// Time:  O(n)
// Space: O(h)

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */

// dfs solution with stack
class Solution {
public:
    int maxSumBST(TreeNode* root) {
        using RET = tuple<bool, int, int, int>;
        int result = 0;
        RET ret;
        vector<tuple<TreeNode*, shared_ptr<vector<RET>>, RET *>> stk = {{root, nullptr, &ret}};
        while (!stk.empty()) {
            const auto [node, tmp, ret] = stk.back(); stk.pop_back();
            if (tmp) {
                const auto& [lvalid, lsum, lmin, lmax] = (*tmp)[0];
                const auto& [rvalid, rsum, rmin, rmax] = (*tmp)[1];
                if (lvalid && rvalid && lmax < node->val && node->val < rmin) {
                    const auto& total = lsum + node->val + rsum;
                    result = max(result, total);
                    *ret = {true, total, min(lmin, node->val), max(node->val, rmax)};
                    continue;
                }
                *ret = {false, 0, 0, 0};
                continue;
            }
            if (!node) {
                *ret = {true, 0,
                        numeric_limits<int>::max(),
                        numeric_limits<int>::min()};
                continue;
            }
            const auto& new_tmp = make_shared<vector<RET>>(2);
            stk.emplace_back(node, new_tmp, ret);
            stk.emplace_back(node->right, nullptr, &((*new_tmp)[1]));
            stk.emplace_back(node->left, nullptr, &((*new_tmp)[0]));
        }
        return result;
    }
};

// Time:  O(n)
// Space: O(h)
// dfs solution with recursion
class Solution2 {
public:
    int maxSumBST(TreeNode* root) {
        int result = 0;
        dfs(root, &result);
        return result;
    }

private:
    tuple<bool, int, int, int> dfs(TreeNode *node, int *result) {
        if (!node) {
            return {true, 0,
                    numeric_limits<int>::max(),
                    numeric_limits<int>::min()};
        }
        const auto& [lvalid, lsum, lmin, lmax] = dfs(node->left, result);
        const auto& [rvalid, rsum, rmin, rmax] = dfs(node->right, result);
        if (lvalid && rvalid && lmax < node->val && node->val < rmin) {
            const auto& total = lsum + node->val + rsum;
            *result = max(*result, total);
            return {true, total, min(lmin, node->val), max(node->val, rmax)};
        }
        return {false, 0, 0, 0};
    }
};