[leetcode] Binary Tree Maximum Path Sum

Given a binary tree, find the maximum path sum.

The path may start and end at any node in the tree.

For example:
Given the below binary tree,

       1
      / \
     2   3

Return 6. 

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int maxPathSum(TreeNode *root) {
        if (root == NULL)
            return 0;
        int result = INT_MIN;
            
        int maxRoot = maxPathSum(root, result);
        return result;
    }
    
    int maxPathSum(TreeNode *root,int& result){
        if (root == NULL)
            return 0;
            
        int left = maxPathSum(root->left, result);
        int right = maxPathSum(root->right, result);
        
        int temp;   
        int maxVal = max(left,right);
        temp = max(maxVal+root->val,root->val);
        temp = max(temp, left+right+root->val);
        if (temp>result)
            result = temp;
        if (maxVal > 0)
            return maxVal+root->val;
        else
            return root->val;
    }
};

1. 注意比較最大值的時候，四種情況都要考慮到：
    只有一個點，左子樹+點，右子樹+點，左子樹+右子樹+點

2, result爲包括某一點在內的，左右路徑的最大值