124. 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.

• new solution update 2022.03.10

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
    int res = INT_MIN;
    int helper(TreeNode* node) {
        if(!node) return 0;
        int leftSum = helper(node->left);
        int rightSum = helper(node->right);
        
        int innerSum = max({node->val + leftSum, node->val + rightSum, node->val + leftSum + rightSum, node->val});
        res = max(res, innerSum);
        int pathSum = max({node->val, leftSum + node->val, rightSum + node->val});
        return pathSum;
    }
public:
    int maxPathSum(TreeNode* root) {
        helper(root);
        return res;
    }
};

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
    pair<int, int> search(TreeNode* node) {
        if(node->left and node->right) {//has left and right
            auto[leftPathToParent, leftPathInner] = search(node->left);
            auto[rightPathToParent, rightPathInner] = search(node->right);

            return {max(max(leftPathToParent, rightPathToParent) + node->val, node->val),
                    max({leftPathInner, rightPathInner, leftPathToParent + rightPathToParent + node->val, node->val, max(leftPathToParent, rightPathToParent) + node->val})};
        } else if(node->left) {//left only
            auto[leftPathToParent, leftPathInner] = search(node->left);

            return {max(leftPathToParent + node->val, node->val),
                    max({leftPathInner, leftPathToParent + node->val, node->val, leftPathToParent})};
        } else if(node->right) {//right only
            auto[rightPathToParent, rightPathInner] = search(node->right);

            return {max(rightPathToParent + node->val, node->val),
                    max({rightPathInner, rightPathToParent + node->val, node->val, rightPathToParent})};
        } else {//no child node
            return {node->val, node->val};
        }
    }
public:
    int maxPathSum(TreeNode* root) {
        auto [pathToParent, pathInner] = search(root);
        return max(pathToParent, pathInner);
    }
};