construct quad tree leetcode 427 python

certainly! the problem of constructing a quad tree is a common one on leetcode (problem 427). a quad tree is a tree data structure used to partition a two-dimensional space by recursively subdividing it into four quadrants or regions. this can be useful for various applications like image compression, spatial indexing, and more.

problem statement

you are given a 2d grid of `0`s and `1`s representing a binary image. each cell in the grid is either white (0) or black (1). your task is to construct a quad tree representation of the grid.

quad tree definition

a quad tree is defined as follows:
- if the grid is uniform (all values are the same), then the node is a leaf node with the corresponding value.
- if the grid is not uniform, then it can be divided into four quadrants (top-left, top-right, bottom-left, bottom-right), and the node should have four children corresponding to these quadrants.

class definition

the quad tree node can be defined as follows in python:

steps to construct the quad tree

1. **check if the current grid is uniform**: if all elements in the grid are the same, create a leaf node.
2. **recursively divide the grid**: if the grid is not uniform, divide it into four equal parts and recursively construct the quad tree for each part.
3. **assign the child nodes**: after constructing the four quadrants, assign them to the current node.

implementation

here is a python implementation of the quad tree construction based on the above logic:

explanation of the code

1. **node class**: this class initializes a node for the quad tree with its value, leaf status, and pointers to its four children.
2. **isuniform function**: this helper function checks if all values in the specified region of the grid are the same.
3. **buildtree function**: this recursive function constructs the quad tree:
- it first checks if the current region is uniform.
- if it is, it creates a leaf node.
- if it isn't, it divides the region into four quadrants ...

#QuadTree #LeetCode #windows
quad tree
LeetCode 427
Python
data structures
recursive algorithm
spatial partitioning
binary tree
image representation
node definition
region division
depth-first search
tree construction
2D grid
coordinate system
efficient storage