Path Sum III问题及解法

问题描述：

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.

示例：

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

问题分析：

求解树上某一段连续路径的和是否等于给定值，然后求出这些路径的得数目。可以考虑利用DFS求解。

过程详见代码：

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int temp;
    int pathSum(TreeNode* root, int sum) {
    	temp = sum;
    	if(root == NULL) return 0;
    	return pathSum2(root,sum) + pathSum(root->left,sum) + pathSum(root->right,sum);
    }
    int pathSum2(TreeNode* root, int sum) 
    {
    	int res = 0;
    	if(root == NULL) return 0;
    	if(root->val == sum) res = 1;
    	return res + pathSum2(root->left,sum - root->val) + pathSum2(root->right,sum - root->val);
	}
};