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

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

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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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  
?> 

Output:

Time Complexity: O(n)

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Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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