<p>The thief has found himself a new place for his thievery again. There is only one entrance to this area, called <code>root</code>.</p>

<p>Besides the <code>root</code>, each house has one and only one parent house. After a tour, the smart thief realized that all houses in this place form a binary tree. It will automatically contact the police if <strong>two directly-linked houses were broken into on the same night</strong>.</p>

<p>Given the <code>root</code> of the binary tree, return <em>the maximum amount of money the thief can rob <strong>without alerting the police</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/10/rob1-tree.jpg" style="width: 277px; height: 293px;" />
<pre>
<strong>Input:</strong> root = [3,2,3,null,3,null,1]
<strong>Output:</strong> 7
<strong>Explanation:</strong> Maximum amount of money the thief can rob = 3 + 3 + 1 = 7.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/10/rob2-tree.jpg" style="width: 357px; height: 293px;" />
<pre>
<strong>Input:</strong> root = [3,4,5,1,3,null,1]
<strong>Output:</strong> 9
<strong>Explanation:</strong> Maximum amount of money the thief can rob = 4 + 5 = 9.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 10<sup>4</sup>]</code>.</li>
	<li><code>0 &lt;= Node.val &lt;= 10<sup>4</sup></code></li>
</ul>

/**
 * 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 {
public:
    int rob(const TreeNode* const root) {
        return BuildRobbingTree_r(root)->val;
    }

    TreeNode* BuildRobbingTree_r(const TreeNode* const node) {
        if (node == nullptr)
            return nullptr;

        TreeNode* const left = BuildRobbingTree_r(node->left);
        TreeNode* const right = BuildRobbingTree_r(node->right);

        int rob_this_node_res = node->val;
        int leave_this_node_res = 0;

        if (left != nullptr) {
            leave_this_node_res += left->val;
            if (left->left != nullptr)
                rob_this_node_res += left->left->val;
            if (left->right != nullptr)
                rob_this_node_res += left->right->val;
        }
        if (right != nullptr) {
            leave_this_node_res += right->val;
            if (right->left != nullptr)
                rob_this_node_res += right->left->val;
            if (right->right != nullptr)
                rob_this_node_res += right->right->val;
        }

        const int max_profit = std::max(rob_this_node_res, leave_this_node_res);

        return new TreeNode(max_profit, left, right);
    }
};
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