How do you solve Check if Grid can be Cut into Sections on LeetCode?

Check if Grid can be Cut into Sections (LeetCode #3394) 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 how to identify unique cut positions is crucial for optimizing the solution.

What is the brute force solution for Check if Grid can be Cut into Sections?

The brute force approach for Check if Grid can be Cut into Sections is Brute Force, with O(n²) time complexity and O(n) space complexity. The brute force approach checks every possible pair of horizontal and vertical cuts to see if they can divide the grid into three sections, each containing at least one rectangle. This method is straightforward but inefficient for larger grids. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Check if Grid can be Cut into Sections?

Check if Grid can be Cut into Sections uses the following concepts: Array, Sorting. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Check if Grid can be Cut into Sections?

Always clarify the problem requirements and constraints before diving into coding. Think about the implications of the grid size; optimize for larger inputs. Practice explaining your thought process while coding, as it helps in interviews.

What are common mistakes when solving Check if Grid can be Cut into Sections?

Failing to check all possible combinations of cuts, which can lead to incorrect results. Not considering edge cases where rectangles might be tightly packed.

#3394

Check if Grid can be Cut into Sections

Medium

ArraySortingHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(n)

The optimal approach focuses on identifying the unique cut positions and checking if we can create three sections with at least one rectangle in each section. This is done in a single pass for both horizontal and vertical cuts, making it much more efficient.

⚙️

Algorithm

4 steps

1Step 1: Create sets for unique horizontal and vertical cut positions from the rectangle coordinates.
2Step 2: Sort the unique cut positions.
3Step 3: Use a single pass to count rectangles in each section for both horizontal and vertical cuts.
4Step 4: Check if there exists a pair of cuts that divides the rectangles into three sections with at least one rectangle in each.

solution.py19 lines

1def can_cut_grid(n, rectangles):
2    horizontal_cuts = sorted(set(y2 for _, y1, _, y2 in rectangles))
3    vertical_cuts = sorted(set(x2 for x1, _, x2, _ in rectangles))
4    return check_cuts(rectangles, horizontal_cuts, True) or check_cuts(rectangles, vertical_cuts, False)
5
6def check_cuts(rectangles, cuts, is_horizontal):
7    for i in range(len(cuts) - 1):
8        sections = [0, 0, 0]
9        for x1, y1, x2, y2 in rectangles:
10            if is_horizontal:
11                if y2 <= cuts[i]: sections[0] += 1
12                elif y1 >= cuts[i + 1]: sections[2] += 1
13                else: sections[1] += 1
14            else:
15                if x2 <= cuts[i]: sections[0] += 1
16                elif x1 >= cuts[i + 1]: sections[2] += 1
17                else: sections[1] += 1
18        if all(s > 0 for s in sections): return True
19    return False

ℹ

Complexity note: The time complexity is O(n) because we only pass through the rectangles a limited number of times, and the space complexity is O(n) due to storing unique cut positions.

1Understanding how to identify unique cut positions is crucial for optimizing the solution.
2Using sets to store cut positions helps in avoiding duplicates and simplifies the logic.

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