# 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.

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```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 ``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

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## Javascript

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Output:

`72`

Time Complexity: O(n)

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