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

题解：

class Solution {
public:
    void getSum(TreeNode* t, int val, int sum, int &cnt) {
        if (t != NULL) {
            val += t->val;
            if (val == sum) {
                cnt++;
            }
            getSum(t->left, val, sum, cnt);
            getSum(t->right, val, sum, cnt);
        }
    }
    void preOrder(TreeNode* root, int sum, int &res) {
        if (root != NULL) {
            int cnt = 0;
            getSum(root, 0, sum, cnt);
            res += cnt;
            preOrder(root->left, sum, res);
            preOrder(root->right, sum, res);
        }
    }
    int pathSum(TreeNode* root, int sum) {
        int res = 0;
        preOrder(root, sum, res);
        return res;
    }
};