How do you solve Rectangle Area II on LeetCode?

Rectangle Area II (LeetCode #850) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Understanding how to handle overlapping areas is crucial.

What is the brute force solution for Rectangle Area II?

The brute force approach for Rectangle Area II is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach calculates the area of each rectangle and then checks for overlaps by iterating through each pair of rectangles. This method is straightforward but inefficient for larger inputs. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Rectangle Area II?

Rectangle Area II uses the following concepts: Array, Segment Tree, Sweep Line, Ordered Set. The recommended patterns to study are: Sweep Line, Segment Tree.

What are the interview tips for Rectangle Area II?

Explain your thought process clearly while coding. Discuss the trade-offs of different approaches. Practice drawing diagrams to visualize overlapping rectangles.

What are common mistakes when solving Rectangle Area II?

Not considering edge cases like rectangles that touch but do not overlap. Failing to account for the modulo operation in the final result.

#850

Rectangle Area II

Hard

ArraySegment TreeSweep LineOrdered SetSweep LineSegment Tree

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

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

The optimal solution uses a sweep line algorithm combined with a segment tree to efficiently calculate the area covered by rectangles, handling overlaps without explicitly checking each pair.

⚙️

Algorithm

3 steps

1Step 1: Create events for the start and end of each rectangle.
2Step 2: Sort events by x-coordinate. For each event, update the segment tree to reflect the active rectangles.
3Step 3: Calculate the area covered by the active rectangles between consecutive x-coordinates.

solution.py35 lines

1# Full working Python code
2class Solution:
3    def computeArea(self, rectangles):
4        events = []
5        for x1, y1, x2, y2 in rectangles:
6            events.append((x1, y1, y2, 1))  # Start of rectangle
7            events.append((x2, y1, y2, -1)) # End of rectangle
8        events.sort()
9
10        def calculate_active_length(active_intervals):
11            length = 0
12            prev_y = -1
13            for y1, y2 in active_intervals:
14                if y1 > prev_y:
15                    length += y2 - y1
16                    prev_y = y2
17                elif y2 > prev_y:
18                    length += y2 - prev_y
19                    prev_y = y2
20            return length
21
22        active_intervals = []
23        total_area = 0
24        prev_x = events[0][0]
25
26        for x, y1, y2, typ in events:
27            total_area += calculate_active_length(active_intervals) * (x - prev_x)
28            if typ == 1:
29                active_intervals.append((y1, y2))
30            else:
31                active_intervals.remove((y1, y2))
32            active_intervals.sort()
33            prev_x = x
34
35        return total_area % (10**9 + 7)

ℹ

Complexity note: The complexity is dominated by the sorting of events, which is O(n log n), and maintaining the active intervals using a map or segment tree.

1Understanding how to handle overlapping areas is crucial.
2Using data structures like segment trees can significantly optimize the area calculation.

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