Product of all nodes in a Binary Tree

Last Updated : 11 Jul, 2025

Given a Binary Tree. The task is to write a program to find the product of all of the nodes of the given binary tree.

In the above binary tree, 

Product = 15*10*8*12*20*16*25 = 115200000

The idea is to recursively: 

  • Find the product of the left subtree.
  • Find the product of the right subtree.
  • Multiply the product of left and right subtrees with the current node's data and return.

Below is the implementation of the above approach: 

C++ 
// Program to print product of all
// the nodes of a binary tree
#include <iostream>
using namespace std;

// Binary Tree Node
struct Node {
    int key;
    Node *left, *right;
};

/* utility that allocates a new Node 
   with the given key */
Node* newNode(int key)
{
    Node* node = new Node;
    node->key = key;
    node->left = node->right = NULL;
    return (node);
}

// Function to find product of
// all the nodes
int productBT(Node* root)
{
    if (root == NULL)
        return 1;

    return (root->key * productBT(root->left) * productBT(root->right));
}

// Driver Code
int main()
{
    // Binary Tree is:
    //       1
    //      /  \
    //     2    3
    //    / \  / \
    //   4   5 6  7
    //          \
    //           8
    Node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->right->left = newNode(6);
    root->right->right = newNode(7);
    root->right->left->right = newNode(8);

    int prod = productBT(root);

    cout << "Product of all the nodes is: "
         << prod << endl;

    return 0;
}
Java 
  
// Java Program to print product of all
// the nodes of a binary tree 
import java.util.*;
class solution
{

// Binary Tree Node
static class Node {
    int key;
    Node left, right;
};

/* utility that allocates a new Node 
   with the given key */
static Node newNode(int key)
{
    Node node = new Node();
    node.key = key;
    node.left = node.right = null;
    return (node);
}

// Function to find product of
// all the nodes
static int productBT(Node root)
{
    if (root == null)
        return 1;

    return (root.key * productBT(root.left) * productBT(root.right));
}

// Driver Code
public static void main(String args[])
{
    // Binary Tree is:
    //       1
    //      /  \
    //     2    3
    //    / \  / \
    //   4   5 6  7
    //          \
    //           8
    Node root = newNode(1);
    root.left = newNode(2);
    root.right = newNode(3);
    root.left.left = newNode(4);
    root.left.right = newNode(5);
    root.right.left = newNode(6);
    root.right.right = newNode(7);
    root.right.left.right = newNode(8);

    int prod = productBT(root);

    System.out.println( "Product of all the nodes is: "+prod);

}
}
//contributed by Arnab Kundu
Python3 
# Python3 Program to print product of 
# all the nodes of a binary tree 

# Binary Tree Node 

""" utility that allocates a new Node 
with the given key """
class newNode: 

    # Construct to create a new node 
    def __init__(self, key): 
        self.key = key
        self.left = None
        self.right = None
        
# Function to find product of 
# all the nodes 
def productBT( root) :

    if (root == None):
        return 1

    return (root.key * productBT(root.left) * 
                       productBT(root.right)) 

# Driver Code 
if __name__ == '__main__':
    
    # Binary Tree is: 
    #     1 
    #     / \ 
    #     2 3 
    # / \ / \ 
    # 4 5 6 7 
    #         \ 
    #         8 
    root = newNode(1) 
    root.left = newNode(2) 
    root.right = newNode(3) 
    root.left.left = newNode(4) 
    root.left.right = newNode(5) 
    root.right.left = newNode(6) 
    root.right.right = newNode(7) 
    root.right.left.right = newNode(8) 

    prod = productBT(root) 

    print("Product of all the nodes is:", prod)
    
# This code is contributed by
# Shubham Singh(SHUBHAMSINGH10)
C# 
// C# Program to print product of all
// the nodes of a binary tree 
using System;

class GFG
{

    // Binary Tree Node
    class Node
    {
        public int key;
        public Node left, right;
    };

    /* utility that allocates a new Node 
    with the given key */
    static Node newNode(int key)
    {
        Node node = new Node();
        node.key = key;
        node.left = node.right = null;
        return (node);
    }

    // Function to find product of
    // all the nodes
    static int productBT(Node root)
    {
        if (root == null)
            return 1;

        return (root.key * productBT(root.left) *
                        productBT(root.right));
    }

    // Driver Code
    public static void Main()
    {
        // Binary Tree is:
        //     1
        //     / \
        //     2 3
        // / \ / \
        // 4 5 6 7
        //         \
        //         8
        Node root = newNode(1);
        root.left = newNode(2);
        root.right = newNode(3);
        root.left.left = newNode(4);
        root.left.right = newNode(5);
        root.right.left = newNode(6);
        root.right.right = newNode(7);
        root.right.left.right = newNode(8);

        int prod = productBT(root);

        Console.WriteLine( "Product of all " +
                        "the nodes is: " + prod);
    }
}

/* This code is contributed PrinciRaj1992 */
JavaScript 
  
<script>
// javascript Program to print product of all
// the nodes of a binary tree 
// Binary Tree Node
class Node {
    constructor(val) {
        this.key = val;
        this.left = null;
        this.right = null;
    }
}
/* utility that allocates a new Node 
   with the given key */
function newNode(key)
{
    var node = new Node();
    node.key = key;
    node.left = node.right = null;
    return (node);
}

// Function to find product of
// all the nodes
function productBT(root)
{
    if (root == null)
        return 1;

    return (root.key * productBT(root.left) * productBT(root.right));
}

// Driver Code

    // Binary Tree is:
    //       1
    //      /  \
    //     2    3
    //    / \  / \
    //   4   5 6  7
    //          \
    //           8
    var root = newNode(1);
    root.left = newNode(2);
    root.right = newNode(3);
    root.left.left = newNode(4);
    root.left.right = newNode(5);
    root.right.left = newNode(6);
    root.right.right = newNode(7);
    root.right.left.right = newNode(8);

    var prod = productBT(root);

    document.write( "Product of all the nodes is: "+prod);

// This code contributed by gauravrajput1 
</script>
JavaScript 
  
<script>
// javascript Program to print product of all
// the nodes of a binary tree 
// Binary Tree Node
class Node {
    constructor(val) {
        this.key = val;
        this.left = null;
        this.right = null;
    }
}

/* utility that allocates a new Node 
   with the given key */
function newNode(key)
{
    var node = new Node();
    node.key = key;
    node.left = node.right = null;
    return (node);
}

// Function to find product of
// all the nodes
function productBT(root)
{
    if (root == null)
        return 1;

    return (root.key * productBT(root.left) * productBT(root.right));
}

// Driver Code

    // Binary Tree is:
    //       1
    //      /  \
    //     2    3
    //    / \  / \
    //   4   5 6  7
    //          \
    //           8
    var root = newNode(1);
    root.left = newNode(2);
    root.right = newNode(3);
    root.left.left = newNode(4);
    root.left.right = newNode(5);
    root.right.left = newNode(6);
    root.right.right = newNode(7);
    root.right.left.right = newNode(8);

    var prod = productBT(root);

    document.write( "Product of all the nodes is: "+prod);

// This code contributed by umadevi9616 
</script>

Output
Product of all the nodes is: 40320

Complexity Analysis

  • Time complexity : O(n)
    • As we are traversing the tree only once.
  • Auxiliary Complexity: O(h)
    • Here h is the height of the tree. The extra space is used in recursion call stack. In the worst case(when the tree is skewed) this can go upto O(n).
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