A path in a binary tree is a sequence of nodes where each pair of adjacent nodes in the sequence has an edge connecting them. A node can only appear in the sequence at most once. Note that the path does not need to pass through the root.
The path sum of a path is the sum of the node's values in the path.
Given the root of a binary tree, return the maximum path sum of any non-empty path.
Example 1:
Input: root = [1,2,3]
Output: 6
Explanation: The optimal path is 2 -> 1 -> 3 with a path sum of 2 + 1 + 3 = 6.
Example 2:
Input: root = [-10,9,20,null,null,15,7]
Output: 42
Explanation: The optimal path is 15 -> 20 -> 7 with a path sum of 15 + 20 + 7 = 42.
Constraints:
$[1, 3*10^4]$.1000 <= Node.val <= 1000題目給了一個二元樹根結點 root
定義一個 path 的 sum 代表把在 path 上所有的結點值相加
找出一個樹的 path 所能形成最大 sum，且每個結點在路徑只能出現一次
這個問題的核心在於要如何找出最大值