337. House RobberIII

题目：
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:

     3
    / \
   2   3
    \   \ 
     3   1

Maximum amount of money the thief can rob = 3 + 3 + 1 = 7.
Example 2:

     3
    / \
   4   5
  / \   \ 
 1   3   1

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

解答：
1.最原始的想法是对每个点分两种情况考虑：如果取这个点，那么下一次取的就是它的孙结点；如果不取这个点，那么下一次取的就是它的子结点：
代码：

private Map<TreeNode, Integer> map = new HashMap<>();
public int rob(TreeNode root) {
    if (root == null) return 0;
    if (map.containsKey(root)) return map.get(root);
    
    int result = 0;
    if (root.left != null) {
        result += rob(root.left.left) + rob(root.left.right);
    }
    if (root.right != null) {
        result += rob(root.right.left) + rob(root.right.right);
    }
    
    result = Math.max(root.val + result, rob(root.left) + rob(root.right));
    map.put(root, result);
    
    return result;
}

这里用map来记下当前结点的和，避免一些重复记算。

2.Greedy算法

public int[] Helper(TreeNode root) {
    if (root == null) return new int[2];
    //记录下取和不取两种情况的最大值
    int[] left = Helper(root.left);
    int[] right = Helper(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;
}

public int rob(TreeNode root) {
    int[] res = Helper(root);
    return Math.max(res[0], res[1]);
}