# Binary Tree Maximum Path Sum

{% embed url="<https://www.lintcode.com/problem/94/>" %}

## Solution 1 (Java)

```java
/**
 * Definition of TreeNode:
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left, right;
 *     public TreeNode(int val) {
 *         this.val = val;
 *         this.left = this.right = null;
 *     }
 * }
 */

public class Solution {

    private int maxPathSum = Integer.MIN_VALUE;

    /**
     * @param root: The root of binary tree.
     * @return: An integer
     */
    public int maxPathSum(TreeNode root) {
        dfs(root);
        return maxPathSum;
    }

    private int dfs(TreeNode root) {
        if (root == null)
            return 0;
        
        int left = dfs(root.left);
        int right = dfs(root.right);

        maxPathSum = Math.max(maxPathSum, left + root.val);
        maxPathSum = Math.max(maxPathSum, right + root.val);
        maxPathSum = Math.max(maxPathSum, root.val);
        maxPathSum = Math.max(maxPathSum, left + right + root.val);

        return Math.max(Math.max(left, right), 0) + root.val;
    }
}
```

### Notes

There are 4 types of paths that can be candidates for the maximum path sum.

1. Max path of left tree + root
2. Max path of right tree + root
3. Only the root
4. Max single path of left tree + root + max single path of right tree


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://blog.yushunchen.com/algo/binary-tree/4.-divide-and-conquer/binary-tree-maximum-path-sum.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.