337. House Robber III

The thief has found himself a new place for his thievery again. There is only one entrance to this area, called 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 form a binary tree. It will automatically contact the police if two directly-linked houses were broken into on the same night.

Given the root of the binary tree, return the maximum amount of money the thief can rob without alerting the police.

• new solution update 2022.03.08

/**
 * 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> helper(TreeNode* node) {
        if(!node) return {0,0};
        auto [lrob, lpass] = helper(node->left);
        auto [rrob, rpass] = helper(node->right);
        
        return {lpass + rpass, max(lrob + rrob + node->val, lpass + rpass)};
    }
public:
    int rob(TreeNode* root) {
        auto [res1, res2] = helper(root);
        return max(res1, res2);
    }
};

/**
 * 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 {
    unordered_map<TreeNode*, int> dp[2];
public:
    int rob(TreeNode* node, bool canRob = true) {
        if(!node) return 0;
        if(dp[canRob].count(node)) return dp[canRob][node];
        int &res = dp[canRob][node] = rob(node->left, true) + rob(node->right, true);;
        if(canRob) res = max(res, node->val + rob(node->left, false) + rob(node->right, false));
        return res;
    }
};