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Product of nodes at k-th level in a tree represented as string
  • Difficulty Level : Medium
  • Last Updated : 03 Nov, 2020

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
TREE
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++

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// 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;
}

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Java

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// 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.

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Python3

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# 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

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C#

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// 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 

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PHP

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<?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 
?>

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Output:

72

Time Complexity: O(n)

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