LeetCode-in-All
124. Binary Tree Maximum Path Sum
Hard
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 * 104]. -1000 <= Node.val <= 1000
Solution
/**
* Definition for a binary tree node.
* class TreeNode {
* public $val = null;
* public $left = null;
* public $right = null;
* function __construct($val = 0, $left = null, $right = null) {
* $this->val = $val;
* $this->left = $left;
* $this->right = $right;
* }
* }
*/
class Solution {
private $max;
function __construct() {
$this->max = PHP_INT_MIN;
}
private function helper($root) {
if ($root == null) {
return 0;
}
// to avoid the -ve values in left side we will compare them with 0
$left = max(0, $this->helper($root->left));
$right = max(0, $this->helper($root->right));
$current = $root->val + $left + $right;
if ($current > $this->max) {
$this->max = $current;
}
return $root->val + max($left, $right);
}
/**
* @param TreeNode $root
* @return Integer
*/
function maxPathSum($root) {
$this->helper($root);
return $this->max;
}
}