## 題解

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def maxPathSum(self, root: Optional[TreeNode]) -> int:
        max_path = float("-inf")
        def dfs(root: TreeNode):
            nonlocal max_path
            if not root:
                return 0
            left_sum = max(dfs(root.left),0)
            right_sum = max(dfs(root.right),0)
            max_path = max(max_path,root.val + left_sum + right_sum) # 計算最大路徑總和
            return root.val + max(left_sum,right_sum) # 選擇最大的子樹，避免路徑分岔
        
        dfs(root)
        return max_path