47. leetcode 437. Path Sum III

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。