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# 1516. Move Sub-Tree of N-Ary Tree

Given the `root` of an N-ary tree of unique values, and two nodes of the tree `p` and `q`.

You should move the subtree of the node `p` to become a direct child of node `q`. If `p` is already a direct child of `q`, don't change anything. Node `p` must be the last child in the children list of node `q`.

Return the root of the tree after adjusting it.

There are 3 cases for nodes `p` and `q`:

1. Node `q` is in the sub-tree of node `p`.
2. Node `p` is in the sub-tree of node `q`.
3. Neither node `p` is in the sub-tree of node `q` nor node `q` is in the sub-tree of node `p`.

In cases 2 and 3, you just need to move `p` (with its sub-tree) to be a child of `q`, but in case 1 the tree may be disconnected, thus you need to reconnect the tree again. Please read the examples carefully before solving this problem.

Nary-Tree input serialization is represented in their level order traversal, each group of children is separated by the null value (See examples).

For example, the above tree is serialized as [1,null,2,3,4,5,null,null,6,7,null,8,null,9,10,null,null,11,null,12,null,13,null,null,14].

Example 1:

```Input: root = [1,null,2,3,null,4,5,null,6,null,7,8], p = 4, q = 1
Output: [1,null,2,3,4,null,5,null,6,null,7,8]
Explanation: This example follows the second case as node p is in the sub-tree of node q. We move node p with its sub-tree to be a direct child of node q.
Notice that node 4 is the last child of node 1.```

Example 2:

```Input: root = [1,null,2,3,null,4,5,null,6,null,7,8], p = 7, q = 4
Output: [1,null,2,3,null,4,5,null,6,null,7,8]
Explanation: Node 7 is already a direct child of node 4. We don't change anything.
```

Example 3:

```Input: root = [1,null,2,3,null,4,5,null,6,null,7,8], p = 3, q = 8
Output: [1,null,2,null,4,5,null,7,8,null,null,null,3,null,6]
Explanation: This example follows case 3 because node p is not in the sub-tree of node q and vice-versa. We can move node 3 with its sub-tree and make it as node 8's child.
```

Example 4:

```Input: root = [1,null,2,3,null,4,5,null,6,null,7,8], p = 2, q = 7
Output: [1,null,7,3,null,2,null,6,null,4,5,null,null,8]
Explanation: Node q is in the sub-tree of node p, so this is case 1.
The first step, we move node p (with all of its sub-tree except for node q) and add it as a child to node q.
Then we will see that the tree is disconnected, you need to reconnect node q to replace node p as shown.
```

Example 5:

```Input: root = [1,null,2,3,null,4,5,null,6,null,7,8], p = 1, q = 2
Output: [2,null,4,5,1,null,7,8,null,null,3,null,null,null,6]
Explanation: Node q is in the sub-tree of node p, so this is case 1.
The first step, we move node p (with all of its sub-tree except for node q) and add it as a child to node q.
As node p was the root of the tree, node q replaces it and becomes the root of the tree.
```

Constraints:

• The total number of nodes is between `[2, 1000]`.
• Each node has a unique value.
• `p != null`
• `q != null`
• `p` and `q` are two different nodes (i.e. ```p != q```).

Hard

Prime

Unknown

### Problem Solution

1516-Move-Sub-Tree-of-N-Ary-Tree