558\. Logical OR of Two Binary Grids Represented as Quad-Trees

Medium

A Binary Matrix is a matrix in which all the elements are either **0** or **1**.

Given `quadTree1` and `quadTree2`. `quadTree1` represents a `n * n` binary matrix and `quadTree2` represents another `n * n` binary matrix.

Return _a Quad-Tree_ representing the `n * n` binary matrix which is the result of **logical bitwise OR** of the two binary matrixes represented by `quadTree1` and `quadTree2`.

Notice that you can assign the value of a node to **True** or **False** when `isLeaf` is **False**, and both are **accepted** in the answer.

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.
*   `isLeaf`: True if the node is leaf node on the tree or False if the node has the 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:

1.  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.
2.  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.
3.  Recurse for each of the children with the proper sub-grid.

![](https://assets.leetcode.com/uploads/2020/02/11/new_top.png)

If you want to know more about the Quad-Tree, you can refer to the [wiki](https://en.wikipedia.org/wiki/Quadtree).

**Quad-Tree format:**

The input/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:**

![](https://assets.leetcode.com/uploads/2020/02/11/qt1.png) ![](https://assets.leetcode.com/uploads/2020/02/11/qt2.png)

**Input:** quadTree1 = [[0,1],[1,1],[1,1],[1,0],[1,0]] , quadTree2 = [[0,1],[1,1],[0,1],[1,1],[1,0],null,null,null,null,[1,0],[1,0],[1,1],[1,1]]

**Output:** [[0,0],[1,1],[1,1],[1,1],[1,0]]

**Explanation:** quadTree1 and quadTree2 are shown above. You can see the binary matrix which is represented by each Quad-Tree. If we apply logical bitwise OR on the two binary matrices we get the binary matrix below which is represented by the result Quad-Tree. Notice that the binary matrices shown are only for illustration, you don't have to construct the binary matrix to get the result tree. ![](https://assets.leetcode.com/uploads/2020/02/11/qtr.png) 

**Example 2:**

**Input:** quadTree1 = [[1,0]], quadTree2 = [[1,0]]

**Output:** [[1,0]]

**Explanation:** Each tree represents a binary matrix of size 1\*1. Each matrix contains only zero. The resulting matrix is of size 1\*1 with also zero. 

**Constraints:**

*   `quadTree1` and `quadTree2` are both **valid** Quad-Trees each representing a `n * n` grid.
*   <code>n == 2<sup>x</sup></code> where `0 <= x <= 9`.