• Question
• Solution

Question

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
    / \
   2   3
    \   \ 
     3   1

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

Solution

Result: Accepted Time: 15 ms

Here should be some explanations.

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
 
 struct State{
     int a,b;
     int get_max()
     {
         return a > b ? a : b;
     }
     State():a(0),b(0){}
     State(int aa,int bb):a(aa),b(bb){}
 };
 
State robber(TreeNode * root)
{
    if(root == NULL)
        return State();
    State left = robber(root->left);
    State right = robber(root->right);
    return State(left.get_max() + right.get_max(), left.a + right.a + root->val);
}
class Solution {
public:
    int rob(TreeNode* root) {
        return robber(root).get_max();
    }
};

Complexity Analytics

• Time Complexity: $O(n)$
• Space Complexity: $O(1)$