House Robber III

Description

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]
 <font color="red">3</font>
/ \

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.

Solution(javascript)

const rob = (root) => {
  const memo = new Map()
  const aux = (node) => {
    if (memo.get(node) !== undefined) {
      return memo.get(node)
    }
    if (!node) {
      return 0
    }
    const grandchildren = []
    if (node.left) {
      grandchildren.push(node.left.left)
      grandchildren.push(node.left.right)
    }
    if (node.right) {
      grandchildren.push(node.right.left)
      grandchildren.push(node.right.right)
    }
    memo.set(node, Math.max(
      aux(node.left) + aux(node.right),
      grandchildren.reduce((acc, child) => aux(child) + acc, node.val),
    ))
    return memo.get(node)
  }
  return aux(root, 0)
}