Class Node
- java.lang.Object
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- g0501_0600.s0558_logical_or_of_two_binary_grids_represented_as_quad_trees.Node
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public class Node extends Object
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
andquadTree2
.quadTree1
represents an * n
binary matrix andquadTree2
represents anothern * 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 byquadTree1
andquadTree2
.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:
- 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:
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
orval
is True we represent it as 1 in the list[isLeaf, val]
and if the value ofisLeaf
orval
is False we represent it as 0.Example 1:
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.
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
andquadTree2
are both valid Quad-Trees each representing an * n
grid.n == 2x
where0 <= x <= 9
.
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Field Summary
Fields Modifier and Type Field Description Node
bottomLeft
Node
bottomRight
boolean
isLeaf
Node
topLeft
Node
topRight
boolean
val
-