package leetcode_1To300;

/**
 * 本代码来自 Cspiration，由 @Cspiration 提供
 * 题目来源：http://leetcode.com
 * - Cspiration 致力于在 CS 领域内帮助中国人找到工作，让更多海外国人受益
 * - 现有课程：Leetcode Java 版本视频讲解（1-900题）（上）（中）（下）三部
 * - 算法基础知识（上）（下）两部；题型技巧讲解（上）（下）两部
 * - 节省刷题时间，效率提高2-3倍，初学者轻松一天10题，入门者轻松一天20题
 * - 讲师：Edward Shi
 * - 官方网站：https://cspiration.com
 * - 版权所有，转发请注明出处
 */
public class _124_BinaryTreeMaximumPathSum {
    /**
     * 124. Binary Tree Maximum Path Sum
     * 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 must contain at least one node and does not
     need to go through the root.

     For example:
     Given the below binary tree,

       1
      / \
     2   3
     Return 6.

          3
         / \
        9  20
      /  \
     15   7


     time : O(n)
     space : O(n)

     */

    int res;

    public int maxPathSum(TreeNode root) {
        if (root == null) return 0;
        res = Integer.MIN_VALUE;
        helper(root);
        return res;
    }

    public int helper(TreeNode root) {
        if (root == null) return 0;
        int left = Math.max(0, helper(root.left));
        int right = Math.max(0, helper(root.right));
        res = Math.max(res, left + right + root.val);
        return Math.max(left, right) + root.val;
    }
}