Problem

Given a non-empty 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.

Example 1:

Input: [1,2,3]

       1
      / \
     2   3

Output: 6

Example 2:

Input: [-10,9,20,null,null,15,7]

   -10
   / \
  9  20
    /  \
   15   7

Output: 42

Solution

/**
 * Definition for a binary tree node.
 * function TreeNode(val) {
 *     this.val = val;
 *     this.left = this.right = null;
 * }
 */
/**
 * @param {TreeNode} root
 * @return {number}
 */
var maxPathSum = function(root) {
  var max = Number.MIN_SAFE_INTEGER;
  var maxSum = function (node) {
    if (!node) return 0;
    var left = Math.max(maxSum(node.left), 0);
    var right = Math.max(maxSum(node.right), 0);
    max = Math.max(left + right + node.val, max);
    return Math.max(left, right) + node.val;
  };
  maxSum(root);
  return max;
};

Explain:

注意此题找的是路径 path，你用到的节点需要连通在一条路上。 所以 return Math.max(left, right) + node.val 而不是 return left + right + node.val。

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).