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 value in range from 0 to 9. We need to find sum of elements at K-th level from 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

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

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

C++

// C++ implementation to find sum of 
// digits of elements at k-th level 
#include <bits/stdc++.h> 
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<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 program to test above 
int main() 
{ 
    string tree = "(0(5(6()())(4()(9()())))(7(1()())(3()())))"; 
    int k = 2; 
    cout << sumAtKthLevel(tree, k); 
    return 0; 
} 

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<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)  
                sum += (tree.charAt(i)-'0');  
        }  
    }  
  
    // required sum  
    return sum;  
}  
  
// Driver program to test above  
public static void main(String[] args)  
{  
    String tree = "(0(5(6()())(4()(9()())))(7(1()())(3()())))";  
    int k = 2;  
    System.out.println(sumAtKthLevel(tree, k));  
} 
}  

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  
        elif (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 

Output:

Time Complexity: O(n)

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 which are at level k only.

Following is the C++ implementation of the same:

// C++ implementation to find sum of  
// digits of elements at k-th level  
#include <bits/stdc++.h>  
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;  
} 

Time Complexity: O(n)

This article is contributed by Ayush Jauhari. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

My Personal Notes

Suggest a Topic

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

C++

Java

Python3

C#

Recommended Posts: