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/\\3211/ \\3 -21Return 3. The paths that sum to 8 are: 1. 5 -> 3 2. 5 -> 2 -> 1 3. -3 -> 11

**Approach 1:**

/** * Definition for a binary tree node. * public class TreeNode { * int val; * TreeNode left; * TreeNode right; * TreeNode(int x) { val = x; } * } */ public class Solution { public int pathSum(TreeNode root, int sum) { if (root == null) return 0; return pathSumFrom(root, sum) + pathSum(root.left, sum) + pathSum(root.right, sum); } private int pathSumFrom(TreeNode node, int sum) { if (node == null) return 0; return (node.val == sum ? 1 : 0) + pathSumFrom(node.left, sum - node.val) + pathSumFrom(node.right, sum - node.val); } }