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.

  3
 / 2   3
 \   \ 
  3   1

Maximum amount of money the thief can rob = 3 + 3 + 1 = 7.

    3
   /   4   5
 / \   \ 
1   3   1

Maximum amount of money the thief can rob = 4 + 5 = 9.

這題一開始用遞歸 結果超時；隨機加cache變成DP。。通過了

helper1表示搶root

helper2表示不搶root；此處註意不搶root時 即可以搶root.left和root.right 也可以不搶它們 二取其一 所以註意42-47行

 1 /**
 2  * Definition of TreeNode:
 3  * public class TreeNode {
 4  *     public int val;
 5  *     public TreeNode left, right;
 6  *     public TreeNode(int x) { val = x; }
 7  * }
 8  */
 9 public class
 
 Solution {
10     /**
11      * @param root: The root of binary tree.
12      * @return: The maximum amount of money you can rob tonight
13      */
14      Map<TreeNode, Integer> map1 = new HashMap<TreeNode, Integer>();
15      Map<TreeNode, Integer> map2 = new HashMap<TreeNode, Integer>();
16     public int houseRobber3(TreeNode root) {
17         // write your code here
18         if(root==null) return 0;
19         return Math.max(helper1(root), helper2(root));
20     }
21     // include root
22     private int helper1(TreeNode root){
23         if(map1.containsKey(root)){
24             return map1.get(root);
25         }
26         int sum = root.val;
27         if(root.left!=null){
28             sum += helper2(root.left);
29         }
30         if(root.right!=null){
31             sum += helper2(root.right);
32         }
33         map1.put(root, sum);
34         return sum;
35     }
36     // not include root
37     private int helper2(TreeNode root){
38         if(map2.containsKey(root)){
39             return map2.get(root);
40         }
41         int sum = 0;
42         if(root.left!=null){
43             sum += Math.max(helper1(root.left), helper2(root.left));
44         }
45         if(root.right!=null){
46             sum += Math.max(helper1(root.right), helper2(root.right));
47         }
48         map2.put(root, sum);
49         return sum;
50     }
51 }

House Robber III