[leetcode] 124. Binary Tree Maximum Path Sum

Description

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

分析

题目的意思是：
给出一个二叉树，找出节点和最大的路径。

• 这虽然是一个二叉树遍历的过程，但是结点的值可能为负数，这样我们在计算最大路径值的时候，要注意把求和为负值的分支舍去，保留返回为正值的分支。
• 递归的代码写得非常的简洁漂亮，这种编程模式在刷题的时候经常看见，最好记住。

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 {
    int sum=INT_MIN;
public:
    int maxPathSum(TreeNode* root) {
      preorder(root);
      return sum;
    }
    int preorder(TreeNode* root){
        if(!root){
            return 0;
        }
        int left=max(0,preorder(root->left));
        int right=max(0,preorder(root->right));
        sum=max(sum,root->val+left+right);
        return max(left,right)+root->val;
    }
};

参考文献

​​[编程题]binary-tree-maximum-path-sum​​