437. Path Sum III（路径可以任意点开始，任意点结束）

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

 1 class Solution {
 2 
 3     public int pathSum(TreeNode root, int sum) {
 4         if(root==null) return 0;
 5          int res = path(root,sum)+pathSum(root.right,sum)+pathSum(root.left,sum);
 6         return res;
 7         
 8     }
 9      
10     private int path(TreeNode root, int sum) {
11         int res=0;
12         if(root==null)
13             return res ;
14         if(sum==root.val)
15             res+=1;
16         res+=path(root.left,sum-root.val);
17         res+=path(root.right,sum-root.val);
18         return res;
19     }
20       
21 }