How do you solve Maximize Area of Square Hole in Grid on LeetCode?

Maximize Area of Square Hole in Grid (LeetCode #2943) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n + m log m) time complexity and O(1) space complexity. Key insight: Understanding the gaps between bars is crucial for determining the maximum square area.

What is the time complexity of Maximize Area of Square Hole in Grid?

The optimal solution for Maximize Area of Square Hole in Grid runs in O(n log n + m log m) time and uses O(1) space. The sorting of the bars takes O(n log n) and O(m log m), while calculating the gaps is linear, leading to an overall efficient solution.

What is the brute force solution for Maximize Area of Square Hole in Grid?

The brute force approach for Maximize Area of Square Hole in Grid is Brute Force, with O(n²) time complexity and O(1) space complexity. We can try to find the maximum square hole by checking all possible combinations of removing horizontal and vertical bars. This approach is straightforward but inefficient as it checks every possibility. The optimal Optimal Solution approach improves this to O(n log n + m log m).

What algorithm or data structure is used to solve Maximize Area of Square Hole in Grid?

Maximize Area of Square Hole in Grid uses the following concepts: Array, Sorting. The recommended patterns to study are: Sorting, Array Manipulation.

What are the interview tips for Maximize Area of Square Hole in Grid?

Always clarify the problem and constraints before diving into coding. Think about edge cases, such as when there are no bars to remove. Explain your thought process while coding to demonstrate your understanding.

What are common mistakes when solving Maximize Area of Square Hole in Grid?

Failing to consider the edges of the grid when calculating gaps. Not sorting the bars before calculating gaps.

#2943

Maximize Area of Square Hole in Grid

Medium

ArraySortingSortingArray Manipulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n log n + m log m)Space O(1)

By focusing on the gaps between the bars after sorting, we can efficiently find the maximum square area without checking every combination. This reduces the time complexity significantly.

⚙️

Algorithm

3 steps

1Step 1: Sort the hBars and vBars arrays.
2Step 2: Calculate the maximum gaps between consecutive bars in both arrays, including the edges of the grid.
3Step 3: The maximum area of the square hole is the square of the minimum gap found.

solution.py11 lines

1def maxSquareAreaOptimal(n, m, hBars, vBars):
2    hBars.sort()
3    vBars.sort()
4    max_h_gap = max(hBars[0] - 1, n + 1 - hBars[-1])
5    for i in range(1, len(hBars)):
6        max_h_gap = max(max_h_gap, hBars[i] - hBars[i - 1])
7    max_v_gap = max(vBars[0] - 1, m + 1 - vBars[-1])
8    for i in range(1, len(vBars)):
9        max_v_gap = max(max_v_gap, vBars[i] - vBars[i - 1])
10    return min(max_h_gap, max_v_gap) ** 2
11

ℹ

Complexity note: The sorting of the bars takes O(n log n) and O(m log m), while calculating the gaps is linear, leading to an overall efficient solution.

1Understanding the gaps between bars is crucial for determining the maximum square area.
2Sorting the bars allows us to efficiently calculate the maximum gaps.

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