LeetCode 391: Perfect Rectangle Solution

Master LeetCode problem 391 (Perfect Rectangle), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

391. Perfect Rectangle

Hard

Array Line Sweep

Problem Explanation

Explanation:

The problem requires us to determine if a given set of rectangles forms an exact cover of a rectangular region. An exact cover means that each point within the region is covered by exactly one rectangle and no extra points are covered. To solve this problem, we can follow these steps:

Calculate the total area covered by all rectangles and also keep track of the corners of each rectangle.
The sum of areas of individual rectangles should be equal to the total area covered by all rectangles.
Ensure that all corner points (bottom-left and top-right) of each rectangle are unique and appear an even number of times (except for the four corners of the overall bounding rectangle).

Time complexity: O(n), where n is the number of rectangles. Space complexity: O(n)

Solution Code

class Solution {
    public boolean isRectangleCover(int[][] rectangles) {
        int area = 0;
        Set<String> corners = new HashSet<>();
        
        for (int[] rect : rectangles) {
            area += (rect[2] - rect[0]) * (rect[3] - rect[1]);
            String bottomLeft = rect[0] + "," + rect[1];
            String bottomRight = rect[2] + "," + rect[1];
            String topLeft = rect[0] + "," + rect[3];
            String topRight = rect[2] + "," + rect[3];
            
            if (!corners.add(bottomLeft)) corners.remove(bottomLeft);
            if (!corners.add(bottomRight)) corners.remove(bottomRight);
            if (!corners.add(topLeft)) corners.remove(topLeft);
            if (!corners.add(topRight)) corners.remove(topRight);
        }
        
        if (corners.size() != 4 || !corners.containsAll(Arrays.asList(rectangles[0][0] + "," + rectangles[0][1],
                                                                    rectangles[0][2] + "," + rectangles[0][1],
                                                                    rectangles[0][0] + "," + rectangles[0][3],
                                                                    rectangles[0][2] + "," + rectangles[0][3]))) {
            return false;
        }
        
        return area == (Integer.parseInt(rectangles[0][2] + "," + rectangles[0][3]) - Integer.parseInt(rectangles[0][0] + "," + rectangles[0][1]));
    }
}

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