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