437. Path Sum III
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
问题描述：给定一个二叉树和一个整数，寻找在此二叉树上的自上而下的元素值的和为该整数的路径的个数。
思路：利用递归和树的深度优先搜索（先序遍历）。原树满足条件的解的个数=左子树满足条件解的个数+右子树满足条件解的个数+树的深度优先遍历的序列的子序列中满足条件解的个数。具体请看代码。
