【Leetcode】Binary Tree Maximum Path Sum

题目链接：https://leetcode.com/problems/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.

思路：
dfs递归，判断是否选择左右最大的分支，或者选择root结点。。

算法：

    int max = Integer.MIN_VALUE;

    public int maxPathSum(TreeNode root) {
        dsp(root);
        return max;
    }

    public int dsp(TreeNode root) {
        if (root == null)
            return 0;
        int leftMax = dsp(root.left);// 左子树能返回的最大值
        int rightMax = dsp(root.right);
        max = Math.max(
                Math.max(Math.max(
                        Math.max(leftMax + rightMax + root.val, rightMax
                                + root.val), leftMax + root.val), max),
                root.val);
        return Math.max(Math.max(leftMax + root.val, rightMax + root.val),
                root.val);
    }