题目如下：

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   1Return 3. The paths that sum to 8 are:1.  5 -> 32.  5 -> 2 -> 13. -3 -> 11

解题思路：题目数据量不大，我尝试着用递归嵌套递归的方法，发现也能AC。

代码如下：

# Definition for a binary tree node.# class TreeNode(object):#     def __init__(self, x):#         self.val = x#         self.left = None#         self.right = Noneclass Solution(object):    res = 0    def recursive(self,node,sum):        self.recursive2(node,0,sum)        if node.left != None:            self.recursive(node.left, sum)        if node.right != None:            self.recursive(node.right,sum)    def recursive2(self,node,amount,sum):        if node.val + amount == sum:            self.res += 1        if node.left != None:            self.recursive2(node.left, amount + node.val , sum)        if node.right != None:            self.recursive2(node.right,amount + node.val, sum)    def pathSum(self, root, sum):        """        :type root: TreeNode        :type sum: int        :rtype: int        """        self.res = 0        if root != None:            self.recursive(root,sum)        return self.res