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# 124 Binary Tree Maximum Path Sum

## 124. Binary Tree Maximum Path Sum

## 1. Question

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`.

## 2. Implementation

**(1) DFS**

```java
class Solution {
    public int maxPathSum(TreeNode root) {
        int[] max = new int[1];
        max[0] = Integer.MIN_VALUE;
        findMaxPathSum(root, max);
        return max[0];
    }

    public int findMaxPathSum(TreeNode node, int[] max) {
        if (node == null) {
            return 0;
        }

        int leftPathSum = Math.max(0, findMaxPathSum(node.left, max));
        int rightPathSum = Math.max(0, findMaxPathSum(node.right, max));

        max[0] = Math.max(max[0], node.val + leftPathSum + rightPathSum);
        return node.val + Math.max(leftPathSum, rightPathSum);
    }
}
```

## 3. Time & Space Complexity

**(1) DFS:** 时间复杂度: O(n), 空间复杂度: O(h)