337.打家劫舍-iii.cpp

/*
 * @lc app=leetcode.cn id=337 lang=cpp
 *
 * [337] 打家劫舍 III
 *
 * https://leetcode-cn.com/problems/house-robber-iii/description/
 *
 * algorithms
 * Medium (57.31%)
 * Likes:    432
 * Dislikes: 0
 * Total Accepted:    37.9K
 * Total Submissions: 65.7K
 * Testcase Example:  '[3,2,3,null,3,null,1]'
 *
 * 在上次打劫完一条街道之后和一圈房屋后，小偷又发现了一个新的可行窃的地区。
 * 这个地区只有一个入口，我们称之为“根”。
 * 除了“根”之外，每栋房子有且只有一个“父“房子与之相连。
 * 一番侦察之后，聪明的小偷意识到“这个地方的所有房屋的排列类似于一棵二叉树”。
 * 如果两个直接相连的房子在同一天晚上被打劫，房屋将自动报警。
 * 计算在不触动警报的情况下，小偷一晚能够盗取的最高金额。
 * 
 * 示例 1:
 
 * 输入: [3,2,3,null,3,null,1]
 * 
 * ⁠    3
 * ⁠   / \
 * ⁠  2   3
 * ⁠   \   \ 
 * ⁠    3   1
 * 
 * 输出: 7 
 * 解释: 小偷一晚能够盗取的最高金额 = 3 + 3 + 1 = 7.
 * 
 * 示例 2:
 * 
 * 输入: [3,4,5,1,3,null,1]
 * 
 *     3
 * ⁠   / \
 * ⁠  4   5
 * ⁠ / \   \ 
 * ⁠1   3   1
 * 
 * 输出: 9
 * 解释: 小偷一晚能够盗取的最高金额 = 4 + 5 = 9.
 * 
 * 
 */

// @lc code=start
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 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 * - 题目比较新颖，感觉模式，无从下手，不知道从哪里开始建立模型。
 * https://leetcode-cn.com/problems/house-robber-iii/solution/san-chong-fang-fa-jie-jue-shu-xing-dong-tai-gui-hu/
 * 
 *  完全思考copy 别人的答案 自己失去思考规划问题能力和状态，还有其他考察的
 * 
 * https://leetcode-cn.com/problems/house-robber-iii/solution/tong-yong-si-lu-tuan-mie-da-jia-jie-she-wen-ti-b-2/
 
   
 */
//
class Solution
{
private:
    map<TreeNode *, int> dp;

public:
    //耗时：25*4
    int
    rob(TreeNode *root)
    {
        if (nullptr == root)
        {
            return 0; //假如一个节点都没有，返回0
        }
        if (dp.count(root) == 1)
        {
            return dp[root];
        }
        //不抢爷爷,只能抢爸爸
        int left = rob(root->left);
        int right = rob(root->right);
        int not_rob = left + right;

        //抢爷爷，不能抢爸爸，然后抢4个孙子

        int must_rob = root->val;
        if (root->left)
        {
            must_rob += rob(root->left->left);
            must_rob += rob(root->left->right);
        }

        if (root->right)
        {
            must_rob += rob(root->right->left);
            must_rob += rob(root->right->right);
        }

        int res = max(must_rob, not_rob);
        dp[root] = res;
        return res;
    }
};
// class Solution1
// {
// public:
//     int rob(TreeNode *root)
//     {
//         pair<int, int> res = dfs(root);
//         return max(res.first, res.second);
//     }

// private:
//     pair<int, int> dfs(TreeNode *root)
//     {
//         if (nullptr == root)
//         {
//             return make_pair(0, 0);
//         }

//         pair<int, int> res(0, 0);
//         pair<int, int> left = dfs(root->left);
//         pair<int, int> right = dfs(root->right);

//         // 没抢
//         res.first = max(left.first, left.second) + max(right.first, right.second); //为什么不想加呀
//         // 抢了
//         res.second = left.first + right.first + root->val;

//         return res;
//     }
// };
// Map<TreeNode, Integer> memo = new HashMap<>();
// public int rob(TreeNode root) {
//     if (root == null) return 0;
//     // 利用备忘录消除重叠子问题
//     if (memo.containsKey(root))
//         return memo.get(root);
//     // 抢，然后去下下家
//     int do_it = root.val
//         + (root.left == null ?
//             0 : rob(root.left.left) + rob(root.left.right))
//         + (root.right == null ?
//             0 : rob(root.right.left) + rob(root.right.right));
//     // 不抢，然后去下家
//     int not_do = rob(root.left) + rob(root.right);

//     int res = Math.max(do_it, not_do);
//     memo.put(root, res);
//     return res;
// }

// 作者：labuladong
// 链接：https://leetcode-cn.com/problems/house-robber-iii/solution/tong-yong-si-lu-tuan-mie-da-jia-jie-she-wen-ti-b-2/
// 来源：力扣（LeetCode）
// 著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。