391. Perfect Rectangle

Problem:

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.

Solutions:

Not working solution

public class Solution {
    public boolean isRectangleCover(int[][] rectangles) {
        int blox = Integer.MAX_VALUE, bloy = Integer.MAX_VALUE, trix = Integer.MIN_VALUE, triy = Integer.MIN_VALUE;
        for (int i = 0; i < rectangles.length; i ++) {
            int[] rect = rectangles[i];
            if (!(rect[0] > blox || rect[1] > bloy)) {
                blox = rect[0];
                bloy = rect[1];
            }
            if (!(rect[2] < trix || rect[3] < triy)) {
                trix = rect[2];
                triy = rect[3];
            }
        }

        System.out.println(blox + ", " + bloy + " : " + trix + ", " + triy);
        boolean[][] covered = new boolean[trix - blox][triy - bloy];
        for (int i = 0; i < rectangles.length; i ++) {
            int[] rect = rectangles[i];
            for (int m = rect[0] - blox; m < rect[2] - blox; m ++) {
                for (int n = rect[1] - bloy; n < rect[3] - bloy; n ++) {
                    if (m < 0 || m >= covered.length || n < 0 || n >= covered[0].length) {
                        System.out.println("out of bound");
                        return false;
                    }
                    if (covered[m][n] == true) {
                        return false;
                    }
                    covered[m][n] = true;
                }
            }
        }
        for (int i = 0; i < covered.length; i ++) {
            for (int j = 0; j < covered[0].length; j ++) {
                if (covered[i][j] == false) {
                    return false;
                }
            }
        }
        return true;
    }
}

Working solution

public class Solution {
    public boolean isRectangleCover(int[][] rectangles) {
        int blox = Integer.MAX_VALUE, bloy = Integer.MAX_VALUE, trix = Integer.MIN_VALUE, triy = Integer.MIN_VALUE;
        int area = 0;
        HashMap<String, Integer> data = new HashMap<String, Integer>();
        for (int i = 0; i < rectangles.length; i ++) {
            int[] rect = rectangles[i];
            blox = Math.min(blox, rect[0]);
            bloy = Math.min(bloy, rect[1]);
            trix = Math.max(trix, rect[2]);
            triy = Math.max(triy, rect[3]);
            area += (rect[2] - rect[0]) * (rect[3] - rect[1]);
            if (!isValid(data, rect[0] + "," + rect[1], 1)) {
                return false;    
            }
            if (!isValid(data, rect[0] + "," + rect[3], 2)) {
                return false;    
            }
            if (!isValid(data, rect[2] + "," + rect[1], 4)) {
                return false;    
            }
            if (!isValid(data, rect[2] + "," + rect[3], 8)) {
                return false;    
            }
        }
        int count = 0;
        for (String s:data.keySet()) {
            int val = data.get(s);
            if (val == 1 || val == 2 || val == 4 || val == 8) {
                count ++;
            }
        }
        return count == 4 && (trix - blox) * (triy - bloy) == area;
    }
    private boolean isValid(HashMap<String, Integer> data, String key, int mask) {
        if (data.containsKey(key) && (data.get(key)&mask) != 0) {
            return false;
        }
        int val = 0;
        if (data.containsKey(key)) {
            val = data.get(key);
        }
        val = val | mask;
        data.put(key, val);
        return true;
    }
}

Another working solutions.

public class Solution {
    public boolean isRectangleCover(int[][] rectangles) {
        int blox = Integer.MAX_VALUE, bloy = Integer.MAX_VALUE, trix = Integer.MIN_VALUE, triy = Integer.MIN_VALUE;
        int area = 0;
        Set<String> points = new HashSet<String>();
        for (int i = 0; i < rectangles.length; i ++) {
            int[] rect = rectangles[i];
            blox = Math.min(blox, rect[0]);
            bloy = Math.min(bloy, rect[1]);
            trix = Math.max(trix, rect[2]);
            triy = Math.max(triy, rect[3]);
            area += (rect[2] - rect[0]) * (rect[3] - rect[1]);
            String[] ps = new String[4];
            ps[0] = rect[0] + "," + rect[1];
            ps[1] = rect[0] + "," + rect[3];
            ps[2] = rect[2] + "," + rect[1];
            ps[3] = rect[2] + "," + rect[3];
            for (int j = 0; j < ps.length; j ++) {
                if (points.contains(ps[j])) {
                    points.remove(ps[j]);
                }
                else {
                    points.add(ps[j]);
                }
            }
        }
        String[] ps = new String[4];
        ps[0] = blox + "," + bloy;
        ps[1] = blox + "," + triy;
        ps[2] = trix + "," + bloy;
        ps[3] = trix + "," + triy;
        for (int i = 0; i < ps.length; i ++) {
            if (!points.contains(ps[i])) {
                return false;
            }
        }
        return points.size() == 4 && (trix - blox) * (triy - bloy) == area;
    }
}