0124-Binary Tree Maximum Path Sum.md

Binary Tree Maximum Path Sum

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:

• The number of nodes in the tree is in the range [1, 3 * pow(10, 4)].
• -1000 <= Node.val <= 1000

Solution

Recursive:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     public var val: Int
 *     public var left: TreeNode?
 *     public var right: TreeNode?
 *     public init(_ val: Int) {
 *         self.val = val
 *         self.left = nil
 *         self.right = nil
 *     }
 * }
 */
class Solution {
    func maxPathSum(_ root: TreeNode?) -> Int {
        var result = Int.min
        maxPathSum(root, &result)
        return result
    }
    
    func maxPathSum(_ node: TreeNode?, _ result: inout Int) -> Int {
        guard let node = node else { return 0 }
        let leftSum = max(0, maxPathSum(node.left, &result)), rightSum = max(0, maxPathSum(node.right, &result))
        result = max(result, node.val+leftSum+rightSum)
        return node.val+max(leftSum, rightSum)
    }
}