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

  • Difficulty Level : Medium
  • Last Updated : 27 Apr, 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 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
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
Javascript



<script>
 
// Javascript implementation to find sum of
// digits of elements at k-th level
     
// Function to find sum of digits
// of elements at k-th level
function sumAtKthLevel(tree, k)
{
    let level = -1;
     
    // Initialize result
    let sum = 0;
    let n = tree.length;
     
    for(let 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
let tree = "(0(5(6()())(4()(9()())))(7(1()())(3()())))";
let k = 2;
 
document.write(sumAtKthLevel(tree, k));
 
// This code is contributed by avanitrachhadiya2155
 
</script>
Output: 
14
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 implementation of the same:
C++



// 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;
}
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



<script>
// Javascript 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
    function sumAtKthLevel(tree,k,level)
    {
        if (tree[i++] == '(')
        {
  
            // if subtree is null, just like if root == null
            if (tree[i] == ')')
                return 0;
  
            let 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;
            let leftsum = sumAtKthLevel(tree, k, level + 1);
  
            // Recur for Right Subtree
            ++i;
            let rightsum = sumAtKthLevel(tree, k, level + 1);
  
            // Taking care of ')' after left and right subtree
            ++i;
            return sum + leftsum + rightsum;
        }
        return Number.MIN_VALUE;
    }
     
     // Driver code
    let tree = "(0(5(6()())(4()(9()())))(7(1()())(3()())))";
    let k = 2;
    let i = 0;
    document.write(sumAtKthLevel(tree, k, 0));
     
    // This code is contributed by rag2127
</script>
Output : 
14
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.
 

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