Logical OR of Two Binary Grids Represented as Quad-Trees - Problem

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 matrices represented by quadTree1 and quadTree2.

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.

Quad-Tree Construction Rules:

If the current grid has the same value (all 1's or all 0's), set isLeaf to True and set val to the value of the grid.
If the current grid has different values, set isLeaf to False and divide the current grid into four sub-grids: topLeft, topRight, bottomLeft, bottomRight.

Input & Output

Example 1 — Basic OR Operation

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

› Output: [[0,1],[1,1],[1,1],[1,1],[1,1]]

💡 Note: First tree represents [[0,1],[1,1]], second tree represents [[1,1],[1,0]]. OR operation results in [[1,1],[1,1]] which becomes a single leaf node with value 1.

Example 2 — Single Cell Trees

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

› Output: [[1,1]]

💡 Note: Both trees represent single cells: 0 OR 1 = 1. Result is a single leaf with value 1.

Example 3 — No Simplification Possible

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

› Output: [[0,1],[1,1],[0,1],[1,1],[1,1]]

💡 Note: Trees represent different patterns that when OR'ed together create a mixed result that cannot be simplified to a single leaf.

Constraints

quadTree1 and quadTree2 are both valid Quad-Trees
n == 2^x where 0 ≤ x ≤ 9
Both trees represent the same size grid

Visualization

Tap to expand

Asked in

G Google 15 f Facebook 12 a Amazon 8

The key insight is to leverage the properties of the OR operation: if either quad-tree region contains all 1's, the result is all 1's. The direct recursive approach is optimal, combining trees without converting to matrices. Time: O(n²), Space: O(log n)

Common Approaches

✓ Sort First

⏱️ Time: N/A Space: N/A

Two Pointers

⏱️ Time: N/A Space: N/A

Direct Recursive OR

⏱️ Time: O(n²) Space: O(log n)

Directly combine the two quad-trees by recursively applying OR logic. If either node is a leaf with value true, or both are leaves, handle directly. Otherwise, recursively combine corresponding children.

Matrix Conversion Approach

⏱️ Time: O(n²) Space: O(n²)

First convert both quad-trees to their full matrix representation. Then perform element-wise OR operation on the matrices. Finally, construct a new quad-tree from the resulting matrix.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

28.5K Views

Medium Frequency

~25 min Avg. Time

485 Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen