[LeetCode 解题报告]124. Binary Tree Maximum Path Sum

Given a non-empty binary tree, find the maximum path sum.

For this problem, a path is defined as any sequence of nodes from some starting node to any node in the tree along the parent-child connections. The path must contain at least one node and does not need to go through the root.

Example 1:

Input: [1,2,3]

       1
      / \
     2   3

Output: 6

Example 2:

Input: [-10,9,20,null,null,15,7]

   -10
   / \
  9  20
    /  \
   15   7

Output: 42

考察：最大路径和，对于某个节点只能选择其左子树或者右子树； 

/**
 * 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 maxPathSum(TreeNode* root) {
        int res = INT_MIN;
        maxPathSumDFS(root, res);
        return res;
        
    }
    
    int maxPathSumDFS(TreeNode* node, int &res) {
        if (node == NULL)
            return 0;
        
        int left = max(maxPathSumDFS(node->left, res), 0);
        int right = max(maxPathSumDFS(node->right, res), 0);
        res = max(res, left + right + node->val);
        return max(left+node->val, right+node->val);
    }
};