    root->left = newNode(2);
    root->right = newNode(10);
    root->right->left = newNode(2);
    root->right->right = newNode(5);

    int L = 4, R = 15;
    cout << countRange(root, L, R, 0);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;
class GFG{

  // Class for node of the Tree
  static class Node {

    int val;
    Node left, right;
  };

  // Function to create a new Binary node
  static Node newNode(int item)
  {
    Node temp = new Node();
    temp.val = item;
    temp.left = temp.right = null;

    // Return the newly created node
    return temp;
  }

  // Function to find the count of
  // nodes in the given tree with
  // their value in the range [1, N]
  static int countRange(Node root, int low,
                        int high, int count)
  {
    int val = 0;

    // If root exists
    if (root != null) {

      val += root.val >= low
        && root.val <= high
        ? 1
        : 0;
    }

    // Otherwise return
    else {
      return 0;
    }

    // Add count of current node,
    // count in left subtree, and
    // count in the right subtree
    count = val
      + countRange(root.left,
                   low, high, count)
      + countRange(root.right,
                   low, high, count);

    // Return Answer
    return count;
  }

  // Driver Code
  public static void main(String[] args)
  {
    Node root = null;
    root = newNode(20);
    root.left = newNode(2);
    root.right = newNode(10);
    root.right.left = newNode(2);
    root.right.right = newNode(5);

    int L = 4, R = 15;
    System.out.print(countRange(root, L, R, 0));
  }
}

// This code is contributed by shikhasingrajput

Python3

# Python program for the above approach

# Class for Node of the Tree
class Node:
    def __init__(self, val):
        self.val = val;
        self.left = None;
        self.right = None;

# Function to create a new Binary Node
def newNode(item):
    temp = Node(item);

    # Return the newly created Node
    return temp;

# Function to find the count of
# Nodes in the given tree with
# their value in the range [1, N]
def countRange(root, low, high, count):
    val = 0;

    # If root exists
    if (root != None):

        val += 1 if(root.val >= low and root.val <= high) else 0;


    # Otherwise return
    else:
        return 0;

    # Add count of current Node,
    # count in left subtree, and
    # count in the right subtree
    count = val + countRange(root.left, low, high, count) + countRange(root.right, low, high, count);

    # Return Answer
    return count;


# Driver Code
if __name__ == '__main__':
    root = None;
    root = newNode(20);
    root.left = newNode(2);
    root.right = newNode(10);
    root.right.left = newNode(2);
    root.right.right = newNode(5);

    L = 4;
    R = 15;
    print(countRange(root, L, R, 0));

# This code is contributed by 29AjayKumar

C#

// C# program for the above approach
using System;

public class GFG{

  // Class for node of the Tree
  class Node {

    public int val;
    public Node left, right;
  };

  // Function to create a new Binary node
  static Node newNode(int item)
  {
    Node temp = new Node();
    temp.val = item;
    temp.left = temp.right = null;

    // Return the newly created node
    return temp;
  }

  // Function to find the count of
  // nodes in the given tree with
  // their value in the range [1, N]
  static int countRange(Node root, int low,
                        int high, int count)
  {
    int val = 0;

    // If root exists
    if (root != null) {

      val += root.val >= low
        && root.val <= high
        ? 1
        : 0;
    }

    // Otherwise return
    else {
      return 0;
    }

    // Add count of current node,
    // count in left subtree, and
    // count in the right subtree
    count = val
      + countRange(root.left,
                   low, high, count)
      + countRange(root.right,
                   low, high, count);

    // Return Answer
    return count;
  }

  // Driver Code
  public static void Main(String[] args)
  {
    Node root = null;
    root = newNode(20);
    root.left = newNode(2);
    root.right = newNode(10);
    root.right.left = newNode(2);
    root.right.right = newNode(5);

    int L = 4, R = 15;
    Console.Write(countRange(root, L, R, 0));
  }
}

// This code is contributed by shikhasingrajput

Javascript

<script>
      // JavaScript code for the above approach

      // Class for node of the Tree
      class Node {

          constructor(val1) {
              this.val = val1;
              this.left = null;
              this.right = null;
          }
      };

      // Function to find the count of
      // nodes in the given tree with
      // their value in the range [1, N]
      function countRange(root, low,
          high, count) {
          let val = 0;

          // If root exists
          if (root != null) {

              val += root.val >= low
                  && root.val <= high
                  ? 1
                  : 0;
          }

          // Otherwise return
          else {
              return 0;
          }

          // Add count of current node,
          // count in left subtree, and
          // count in the right subtree
          count = val
              + countRange(root.left,
                  low, high, count)
              + countRange(root.right,
                  low, high, count);

          // Return Answer
          return count;
      }

      // Driver Code
      let root = null;
      root = new Node(20);
      root.left = new Node(2);
      root.right = new Node(10);
      root.right.left = new Node(2);
      root.right.right = new Node(5);

      let L = 4, R = 15;
      document.write(countRange(root, L, R, 0));

// This code is contributed by Potta Lokesh
  </script>

Output

2

Time Complexity : O(n), where n is the number of nodes in the tree
Auxiliary Space: O(h), where h is the height of the tree.

Another Approach(Iterative): 
The given problem can be solved by using the Level Order Traversal

. Follow the steps below to solve the problem:

1) Create a queue(q) and initialize count variable with 0, and store the nodes in q along wise level order and iterate for next level.
2) Perform level order traversal and check if current node value lie in range then increment the count variable.
3) After completing the above steps, return count variable.

Below is the implementation of above approach:

C++

// C++ program for the above approach
#include<bits/stdc++.h>
using namespace std;

// struct of binary tree node
struct Node{
    int data;
    Node* left;
    Node* right;
};

// function to create a new node
Node* newNode(int data){
    Node* temp = new Node();
    temp->data = data;
    temp->left = temp->right = NULL;
    return temp;
}

// Function to find the count of
// nodes in the given tree with
// their value in the range [1, N]
int countRange(Node* root, int low, int high){
    int count = 0;

    // if root exists
    if(root == NULL) return count;
    queue<Node*> q;
    q.push(root);
    while(!q.empty()){
        Node* temp = q.front();
        q.pop();
        if(temp->data <= high && temp->data >= low){
            count++;
        }
        if(temp->left != NULL) q.push(temp->left);
        if(temp->right != NULL) q.push(temp->right);
    }
    return count;
}

//driver code
int main(){
    Node *root = newNode(20);
    root->left = newNode(2);
    root->right = newNode(10);
    root->right->left = newNode(2);
    root->right->right = newNode(5);

    int L = 4, R = 15;
    cout << countRange(root, L, R);

    return 0;
}

// This code is contributed by Kirti Agarwal(kirtiagarwal23121999)

Output

2

Time Complexity: O(N) where N is the number of nodes in given binary tree.
Auxiliary Space: O(N) due to queue data structure.