和112、113题类似
不过这一题更难一些，需要进行双重递归：即对每个节点做递归，再以该节点为起点进行DFS，搜寻满足条件的路径

class Solution(object):
    def __init__(self):
        self.count = 0
        
    def pathSum(self, root, sum):
        if not root:
            return 0
        
        def helper(root, sum):
            if not root:
                return 
            if sum - root.val == 0:
                self.count += 1
            # if root.left:
            helper(root.left, sum - root.val)
            # if root.right:
            helper(root.right, sum - root.val)
            
        #双重递归
        helper(root, sum)
        self.pathSum(root.left, sum)
        self.pathSum(root.right, sum)
        return self.count