Count nodes having smallest value in the path from root to itself in a Binary Tree

Given a Binary Tree, the task is to count the number of nodes in the given Binary Tree such that the path from the root to that node contains node with value greater than or equal to that node.

Examples:

Input:
               6
             /   \
            7     4
           / \   / \
          3   7 1   2

Output: 5
Explanation:
Root node 6 is considered as its the only node 
in the path from root to itself.
Node 4 has the minimum value in it's path 6->4.
Node 1 has the minimum value in it's path 6->4->1.
Node 2 has the minimum value in it's path 6->4->2.
Node 3 has the minimum value in it's path 6->7->3.

Input:
               8
             /   \
            6     5
           / \   / \
          6   7 3   9

Output: 5
Explanation:
Root node 8 is considered as its the only node
in the path from root to itself.
Node 6 has the minimum value in it's path 8->6.
Node 6 has the minimum value in it's path 8->6->6.
Node 5 has the minimum value in it's path 8->5.
Node 3 has the minimum value in it's path 8->5->3.

Approach: The idea is to do Preorder traversal on the given Binary Tree. Follow the steps below to solve the problem:

1. Create a function to calculate the number of nodes that satisfy the given conditions.
2. If the current node is NULL then return to the previous node.
3. Use a variable minNodeVal to store the minimum node value along the path from the root to the current node.
4. If the value of the current node is less than or equal to minNodeVal then increase the final count by 1 and update the value of minNodeVal.
5. Call the function for the left and right child of the current node and repeat this process for every node to get the total count of the required nodes.

Below is the implementation of the above approach:

C++

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

// Structure of a tree node
struct Node {
    int key;
    Node *left, *right;
};

// Function to create new tree node
Node* newNode(int key)
{
    Node* temp = new Node;
    temp->key = key;
    temp->left = temp->right = NULL;
    return temp;
}

// Function to find the total
// number of required nodes
void countReqNodes(Node* root,
                   int minNodeVal, int& ans)
{
    // If current node is null then
    // return to the parent node
    if (root == NULL)
        return;

    // Check if current node value is
    // less than or equal to minNodeVal
    if (root->key <= minNodeVal) {

        // Update the value of minNodeVal
        minNodeVal = root->key;

        // Update the count
        ans++;
    }

    // Go to the left subtree
    countReqNodes(root->left,
                  minNodeVal, ans);

    // Go to the right subtree
    countReqNodes(root->right,
                  minNodeVal, ans);
}

// Driver Code
int main()
{
    /* Binary Tree creation
               8
             /   \
            /     \
           6       5
          / \     /  \
         /   \   /    \
        6     7 3      9
    */

    Node* root = newNode(8);
    root->left = newNode(6);
    root->right = newNode(5);
    root->left->left = newNode(6);
    root->left->right = newNode(7);
    root->right->left = newNode(3);
    root->right->right = newNode(9);

    int ans = 0, minNodeVal = INT_MAX;

    // Function Call
    countReqNodes(root, minNodeVal, ans);

    // Print the result
    cout << ans;

    return 0;
}

Java

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

class GFG{

// Structure of a tree node
static class Node
{
    int key;
    Node left, right;
};

// Function to create new tree node
static Node newNode(int key)
{
    Node temp = new Node();
    temp.key = key;
    temp.left = temp.right = null;
    return temp;
}
static int ans;

// Function to find the total
// number of required nodes
static void countReqNodes(Node root,
                          int minNodeVal)
{

    // If current node is null then
    // return to the parent node
    if (root == null)
        return;

    // Check if current node value is
    // less than or equal to minNodeVal
    if (root.key <= minNodeVal)
    {

        // Update the value of minNodeVal
        minNodeVal = root.key;

        // Update the count
        ans++;
    }

    // Go to the left subtree
    countReqNodes(root.left,
                  minNodeVal);

    // Go to the right subtree
    countReqNodes(root.right,
                  minNodeVal);
}

// Driver Code
public static void main(String[] args)
{

    /* Binary Tree creation
               8
             /   \
            /     \
           6       5
          / \     /  \
         /   \   /    \
        6     7 3      9
    */

    Node root = newNode(8);
    root.left = newNode(6);
    root.right = newNode(5);
    root.left.left = newNode(6);
    root.left.right = newNode(7);
    root.right.left = newNode(3);
    root.right.right = newNode(9);

    int  minNodeVal = Integer.MAX_VALUE;
    ans = 0;

    // Function Call
    countReqNodes(root, minNodeVal);

    // Print the result
    System.out.print(ans);
}
}

// This code is contributed by Amit Katiyar

Python3

# Python3 program for the above approach
import sys

ans = 0

# Class of a tree node
class Node:

    def __init__(self, key):

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

# Function to find the total
# number of required nodes
def countReqNodes(root, minNodeVal):

    global ans

    # If current node is null then
    # return to the parent node
    if root == None:
        return

    # Check if current node value is
    # less than or equal to minNodeVal
    if root.key <= minNodeVal:

        # Update the value of minNodeVal
        minNodeVal = root.key

        # Update the count
        ans += 1

    # Go to the left subtree
    countReqNodes(root.left, minNodeVal)

    # Go to the right subtree
    countReqNodes(root.right, minNodeVal)

# Driver Code
if __name__ == '__main__':

     # Binary Tree creation
     #           8
     #         /   \
     #        /     \
     #       6       5
     #      / \     /  \
     #     /   \   /    \
     #    6     7 3      9
     #

    root = Node(8)

    root.left = Node(6)
    root.right = Node(5)
    root.left.left = Node(6)
    root.left.right = Node(7)
    root.right.left = Node(3)
    root.right.right = Node(9)

    minNodeVal = sys.maxsize

    # Function Call
    countReqNodes(root, minNodeVal)

    # Print the result
    print(ans)

# This code is contributed by mohit kumar 29

C#

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

class GFG{

// Structure of a tree node
public class Node
{
    public int key;
    public Node left, right;
};

// Function to create new tree node
static Node newNode(int key)
{
    Node temp = new Node();
    temp.key = key;
    temp.left = temp.right = null;
    return temp;
}

static int ans;

// Function to find the total
// number of required nodes
static void countReqNodes(Node root,
                          int minNodeVal)
{

    // If current node is null then
    // return to the parent node
    if (root == null)
        return;

    // Check if current node value is
    // less than or equal to minNodeVal
    if (root.key <= minNodeVal)
    {

        // Update the value of minNodeVal
        minNodeVal = root.key;

        // Update the count
        ans++;
    }

    // Go to the left subtree
    countReqNodes(root.left,
                  minNodeVal);

    // Go to the right subtree
    countReqNodes(root.right,
                  minNodeVal);
}

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

    /* Binary Tree creation
               8
             /   \
            /     \
           6       5
          / \     /  \
         /   \   /    \
        6     7 3      9
    */

    Node root = newNode(8);
    root.left = newNode(6);
    root.right = newNode(5);
    root.left.left = newNode(6);
    root.left.right = newNode(7);
    root.right.left = newNode(3);
    root.right.right = newNode(9);

    int  minNodeVal = int.MaxValue;
    ans = 0;

    // Function Call
    countReqNodes(root, minNodeVal);

    // Print the result
    Console.Write(ans);
}
}

// This code is contributed by Amit Katiyar

Javascript

<script>

// Javascript program for the above approach

// Structure of tree node
class Node
{
    constructor(key)
    {

        this.left = null;
        this.right = null;
        this.key = key;
    }
}

// Function to create new tree node
function newNode(key)
{
    let temp = new Node(key);
    return temp;
}

let ans;

// Function to find the total
// number of required nodes
function countReqNodes(root, minNodeVal)
{

    // If current node is null then
    // return to the parent node
    if (root == null)
        return;

    // Check if current node value is
    // less than or equal to minNodeVal
    if (root.key <= minNodeVal)
    {

        // Update the value of minNodeVal
        minNodeVal = root.key;

        // Update the count
        ans++;
    }

    // Go to the left subtree
    countReqNodes(root.left,
                  minNodeVal);

    // Go to the right subtree
    countReqNodes(root.right,
                  minNodeVal);
}

// Driver code

/* Binary Tree creation
           8
         /   \
        /     \
       6       5
      / \     /  \
     /   \   /    \
    6     7 3      9
*/
let root = newNode(8);
root.left = newNode(6);
root.right = newNode(5);
root.left.left = newNode(6);
root.left.right = newNode(7);
root.right.left = newNode(3);
root.right.right = newNode(9);

let  minNodeVal = Number.MAX_VALUE;
ans = 0;

// Function Call
countReqNodes(root, minNodeVal);

// Print the result
document.write(ans);

// This code is contributed by suresh07

</script>

Output:

5

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