# Sum 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 a value in the range of 0 to 9. We need to find the sum of elements at the K-th level from the root. The root is at level 0.
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 : 14
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 = 14

Input : tree = "(8(3(2()())(6(5()())()))(5(10()())(7(13()())())))"
k = 3
Output : 9
Elements at level k = 3 are 5, 1 and 3
sum of digits of these elements = 5+1+3 = 9```
```1. Input 'tree' in string format and level k
2. Initialize level = -1 and sum = 0
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
sum = sum + (ch-'0')
4. Print sum```

Implementation:

## C++

 `// C++ implementation to find sum of` `// digits of elements at k-th level` `#include ` `using` `namespace` `std;`   `// Function to find sum of digits` `// of elements at k-th level` `int` `sumAtKthLevel(string tree, ``int` `k)` `{` `    ``int` `level = -1;` `    ``int` `sum = 0;  ``// Initialize result` `    ``int` `n = tree.length();`   `    ``for` `(``int` `i=0; i

## Java

 `// Java implementation to find sum of ` `// digits of elements at k-th level ` `class` `GfG { `   `// Function to find sum of digits ` `// of elements at k-th level ` `static` `int` `sumAtKthLevel(String tree, ``int` `k) ` `{ ` `    ``int` `level = -``1``; ` `    ``int` `sum = ``0``; ``// Initialize result ` `    ``int` `n = tree.length(); `   `    ``for` `(``int` `i=``0``; i

## Python3

 `# Python3 implementation to find sum of ` `# digits of elements at k-th level `   `# Function to find sum of digits ` `# of elements at k-th level ` `def` `sumAtKthLevel(tree, k) :`   `    ``level ``=` `-``1` `    ``sum` `=` `0` `# Initialize result ` `    ``n ``=` `len``(tree) `   `    ``for` `i ``in` `range``(n):` `        `  `        ``# increasing level number ` `        ``if` `(tree[i] ``=``=` `'('``) :` `            ``level ``+``=` `1`   `        ``# decreasing level number ` `        ``else` `if` `(tree[i] ``=``=` `')'``): ` `            ``level ``-``=` `1`   `        ``else``:` `        `  `            ``# check if current level is ` `            ``# the desired level or not ` `            ``if` `(level ``=``=` `k) :` `                ``sum` `+``=` `(``ord``(tree[i]) ``-` `ord``(``'0'``)) ` `        `  `    ``# required sum ` `    ``return` `sum`   `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``:` `    ``tree ``=` `"(0(5(6()())(4()(9()())))(7(1()())(3()())))"` `    ``k ``=` `2` `    ``print``(sumAtKthLevel(tree, k))`   `# This code is contributed by` `# Shubham Singh(SHUBHAMSINGH10)`

## C#

 `// C# implementation to find sum of ` `// digits of elements at k-th level `   `using` `System;` `class` `GfG { `   `// Function to find sum of digits ` `// of elements at k-th level ` `static` `int` `sumAtKthLevel(``string` `tree, ``int` `k) ` `{ ` `    ``int` `level = -1; ` `    ``int` `sum = 0; ``// 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) ` `                ``sum += (tree[i]-``'0'``); ` `        ``} ` `    ``} `   `    ``// required sum ` `    ``return` `sum; ` `} `   `// Driver code` `public` `static` `void` `Main() ` `{ ` `    ``string` `tree = ``"(0(5(6()())(4()(9()())))(7(1()())(3()())))"``; ` `    ``int` `k = 2; ` `    ``Console.Write(sumAtKthLevel(tree, k)); ` `}` `} `   `// This code is contributed by Ita_c`

## Javascript

 ``

Output

`14`

Time Complexity: O(n)
Auxiliary Space: O(1)

Recursive Method: The idea is to treat the string as tree without actually creating one, and simply traverse the string recursively in Postorder Fashion and consider nodes that are at level k only.

Following is the implementation of the same:

## C++

 `// C++ implementation to find sum of ` `// digits of elements at k-th level ` `#include ` `using` `namespace` `std; `   `// Recursive Function to find sum of digits ` `// of elements at k-th level ` `int` `sumAtKthLevel(string tree, ``int` `k,``int` `&i,``int` `level) ` `{ ` `       `  `    ``if``(tree[i++]==``'('``)` `    ``{` `      `  `      ``// if subtree is null, just like if root == NULL` `      ``if``(tree[i] == ``')'``)` `           ``return` `0;            ` `    `  `      ``int` `sum=0;` `      `  `      ``// Consider only level k node to be part of the sum` `      ``if``(level == k)` `        ``sum = tree[i]-``'0'``;` `      `  `      ``// Recur for Left Subtree` `      ``int` `leftsum = sumAtKthLevel(tree,k,++i,level+1);` `      `  `      ``// Recur for Right Subtree` `      ``int` `rightsum = sumAtKthLevel(tree,k,++i,level+1); ` `      `  `      ``// Taking care of ')' after left and right subtree ` `      ``++i;` `      ``return` `sum+leftsum+rightsum;        ` `    ``}` `} `   `// Driver program to test above ` `int` `main() ` `{ ` `    ``string tree = ``"(0(5(6()())(4()(9()())))(7(1()())(3()())))"``; ` `    ``int` `k = 2;` `        ``int` `i=0;` `    ``cout << sumAtKthLevel(tree, k,i,0); ` `    ``return` `0; ` `}`

## Java

 `// Java implementation to find sum of ` `// digits of elements at k-th level ` `class` `GFG ` `{` `    ``static` `int` `i;`   `    ``// Recursive Function to find sum of digits` `    ``// of elements at k-th level` `    ``static` `int` `sumAtKthLevel(String tree, ``int` `k, ``int` `level)` `    ``{`   `        ``if` `(tree.charAt(i++) == ``'('``)` `        ``{`   `            ``// if subtree is null, just like if root == null` `            ``if` `(tree.charAt(i) == ``')'``)` `                ``return` `0``;`   `            ``int` `sum = ``0``;`   `            ``// Consider only level k node to be part of the sum` `            ``if` `(level == k)` `                ``sum = tree.charAt(i) - ``'0'``;`   `            ``// Recur for Left Subtree` `            ``++i;` `            ``int` `leftsum = sumAtKthLevel(tree, k, level + ``1``);`   `            ``// Recur for Right Subtree` `            ``++i;` `            ``int` `rightsum = sumAtKthLevel(tree, k, level + ``1``);`   `            ``// Taking care of ')' after left and right subtree` `            ``++i;` `            ``return` `sum + leftsum + rightsum;` `        ``}` `        ``return` `Integer.MIN_VALUE;` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args) ` `    ``{` `        ``String tree = ``"(0(5(6()())(4()(9()())))(7(1()())(3()())))"``;` `        ``int` `k = ``2``;` `        ``i = ``0``;` `        ``System.out.print(sumAtKthLevel(tree, k, ``0``));` `    ``}` `}`   `// This code is contributed by 29AjayKumar`

## Python

 `# Python implementation to find sum of ` `# digits of elements at k-th level `   `# Recursive Function to find sum of digits ` `# of elements at k-th level ` `def` `sumAtKthLevel(tree, k, i, level):` `    `  `    ``if``(tree[i[``0``]] ``=``=` `'('``):` `        ``i[``0``] ``+``=` `1` `        `  `        ``# if subtree is null, just like if root == NULL ` `        ``if``(tree[i[``0``]] ``=``=` `')'``):` `            ``return` `0`            `        `  `        ``sum` `=` `0` `        `  `        ``# Consider only level k node to be part of the sum ` `        ``if``(level ``=``=` `k):` `            ``sum` `=` `int``(tree[i[``0``]])` `            `  `        ``# Recur for Left Subtree ` `        ``i[``0``] ``+``=` `1` `        ``leftsum ``=` `sumAtKthLevel(tree, k, i, level ``+` `1``) ` `            `  `        ``# Recur for Right Subtree ` `        ``i[``0``] ``+``=` `1` `        ``rightsum ``=` `sumAtKthLevel(tree, k, i, level ``+` `1``) ` `            `  `        ``# Taking care of ')' after left and right subtree ` `        ``i[``0``] ``+``=` `1` `        ``return` `sum` `+` `leftsum ``+` `rightsum     ` `    `  `# Driver program to test above ` `tree ``=` `"(0(5(6()())(4()(9()())))(7(1()())(3()())))"` `k ``=` `2` `i ``=` `[``0``] ` `print``(sumAtKthLevel(tree, k, i, ``0``)) `   `# This code is contributed by SHUBHAMSINGH10`

## C#

 `// C# implementation to find sum of ` `// digits of elements at k-th level ` `using` `System;`   `class` `GFG ` `{` `    ``static` `int` `i;`   `    ``// Recursive Function to find sum of digits` `    ``// of elements at k-th level` `    ``static` `int` `sumAtKthLevel(String tree, ``int` `k, ``int` `level)` `    ``{`   `        ``if` `(tree[i++] == ``'('``)` `        ``{`   `            ``// if subtree is null, just like if root == null` `            ``if` `(tree[i] == ``')'``)` `                ``return` `0;`   `            ``int` `sum = 0;`   `            ``// Consider only level k node to be part of the sum` `            ``if` `(level == k)` `                ``sum = tree[i] - ``'0'``;`   `            ``// Recur for Left Subtree` `            ``++i;` `            ``int` `leftsum = sumAtKthLevel(tree, k, level + 1);`   `            ``// Recur for Right Subtree` `            ``++i;` `            ``int` `rightsum = sumAtKthLevel(tree, k, level + 1);`   `            ``// Taking care of ')' after left and right subtree` `            ``++i;` `            ``return` `sum + leftsum + rightsum;` `        ``}` `        ``return` `int``.MinValue;` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main(String[] args) ` `    ``{` `        ``String tree = ``"(0(5(6()())(4()(9()())))(7(1()())(3()())))"``;` `        ``int` `k = 2;` `        ``i = 0;` `        ``Console.Write(sumAtKthLevel(tree, k, 0));` `    ``}` `}`   `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output

`14`

Time Complexity: O(n), the time complexity of this algorithm is O(n) as we need to traverse all the nodes of the tree in order to get the sum of digits of elements at the kth level.
Auxiliary Space: O(1), If we consider the recursive call stack then it will be O(K).

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