原题链接在这里:https://leetcode.com/problems/house-robber-iii/

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.

题解:

List some examples and find out this has to be done with DFS.

One or null node is easy to think, thus use DFS bottom-up, devide and conquer.

Then it must return value on dfs. Each dfs needs current node and return [robRoot, notRobRoot], which denotes rob or skip current node.

robRoot = notRobLeft + notRobRight + root.val

notRobRoot = Math.max(robLeft, notRobLeft) + Math.max(robRight, notRobRight).

Time Complexity: O(n).

Space: O(logn). 用了logn层stack.

AC Java:

 /**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode(int x) { val = x; }
* }
*/
public class Solution {
public int rob(TreeNode root) {
int [] res = dfs(root);
return Math.max(res[0], res[1]);
}
private int [] dfs(TreeNode root){
int [] dp = new int[2];
if(root == null){
return dp;
}
int [] left = dfs(root.left);
int [] right = dfs(root.right);
//dp[0]表示偷root的, 那么左右都不能偷, 所以用left[1], right[1].
dp[0] = left[1] + right[1] + root.val;
//dp[1]表示不偷root的, 那么左右偷不偷都可以, 取最大值
dp[1] = Math.max(left[0], left[1]) + Math.max(right[0], right[1]);
return dp;
}
}

类似House RobberHouse Robber II.

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