427. Construct Quad Tree
Description
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 theval
to True or False whenisLeaf
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 all0's
) setisLeaf
True and setval
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 setval
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 represents 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 == 2x
where0 <= x <= 6
Solutions
Solution 1
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