437. Path Sum III（路径可以任意点开始，任意点结束）

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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

 class Solution {

     public int pathSum(TreeNode root, int sum) {
         if(root==null) return 0;
          int res = path(root,sum)+pathSum(root.right,sum)+pathSum(root.left,sum);
         return res;

     }

     private int path(TreeNode root, int sum) {
         int res=0;
         if(root==null)
             return res ;
         if(sum==root.val)
             res+=1;
         res+=path(root.left,sum-root.val);
         res+=path(root.right,sum-root.val);
         return res;
     }

 }