# 0558. Logical OR of Two Binary Grids Represented as Quad-Trees

https://leetcode.com/problems/logical-or-of-two-binary-grids-represented-as-quad-trees

## Description

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.&#x20;

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.
```

**Example 3:**

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

**Example 4:**

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

**Example 5:**

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

**Constraints:**

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

## ac

```java
```
