//  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
    public int pathSum(TreeNode root, int sum) {
        if (root == null) {
            return 0;
        }
        return pathCount(root, sum) + pathSum(root.left, sum) + pathSum(root.right, sum);
    }
    int pathCount(TreeNode node,int sum) {
        if (node == null) {
            return 0;
        }
        return (node.val == sum ? 1 : 0) + pathCount(node.left, sum - node.val) + pathCount(node.right, sum - node.val);
    }