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.
方法1:(递归算法)
/**
* 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) {
if(root == null) return 0;
helper(root);
return root.val;
}
private int helper(TreeNode root){
if(root == null) return 0;
int leftsub = helper(root.left);
int rightsub = helper(root.right);
int left = root.left == null ? 0 : root.left.val;
int right = root.right == null ? 0 : root.right.val;
root.val = Math.max(root.val + leftsub + rightsub, left + right);
return left + right;
}
}
时间复杂度:O(n)
空间复杂度:O(n)
方法2:(另一种递归思路)
public int rob(TreeNode root) {
if (root == null) return 0;
int val = 0;
if (root.left != null) {
val += rob(root.left.left) + rob(root.left.right);
}
if (root.right != null) {
val += rob(root.right.left) + rob(root.right.right);
}
return Math.max(val + root.val, rob(root.left) + rob(root.right));
}
时间复杂度:O(n)
空间复杂度:O(n)