Given N axis-aligned rectangles where N > 0, determine if they all together form an exact cover of a rectangular region.

Each rectangle is represented as a bottom-left point and a top-right point. For example, a unit square is represented as [1,1,2,2]. (coordinate of bottom-left point is (1, 1) and top-right point is (2, 2)).


Example 1:

rectangles = [
  [1,1,3,3],
  [3,1,4,2],
  [3,2,4,4],
  [1,3,2,4],
  [2,3,3,4]
]

Return true. All 5 rectangles together form an exact cover of a rectangular region.
 

 

Example 2:

rectangles = [
  [1,1,2,3],
  [1,3,2,4],
  [3,1,4,2],
  [3,2,4,4]
]

Return false. Because there is a gap between the two rectangular regions.
 

 

Example 3:

rectangles = [
  [1,1,3,3],
  [3,1,4,2],
  [1,3,2,4],
  [3,2,4,4]
]

Return false. Because there is a gap in the top center.
 

 

Example 4:

rectangles = [
  [1,1,3,3],
  [3,1,4,2],
  [1,3,2,4],
  [2,2,4,4]
]

Return false. Because two of the rectangles overlap with each other.

class Solution {
    // 1. Exact 4 corners
    // 2. Other shared points must occur evenly (cannot be odd)
    // 3. sum(area) = area of 4 corners enclosed areas
    private String delimiter = ",";
    public boolean isRectangleCover(int[][] rectangles) {
        Map<String, Integer> set = new HashMap<>();
        Map<String, int[]> map2 = new HashMap<>();
        int sum = 0;
        for (int i = 0; i < rectangles.length; i++) {
                sum = sum + (rectangles[i][2] - rectangles[i][0]) * (rectangles[i][3] - rectangles[i][1]);
                // bottom-left
                String blKey = generateKey(rectangles[i][0], rectangles[i][1]);
                if (set.containsKey(blKey)) {
                    map2.remove(blKey);
                }
                else {
                    map2.put(blKey, new int[]{rectangles[i][0], rectangles[i][1]});
                }
                set.put(blKey, set.getOrDefault(blKey, 0) + 1);
                // top-right
                String trKey = generateKey(rectangles[i][2], rectangles[i][3]);
                if (set.containsKey(trKey)) {
                    map2.remove(trKey);
                }
                else {
                    map2.put(trKey, new int[]{rectangles[i][2], rectangles[i][3]});
                }
                set.put(trKey, set.getOrDefault(trKey, 0) + 1);
                //top-left
                String tlKey = generateKey(rectangles[i][0], rectangles[i][3]);
                if (set.containsKey(tlKey)) {
                    map2.remove(tlKey);
                }
                else {
                    map2.put(tlKey, new int[]{rectangles[i][0], rectangles[i][3]});
                }
                set.put(tlKey, set.getOrDefault(tlKey, 0) + 1);
                //bottom-right
                String brKey = generateKey(rectangles[i][2], rectangles[i][1]);
                if (set.containsKey(brKey)) {
                    map2.remove(brKey);
                }
                else {
                    map2.put(brKey, new int[]{rectangles[i][2], rectangles[i][1]});
                }
                set.put(brKey, set.getOrDefault(brKey, 0) + 1);
        }
        if (map2.size() == 4) {
            for (String key: set.keySet()) {
                if (set.get(key) % 2 != 0 && set.get(key) != 1) {
                    return false;
                }
            }
            int maxL = Integer.MIN_VALUE;
            int minL = Integer.MAX_VALUE;
            int maxW = Integer.MIN_VALUE;
            int minW = Integer.MAX_VALUE;
            for (String key : map2.keySet()) {
                if(map2.get(key)[0] > maxL) {
                    maxL = map2.get(key)[0];
                }
                if(map2.get(key)[0] < minL) {
                    minL = map2.get(key)[0];
                }
                if(map2.get(key)[1] > maxW) {
                    maxW = map2.get(key)[1];
                }
                if(map2.get(key)[1] < minW) {
                    minW = map2.get(key)[1];
                }
            }
            System.out.println("Sum: " + sum);
            System.out.println("Area: " + (maxL - minL) * (maxW - minW));
            if(sum == (maxL - minL) * (maxW - minW)) {
                return true;
            }
        }
        return false;
    }
    
    private String generateKey(int i, int j) {
        return Integer.toString(i) + delimiter + Integer.toString(j);
    }
}