What is the time complexity of Find the Largest Area of Square Inside Two Rectangles?

The optimal solution for Find the Largest Area of Square Inside Two Rectangles runs in O(n log n) time and uses O(n) space. The time complexity is O(n log n) due to sorting the unique coordinates, while the space complexity is O(n) for storing these coordinates.

What is the brute force solution for Find the Largest Area of Square Inside Two Rectangles?

The brute force approach for Find the Largest Area of Square Inside Two Rectangles is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks every pair of rectangles to find their intersection area. By calculating the maximum square that can fit within this area, we can determine the largest square possible among all pairs. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Find the Largest Area of Square Inside Two Rectangles?

Find the Largest Area of Square Inside Two Rectangles uses the following concepts: Array, Math, Geometry. The recommended patterns to study are: Geometry, Sorting.

What are the interview tips for Find the Largest Area of Square Inside Two Rectangles?

Clarify the problem requirements and constraints before diving into coding. Think about edge cases, such as no intersections or rectangles being adjacent. Discuss your thought process and approach with the interviewer to demonstrate your understanding.

What are common mistakes when solving Find the Largest Area of Square Inside Two Rectangles?

Overlooking cases where rectangles do not intersect. Not considering the maximum square size that can fit in the intersection.

#3047

Find the Largest Area of Square Inside Two Rectangles

Medium

ArrayMathGeometryGeometrySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n log n)Space O(n)

The optimal approach leverages the fact that we only need to consider the edges of rectangles to determine potential square sizes. By focusing on the coordinates of the rectangles, we can efficiently find the maximum square area without checking every pair.

⚙️

Algorithm

4 steps

1Step 1: Create a list of all unique x-coordinates and y-coordinates from the rectangles.
2Step 2: Sort these coordinates and iterate through them to find potential square sizes.
3Step 3: For each pair of adjacent coordinates, calculate the potential square side length and check if it can fit in the overlapping area of rectangles.
4Step 4: Keep track of the maximum area found.

solution.py10 lines

1def maxSquareArea(bottomLeft, topRight):
2    x_coords = sorted(set(x for rect in bottomLeft + topRight for x in rect))
3    y_coords = sorted(set(y for rect in bottomLeft + topRight for y in rect))
4    max_area = 0
5    for i in range(len(x_coords) - 1):
6        for j in range(len(y_coords) - 1):
7            side_length = min(x_coords[i + 1] - x_coords[i], y_coords[j + 1] - y_coords[j])
8            if side_length > 0:
9                max_area = max(max_area, side_length * side_length)
10    return max_area

ℹ

Complexity note: The time complexity is O(n log n) due to sorting the unique coordinates, while the space complexity is O(n) for storing these coordinates.

1Understanding rectangle intersection is crucial for solving this problem.
2The size of the square is limited by the smallest dimension of the intersection area.

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