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

public class Solution {
    int max = Integer.MIN_VALUE;
    
    public int maxPathSum(TreeNode root) {
        helper(root);
        return max;
    }
    

    // helper returns the max branch 
    // plus current node's value
    int helper(TreeNode root) {
        if (root == null) return 0;
        //如果最大值是负值就不选
        int left = Math.max(helper(root.left), 0);
        int right = Math.max(helper(root.right), 0);
        //求的时候考虑包括当前根节点的最大路径
        max = Math.max(max, root.val + left + right);
        //返回根值和左右子树较大的值，只能选一个，不然无法实现
        return root.val + Math.max(left, right);
    }
}

可以从任何地方开始，求根+左+右的最大值。

很难

https://leetcode.wang/leetcode-124-Binary-Tree-Maximum-Path-Sum.html