# 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 ` `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

 ` `

Output:

```72
```

Time Complexity: O(n)

My Personal Notes arrow_drop_up In love with a semicolon because sometimes i miss it so badly)

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