<p>The thief has found himself a new place for his thievery again. There is only one entrance to this area, called <code>root</code>.</p>

<p>Besides the <code>root</code>, 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 <strong>two directly-linked houses were broken into on the same night</strong>.</p>

<p>Given the <code>root</code> of the binary tree, return <em>the maximum amount of money the thief can rob <strong>without alerting the police</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/10/rob1-tree.jpg" style="width: 277px; height: 293px;" />
<pre>
<strong>Input:</strong> root = [3,2,3,null,3,null,1]
<strong>Output:</strong> 7
<strong>Explanation:</strong> Maximum amount of money the thief can rob = 3 + 3 + 1 = 7.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/10/rob2-tree.jpg" style="width: 357px; height: 293px;" />
<pre>
<strong>Input:</strong> root = [3,4,5,1,3,null,1]
<strong>Output:</strong> 9
<strong>Explanation:</strong> Maximum amount of money the thief can rob = 4 + 5 = 9.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 10<sup>4</sup>]</code>.</li>
	<li><code>0 &lt;= Node.val &lt;= 10<sup>4</sup></code></li>
</ul>

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def rob(self, root: Optional[TreeNode]) -> int:
        # def helper(height, root, sums):
        #     if root==None: return
        #     sums[height%2]+=root.val
        #     helper(height+1, root.left, sums)
        #     helper(height+1, root.right,sums)

        # sums=[0,0]
        # helper(0,root,sums)
        # return max(sums)

        def helper(rt, index, dp):
            if index in dp: return dp[index]
            if rt==None: 
                dp[index]=0
                return 0
            x=y=u=v=0
            if rt.left !=None:
                x=helper(rt.left.left, 2*(2*index+1)+1,dp)
                y=helper(rt.left.right, 2*(2*index+1)+2, dp)
            if rt.right!=None:
                u=helper(rt.right.left, 2*(2*index+2)+1, dp)
                v=helper(rt.right.right, 2*(2*index+2)+2, dp)
            dp[index]=max(
                rt.val+x+y+u+v,
                helper(rt.left, 2*index+1, dp)+helper(rt.right, 2*index+2, dp)
            )
            return dp[index]
        return helper(root,0,{})
19400