# Path Sum III

You are given a binary tree in which each node contains an integer value.

Find the number of paths that sum to a given value.

The path does not need to start or end at the root or a leaf, but it must go downwards (traveling only from parent nodes to child nodes).

The tree has no more than 1,000 nodes and the values are in the range -1,000,000 to 1,000,000.

Example:

root = [10,5,-3,3,2,null,11,3,-2,null,1], sum = 8

10
/  \
5   -3
/ \    \
3   2   11
/ \   \
3  -2   1

Return 3. The paths that sum to 8 are:

1.  5 -> 3
2.  5 -> 2 -> 1
3. -3 -> 11


Solution:

Recursion, add a helper function that counts paths starting from a node

/**
* Definition for a binary tree node.
* struct TreeNode {
*     int val;
*     TreeNode *left;
*     TreeNode *right;
*     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
* };
*/
class Solution {
public:

int pathSumHelper(TreeNode* root, int sum){
if(root == NULL) return 0;
return (root->val == sum) + pathSumHelper(root->left, sum-root->val) +pathSumHelper(root->right, sum-root->val);

}

int pathSum(TreeNode* root, int sum) {
if(root == NULL) return 0;
return pathSumHelper(root, sum) + pathSum(root->left, sum) + pathSum(root->right, sum);
}
};