124. Binary Tree Maximum Path Sum

题目：

Given a 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 does not need to go through the root.

For example:
Given the below binary tree,

       1
      / 
     2   3

Return 6.

链接： http://leetcode.com/problems/binary-tree-maximum-path-sum/

题解：

a path被定义为任意starting node通过parent-child link到另一node， 所以我们要考虑左子树和，右子树和以及左右子树和。 需要传递一个数组引用变量，或者定义一个全局变量来传递最终的运算结果。这个也和以前的一些自底向上构建二叉树的题目比较类似，很巧妙。还需要多多研究。

Time Complexity - O(n)，Space Complexity - O(n)

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public int maxPathSum(TreeNode root) {
        int[] max = {Integer.MIN_VALUE};
        int res = maxPathSum(root, max);
        return max[0];
    }
    
    private int maxPathSum(TreeNode root, int[] max) {
        if(root == null)
            return 0;
        int left = maxPathSum(root.left, max);
        int right = maxPathSum(root.right, max);
        int res = Math.max(root.val, Math.max(root.val + left, root.val + right));
        max[0] = Math.max(max[0], Math.max(res, root.val + left + right));
        return res;
    }
}

Update:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    int max = Integer.MIN_VALUE;
    
    public int maxPathSum(TreeNode root) {
        helper(root);
        return max;
    }
    
    private int helper(TreeNode root) {
        if(root == null)
            return 0;
        int left = Math.max(helper(root.left), 0);
        int right = Math.max(helper(root.right), 0);
        max = Math.max(max, root.val + left + right);
        return root.val + Math.max(left, right);
    }
}

 

题外话: 今天头比较晕，上午把工作上的事做得差不多了，下午就一直头晕。一天就做了两道题，而且还做得不是那么清楚。是真的老了吗？？？中午吃了chipotle，晚上去吃了成都23，总的来说还是很疲惫。马上进入11月份，还剩17天假期，怎么使用是个大问题。以前总想着10月份刷题就完成了，然后就是飞来飞去地面试，结果这第一遍还没做到一半，再不抓紧时间，人生真的荒废过去了。 好好刷吧。

Reference：

https://leetcode.com/discuss/43797/elegant-java-solution

https://leetcode.com/discuss/14190/accepted-short-solution-in-java