Product of nodes at k-th level in a tree represented as string

Difficulty Level : Medium
Last Updated : 17 May, 2021

Given an integer ‘K’ and a binary tree in string format. Every node of a tree has value in range from 0 to 9. We need to find product of elements at K-th level from root. The root is at level 0.
Note : Tree is given in the form: (node value(left subtree)(right subtree))
Examples:

Input : tree = "(0(5(6()())(4()(9()())))(7(1()())(3()())))" 
        k = 2
Output : 72
Its tree representation is shown below

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

Elements at level k = 2 are 6, 4, 1, 3
sum of the digits of these elements = 6 * 4 * 1 * 3 = 72 


Input : tree = "(8(3(2()())(6(5()())()))(5(10()())(7(13()())())))" 
        k = 3
Output : 15
Elements at level k = 3 are 5, 1 and 3
sum of digits of these elements = 5 * 1 * 3 = 15

Approach :

1. Input 'tree' in string format and level k
2. Initialize level = -1 and product = 1
3. for each character 'ch' in 'tree'
   3.1  if ch == '(' then
        --> level++
   3.2  else if ch == ')' then
        --> level--
   3.3  else
        if level == k then
           product = product * (ch-'0')
4. Print product

C++

// C++ implementation to find product of
// digits of elements at k-th level
#include <bits/stdc++.h>
using namespace std;
 
// Function to find product of digits
// of elements at k-th level
int productAtKthLevel(string tree, int k)
{
    int level = -1;
    int product = 1; // Initialize result
    int n = tree.length();
 
    for (int i = 0; i < n; i++) {
        // increasing level number
        if (tree[i] == '(')
            level++;
 
        // decreasing level number
        else if (tree[i] == ')')
            level--;
 
        else {
            // check if current level is
            // the desired level or not
            if (level == k)
                product *= (tree[i] - '0');
        }
    }
 
    // required product
    return product;
}
 
// Driver program
int main()
{
    string tree = "(0(5(6()())(4()(9()())))(7(1()())(3()())))";
    int k = 2;
    cout << productAtKthLevel(tree, k);
    return 0;
}

Java

// Java implementation to find product of
// digits of elements at k-th level
 
class GFG
{
    // Function to find product of digits
    // of elements at k-th level
    static int productAtKthLevel(String tree, int k)
    {
        int level = -1;
         
        // Initialize result
        int product = 1;
         
        int n = tree.length();
     
        for (int i = 0; i < n; i++)
        {
            // increasing level number
            if (tree.charAt(i) == '(')
                level++;
     
            // decreasing level number
            else if (tree.charAt(i) == ')')
                level--;
     
            else
            {
                // check if current level is
                // the desired level or not
                if (level == k)
                    product *= (tree.charAt(i) - '0');
            }
        }
     
        // required product
        return product;
    }
     
    // Driver program
    public static void main(String[] args)
    {
        String tree = "(0(5(6()())(4()(9()())))(7(1()())(3()())))";
        int k = 2;
        System.out.println(productAtKthLevel(tree, k));
    }
}
 
// This code is contributed
// by Smitha Dinesh Semwal.

Python3

# Python 3 implementation
# to find product of
# digits of elements
# at k-th level
 
# Function to find
# product of digits
# of elements at
# k-th level
def productAtKthLevel(tree, k):
 
    level = -1
         
        # Initialize result
    product = 1
    n = len(tree)
 
    for i in range(0, n):
 
        # increasing level number
        if (tree[i] == '('):
            level+=1
 
        # decreasing level number
        elif (tree[i] == ')'):
            level-=1
 
        else:
            # check if current level is
            # the desired level or not
            if (level == k):
                product *= (int(tree[i]) - int('0'))
         
     
 
    # required product
    return product
 
 
# Driver program
tree = "(0(5(6()())(4()(9()())))(7(1()())(3()())))"
k = 2
 
print(productAtKthLevel(tree, k))
 
# This code is contributed by
# Smitha Dinesh Semwal

C#

// C# implementation to find
// product of digits of
// elements at k-th level
using System;
 
class GFG
{
    // Function to find product
    // of digits of elements
    // at k-th level
    static int productAtKthLevel(string tree,
                                 int k)
    {
        int level = -1;
         
        // Initialize result
        int product = 1;
         
        int n = tree.Length;
     
        for (int i = 0; i < n; i++)
        {
            // increasing
            // level number
            if (tree[i] == '(')
                level++;
     
            // decreasing
            // level number
            else if (tree[i] == ')')
                level--;
     
            else
            {
                // check if current level is
                // the desired level or not
                if (level == k)
                    product *= (tree[i] - '0');
            }
        }
     
        // required product
        return product;
    }
     
    // Driver Code
    static void Main()
    {
        string tree = "(0(5(6()())(4()(9()())))(7(1()())(3()())))";
        int k = 2;
        Console.WriteLine(productAtKthLevel(tree, k));
    }
}
 
// This code is contributed by Sam007

PHP

<?php
// php implementation to find product of
// digits of elements at k-th level
 
// Function to find product of digits
// of elements at k-th level
function productAtKthLevel($tree, $k)
{
    $level = -1;
    $product = 1; // Initialize result
    $n = strlen($tree);
 
    for ($i = 0; $i < $n; $i++)
    {
         
        // increasing level number
        if ($tree[$i] == '(')
            $level++;
 
        // decreasing level number
        else if ($tree[$i] == ')')
            $level--;
 
        else
        {
            // check if current level is
            // the desired level or not
            if ($level == $k)
                $product *= (ord($tree[$i]) -
                             ord('0'));
        }
    }
 
    // required product
    return $product;
}
 
    // Driver Code
    $tree = "(0(5(6()())(4()(9()())))(7(1()())(3()())))";
    $k = 2;
    echo productAtKthLevel($tree, $k);
 
//This code is contributed by mits
?>

Javascript

<script>
    // Javascript implementation to find
    // product of digits of
    // elements at k-th level
     
    // Function to find product
    // of digits of elements
    // at k-th level
    function productAtKthLevel(tree, k)
    {
        let level = -1;
           
        // Initialize result
        let product = 1;
           
        let n = tree.length;
       
        for (let i = 0; i < n; i++)
        {
            // increasing
            // level number
            if (tree[i] == '(')
                level++;
       
            // decreasing
            // level number
            else if (tree[i] == ')')
                level--;
       
            else
            {
                // check if current level is
                // the desired level or not
                if (level == k)
                    product *= (tree[i].charCodeAt() - '0'.charCodeAt());
            }
        }
       
        // required product
        return product;
    }
     
    let tree = "(0(5(6()())(4()(9()())))(7(1()())(3()())))";
    let k = 2;
    document.write(productAtKthLevel(tree, k));
         
</script>