## Tree - 337. House Robber III

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337. 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**.
``````

java：

``````/**

* Definition for a binary tree node.

* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode(int x) { val = x; }
* }
*/
class Solution {
public int rob(TreeNode root) {
int[] res = robSub(root);
return Math.max(res[0], res[1]);
}

private int[] robSub(TreeNode root) {
if (root == null) return new int[2];

int[] left = robSub(root.left);
int[] right = robSub(root.right);
int[] res = new int[2];

res[0] = Math.max(left[0], left[1]) + Math.max(right[0], right[1]);
res[1] = root.val + left[0] + right[0];

return res;
}
}
``````

go：

``````/**

* Definition for a binary tree node.
* type TreeNode struct {
*     Val int
*     Left *TreeNode
*     Right *TreeNode
* }
*/
func rob(root *TreeNode) int {
var rob, norob int
if root != nil {
rob, norob = recursion(root)
}
return max(rob, norob)
}

// return rob, onrob
func recursion(node *TreeNode) (rob, norob int) {
if node == nil {
return
}

lrob, lnorob := recursion(node.Left)
rrob, rnorob := recursion(node.Right)

rob = node.Val + lnorob + rnorob
norob = max(lrob, lnorob) + max(rrob, rnorob)
return
}

func max(i, j int) int {
if i > j {
return i
}
return j
}
``````