Find Maximum Level Sum in Binary Tree using Recursion

Given a Binary Tree having positive and negative nodes, the task is to find the maximum sum level in it and print the maximum sum.

Examples:

Input:
      4
    /   \
   2     -5
  / \    / \
-1   3 -2   6
Output: 6
Sum of all nodes of the 1st level is 4.
Sum of all nodes of the 2nd level is -3.
Sum of all nodes of the 3rd level is 6.
Hence, the maximum sum is 6.

Input:
      1
    /   \
   2      3
 /  \      \
4    5      8
          /   \
         6     7  
Output: 17

Approach: Find the maximum level in the given binary tree then create an array sum[] where sum[i] will store the sum of the elements at level i.
Now, write a recursive function that takes a node of the tree and its level as the argument and updates the sum for the current level then makes recursive calls for the children with the updated level as one more than the current level (this is because children are at a level one more than their parent). Finally, print the maximum value from the sum[] array.



Below is the implementation of the above approach:

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// A binary tree node has data, pointer to
// the left child and the right child
struct Node {
    int data;
    struct Node *left, *right;
};
  
// Helper function that allocates a
// new node with the given data and
// NULL left and right pointers
struct Node* newNode(int data)
{
    struct Node* node = new Node;
    node->data = data;
    node->left = node->right = NULL;
    return (node);
}
  
// Function to return the maximum
// levels in the given tree
int maxLevel(struct Node* root)
{
    if (root == NULL)
        return 0;
    return (1 + max(maxLevel(root->left),
                    maxLevel(root->right)));
}
  
// Function to find the maximum sum of a
// level in the tree using recursion
void maxLevelSum(struct Node* root, int max_level,
                 int sum[], int current)
{
    // Base case
    if (root == NULL)
        return;
  
    // Add current node's data to
    // its level's sum
    sum[current] += root->data;
  
    // Recursive call for the left child
    maxLevelSum(root->left, max_level, sum,
                current + 1);
  
    // Recursive call for the right child
    maxLevelSum(root->right, max_level, sum,
                current + 1);
}
  
// Function to find the maximum sum of a
// level in the tree using recursion
int maxLevelSum(struct Node* root)
{
  
    // Maximum levels in the given tree
    int max_level = maxLevel(root);
  
    // To store the sum of every level
    int sum[max_level + 1] = { 0 };
  
    // Recursive function call to
    // update the sum[] array
    maxLevelSum(root, max_level, sum, 1);
  
    // To store the maximum sum for a level
    int maxSum = 0;
  
    // For every level of the tree, update
    // the maximum sum of a level so far
    for (int i = 1; i <= max_level; i++)
        maxSum = max(maxSum, sum[i]);
  
    // Return the maximum sum
    return maxSum;
}
  
// Driver code
int main()
{
    struct Node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->right->right = newNode(8);
    root->right->right->left = newNode(6);
    root->right->right->right = newNode(7);
  
    /* Constructed Binary tree is: 
                
               / \ 
              2   3 
             / \   \ 
            4   5   8 
                   / \ 
                  6   7   */
  
    cout << maxLevelSum(root);
  
    return 0;
}

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Output:

17


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