124. Binary Tree Maximum Path Sum

• Difficulty: Hard

• Topics: Tree, Depth-first Search

• Similar Questions:

  • Path Sum

  • Sum Root to Leaf Numbers

  • Path Sum IV

  • Longest Univalue Path

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

Solutions:

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int maxPathSum(TreeNode* root) {
        int maxPathToRoot;
        return helper(root, maxPathToRoot);
    }

    int helper(TreeNode* root, int& maxPathToRoot) {
        if (root == nullptr) {
            maxPathToRoot = 0;
            return 0;
        }

        int ret = INT_MIN;
        int leftMaxPathToRoot = 0;
        int rightMaxPathToRoot = 0;

        if (root->left) {
            ret = max(ret, helper(root->left, leftMaxPathToRoot));
        }

        if (root->right) {
            ret = max(ret, helper(root->right, rightMaxPathToRoot));
        }

        maxPathToRoot = root->val + max(0, max(leftMaxPathToRoot, rightMaxPathToRoot));
        return max(ret, root->val + max(0, leftMaxPathToRoot) + max(0, rightMaxPathToRoot));
    }
};