427. Construct Quad Tree

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Given a `n * n`

matrix `grid`

of `0's`

and `1's`

only. We want to represent `grid`

with a Quad-Tree.

Return *the root of the Quad-Tree representing *`grid`

.

A Quad-Tree is a tree data structure in which each internal node has exactly four children. Besides, each node has two attributes:

`val`

: True if the node represents a grid of 1's or False if the node represents a grid of 0's. Notice that you can assign the`val`

to True or False when`isLeaf`

is False, and both are accepted in the answer.`isLeaf`

: True if the node is a leaf node on the tree or False if the node has four children.

class Node { public boolean val; public boolean isLeaf; public Node topLeft; public Node topRight; public Node bottomLeft; public Node bottomRight; }

We can construct a Quad-Tree from a two-dimensional area using the following steps:

- If the current grid has the same value (i.e all
`1's`

or all`0's`

) set`isLeaf`

True and set`val`

to the value of the grid and set the four children to Null and stop. - If the current grid has different values, set
`isLeaf`

to False and set`val`

to any value and divide the current grid into four sub-grids as shown in the photo. - Recurse for each of the children with the proper sub-grid.

If you want to know more about the Quad-Tree, you can refer to the wiki.

**Quad-Tree format:**

You don't need to read this section for solving the problem. This is only if you want to understand the output format here. The output represents the serialized format of a Quad-Tree using level order traversal, where `null`

signifies a path terminator where no node exists below.

It is very similar to the serialization of the binary tree. The only difference is that the node is represented as a list `[isLeaf, val]`

.

If the value of `isLeaf`

or `val`

is True we represent it as **1** in the list `[isLeaf, val]`

and if the value of `isLeaf`

or `val`

is False we represent it as **0**.

**Example 1:**

Input:grid = [[0,1],[1,0]]Output:[[0,1],[1,0],[1,1],[1,1],[1,0]]Explanation:The explanation of this example is shown below: Notice that 0 represnts False and 1 represents True in the photo representing the Quad-Tree.

**Example 2:**

Input:grid = [[1,1,1,1,0,0,0,0],[1,1,1,1,0,0,0,0],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,0,0,0,0],[1,1,1,1,0,0,0,0],[1,1,1,1,0,0,0,0],[1,1,1,1,0,0,0,0]]Output:[[0,1],[1,1],[0,1],[1,1],[1,0],null,null,null,null,[1,0],[1,0],[1,1],[1,1]]Explanation:All values in the grid are not the same. We divide the grid into four sub-grids. The topLeft, bottomLeft and bottomRight each has the same value. The topRight have different values so we divide it into 4 sub-grids where each has the same value. Explanation is shown in the photo below:

**Constraints:**

`n == grid.length == grid[i].length`

`n == 2`

where^{x}`0 <= x <= 6`

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