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Language/Type: C++ binary trees pointers recursion
Author: Marty Stepp (on 2016/06/16)

Write a member function named limitPathSum that could be added to the BinaryTree class. Your function should accept an integer value representing a maximum, and remove nodes to guarantee that the sum of values on any path from the root to a node does not exceed that maximum. For example, if variable tree refers to the tree below at left, the call of tree.limitPathSum(50); will require removing node 12 because the sum from the root down to that node is more than 50 (29 + 17 + -7 + 12 = 51). Similarly, we have to remove node 37 because its sum is (29 + 17 + 37 = 83). When you remove a node, you remove anything under it, so removing 37 also removes 16. We also remove the node with 14 because its sum is (29 + 15 + 14 = 58). If the data stored at the root is greater than the given maximum, remove all nodes, leaving an empty (NULL) tree. Free the memory associated with each node you remove, but only remove the nodes that are necessary to remove.

tree after tree.limitPathSum(50);
         /    \
      17        15
     /  \      /  \
   -7    37   4    14
  /  \     \      /  \
11   12    16   -9    19
         /    \
      17        15
     /         /
   -7         4

Constraints: Do not construct any new BinaryTreeNode objects in solving this problem (though you may create as many BinaryTreeNode* pointer variables as you like). Do not use any auxiliary data structures to solve this problem (no array, vector, stack, queue, string, etc).

Write the member function as it would appear in BinaryTree.cpp. You do not need to declare the function header that would appear in BinaryTree.h. Assume that you are adding this method to the BinaryTree class as defined below:

class BinaryTree {
    BinaryTreeNode* root;   // NULL for an empty tree
    your code goes here;

struct BinaryTreeNode {
    int data;
    BinaryTreeNode* left;
    BinaryTreeNode* right;
Type your C++ solution code here:

This is a member function problem. Submit a member function that will become part of an existing C++ class. You do not need to write the complete class, just the member function described in the problem.

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