# 1110. Delete Nodes And Return Forest

```
T: O(n)
S: O(n)
```

```java
/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    public List<TreeNode> delNodes(TreeNode root, int[] to_delete) {
        Set<TreeNode> result = new HashSet<>();
        result.add(root);

        Set<Integer> toDelete = new HashSet<>();
        for (int d : to_delete) {
            toDelete.add(d);
        }
        dfs(root, toDelete, result);

        return new ArrayList(result);
    }
    private TreeNode dfs(TreeNode node, Set<Integer> toDelete, Set<TreeNode> result) {
        if (node == null) {
            return null;
        }
        TreeNode res = node;
        if (toDelete.contains(node.val)) { // current node is deleting, so children become the root of new tree

            if (node.left != null) {
                result.add(node.left);
            }
            if (node.right != null) {
                result.add(node.right);
            }
            res = null; // return null
            result.remove(node); // remove itself in result
        }
        node.left = dfs(node.left, toDelete, result); // receive return value from children to link back to current node
        node.right = dfs(node.right, toDelete, result);
        return res;
    }
}

/***
This question is not to delete a tree and move a node ...(not 450 -> quite hard!)

is breaking a tree into "several trees"! so become a forest! -> 
!!!!key!!!: "so result only add "root" for each tree!""

ex: if only delete 2
   1
 2.  3
4 5. 6 7   

then 
4, 5 become 2 new roots for 2 trees 
1 is still root (so that's why need to re-link, I mean this -> node.left = dfs(node.left, toDelete, result); 
dfs will return null -> node.left = null)

so ans is [1,null, 3,6, 7] [4] [5]. (3 trees)

ex: if delete 1
then root become 2, 3 -> 2 trees

T: O(n)
S: O(n)
 */
```


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