Construct Quad Tree Python Solution with Tests

LeetCode 427, Medium. Topics: Array, Divide and Conquer, Tree, Matrix. View on LeetCode. Generate this problem as a practice environment: tested reference solution, 15 parametrized pytest cases, and a playground notebook:

lcpy gen -n 427   # by problem number
lcpy gen -s construct_quad_tree   # by problem name

Problem

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 the val to True or False when isLeaf 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 all 0's) set isLeaf True and set val 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 set val 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.

Quad-Tree format: 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. The node is represented as a list [isLeaf, val].

Examples

Input: grid = [[0,1],[1,0]]
Output: [[0,1],[1,0],[1,1],[1,1],[1,0]]
Explanation: The root is not a leaf. Its four children (top-left, top-right, bottom-left, bottom-right) are leaves.

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]]

Constraints

n == grid.length == grid[i].length
n == 2^x where 0 <= x <= 6

Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

from __future__ import annotations


# ruff: noqa: N803
class Node:
    def __init__(
        self,
        val: bool,
        isLeaf: bool,
        topLeft: Node | None = None,
        topRight: Node | None = None,
        bottomLeft: Node | None = None,
        bottomRight: Node | None = None,
    ) -> None:
        self.val = val
        self.isLeaf = isLeaf
        self.topLeft = topLeft
        self.topRight = topRight
        self.bottomLeft = bottomLeft
        self.bottomRight = bottomRight


class Solution:
    # Time: O(n^2) every cell visited once per level, log n levels
    # Space: O(log n) recursion depth (tree height)
    def construct(self, grid: list[list[int]]) -> Node:
        def build(row: int, col: int, size: int) -> Node:
            first = grid[row][col]
            uniform = True
            for r in range(row, row + size):
                for c in range(col, col + size):
                    if grid[r][c] != first:
                        uniform = False
                        break
                if not uniform:
                    break
            if uniform:
                return Node(val=bool(first), isLeaf=True)
            half = size // 2
            return Node(
                val=True,
                isLeaf=False,
                topLeft=build(row, col, half),
                topRight=build(row, col + half, half),
                bottomLeft=build(row + half, col, half),
                bottomRight=build(row + half, col + half, half),
            )

        return build(0, 0, len(grid))

Complexity

Time	Space
O(n^2) every cell visited once per level, log n levels	O(log n) recursion depth (tree height)

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Construct Quad Tree Python Solution with Tests

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