How do you solve Fill a Special Grid on LeetCode?

Fill a Special Grid (LeetCode #3537) 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: Recursive structure mirrors the grid's quadrant division.

What is the time complexity of Fill a Special Grid?

The optimal solution for Fill a Special Grid runs in O(n) time and uses O(n) space. The recursive approach efficiently fills the grid in O(n) time by leveraging the structure of quadrants.

What is the brute force solution for Fill a Special Grid?

The brute force approach for Fill a Special Grid is Brute Force, with O(n²) time complexity and O(1) space complexity. Fill the grid by checking all possible placements of numbers. This method is inefficient as it doesn't leverage the structure of the problem. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Fill a Special Grid?

Fill a Special Grid uses the following concepts: Array, Divide and Conquer, Matrix. The recommended patterns to study are: Divide and Conquer, Recursion.

What are the interview tips for Fill a Special Grid?

Explain your thought process clearly. Use diagrams to illustrate your approach. Practice similar recursive problems to build intuition.

What are common mistakes when solving Fill a Special Grid?

Not properly managing indices during recursion. Failing to respect the order of filling quadrants.

#3537

Fill a Special Grid

Medium

ArrayDivide and ConquerMatrixDivide 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)

Utilize recursion to fill quadrants systematically, ensuring the special conditions are met without redundant checks.

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Algorithm

3 steps

1Step 1: Define a recursive function to fill the grid based on the current quadrant size.
2Step 2: Calculate the starting number for the current quadrant and fill it with the appropriate range of numbers.
3Step 3: Recursively call the function for each quadrant, adjusting the starting number accordingly.

solution.py18 lines

1# Full working Python code
2
3def fill_grid(n):
4    size = 2 ** n
5    grid = [[0] * size for _ in range(size)]
6    def fill(x, y, size, start):
7        if size == 1:
8            grid[x][y] = start
9            return start + 1
10        mid = size // 2
11        start = fill(x, y + mid, mid, start)
12        start = fill(x + mid, y + mid, mid, start)
13        start = fill(x + mid, y, mid, start)
14        return fill(x, y, mid, start)
15    fill(0, 0, size, 0)
16    return grid
17
18print(fill_grid(2))

ℹ

Complexity note: The recursive approach efficiently fills the grid in O(n) time by leveraging the structure of quadrants.

1Recursive structure mirrors the grid's quadrant division.
2Each quadrant can be treated independently while maintaining overall constraints.

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