# House Robber III

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.

**Example 1:**

```
Input: 
[3,2,3,null,3,null,1]


3

    / \
   2   3
    \   \ 

3   1

Output:
 7 

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

**Example 2:**

```
Input: 
[3,4,5,1,3,null,1]

     3
    / \

4
5

  / \   \ 
 1   3   1


Output:
 9

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

分析

dfs返回的是【不选，选】

```
# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
    def rob(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """

        res = self.helper(root)
        return max(res)

    def helper(self,root):
         # every house you have two option, rob or not rob. 
        # [value1, value2] value1: not rob current house, rob current house
        if not root:
            return [0,0]
        if not root.left and not root.right:
            return [0,root.val]
        left = self.helper(root.left)
        right = self.helper(root.right)
        return [max(left[0],left[1])+max(right[0],right[1]), root.val+left[0]+right[0]]
```


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