The thief has found himself a new place for his thievery again. There is only one entrance to this area, called the "root." Besides the root, each house has one and only one parent house. After a tour, the smart thief realized that "all houses in this place forms a binary tree". It will automatically contact the police if two directly-linked houses were broken into on the same night.

Determine the maximum amount of money the thief can rob tonight without alerting the police.


class Solution {
    int houseRobber3(TreeNode* root) {
        unordered_map<TreeNode*, int> m;
        return dfs(root, m);
    int dfs(TreeNode *root, unordered_map<TreeNode*, int> &m) {
        if (!root) return 0;
        if (m.count(root)) return m[root];
        int val = 0;
        if (root->left) {
            val += dfs(root->left->left, m) + dfs(root->left->right, m);
        if (root->right) {
            val += dfs(root->right->left, m) + dfs(root->right->right, m);
        val = max(val + root->val, dfs(root->left, m) + dfs(root->right, m));
        m[root] = val;
        return val;

House Robber III