How do you solve Construct Quad Tree on LeetCode?

Construct Quad Tree (LeetCode #427) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding the structure of a Quad-Tree is crucial.

What is the brute force solution for Construct Quad Tree?

The brute force approach for Construct Quad Tree is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves checking each cell in the grid to see if all values are the same. If they are, we create a leaf node; if not, we divide the grid into four quadrants and repeat the process. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Construct Quad Tree?

Construct Quad Tree uses the following concepts: Array, Divide and Conquer, Tree, Matrix. The recommended patterns to study are: Divide and Conquer, Recursion.

What are the interview tips for Construct Quad Tree?

Explain your thought process clearly. Ask clarifying questions about the input. Consider edge cases like empty grids or single-cell grids.

What are common mistakes when solving Construct Quad Tree?

Not checking for uniformity correctly. Forgetting to handle base cases properly.

#427

Construct Quad Tree

Medium

ArrayDivide and ConquerTreeMatrixDivide and ConquerRecursion

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses a recursive approach to divide the grid into quadrants only when necessary. By checking if the current section of the grid is uniform, we can quickly create leaf nodes and avoid unnecessary divisions.

⚙️

Algorithm

4 steps

1Step 1: Define a recursive function that checks if the current section of the grid is uniform.
2Step 2: If it is uniform, create a leaf node and return it.
3Step 3: If not, divide the grid into four quadrants and recursively call the function for each quadrant.
4Step 4: Assign the resulting nodes to the corresponding children of the current node.

solution.py33 lines

1class Node:
2    def __init__(self, val=False, isLeaf=False):
3        self.val = val
4        self.isLeaf = isLeaf
5        self.topLeft = None
6        self.topRight = None
7        self.bottomLeft = None
8        self.bottomRight = None
9
10
11def construct(grid):
12    def isUniform(x1, y1, x2, y2):
13        val = grid[x1][y1]
14        for i in range(x1, x2):
15            for j in range(y1, y2):
16                if grid[i][j] != val:
17                    return False, None
18        return True, val
19
20    def build(x1, y1, x2, y2):
21        uniform, val = isUniform(x1, y1, x2, y2)
22        if uniform:
23            return Node(val == 1, True)
24        mid_x = (x1 + x2) // 2
25        mid_y = (y1 + y2) // 2
26        node = Node(False, False)
27        node.topLeft = build(x1, y1, mid_x, mid_y)
28        node.topRight = build(x1, mid_y, mid_x, y2)
29        node.bottomLeft = build(mid_x, y1, x2, mid_y)
30        node.bottomRight = build(mid_x, mid_y, x2, y2)
31        return node
32
33    return build(0, 0, len(grid), len(grid))

ℹ

Complexity note: The time complexity is O(n) because each cell is processed once. The space complexity is O(n) due to the recursive call stack and the nodes created for the Quad-Tree.

1Understanding the structure of a Quad-Tree is crucial.
2Recognizing when to stop recursion helps optimize the solution.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.