Leetcode:perfect Rectangle

 Given n axis-aligned rectangles where n > 0, determine if   They all together form an exact cover of a rectangular. Each rectangle are 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 are (1, 1) and Top-right Point is (2, 2 1: 
 rectangles  = [[ 1,1,3,3 ", [ 3,1,4,2 3,2,4,4 1,3,2,4 2,3,3,4 true . All 5 rectangles together form an exact cover of a rectangular region. Example  2:  

= [  [1,1,2,3],  [1,3,2,4],  [3,1,4,2],  [3,2,4,4   False3:

= [  [1,1,3,3],  [3,1,4,2],  [1,3,2,4],  [3,2,4,4  false4:

= [  [1,1,3,3],  [3,1,4,2],  [1,3,2,4],  [2,2,4,4   False. Because of the rectangles overlap with each other.

Refer to Https://discuss.leetcode.com/topic/56052/really-easy-understanding-solution-o-n-java

and https://discuss.leetcode.com/topic/55923/o-n-solution-by-counting-corners-with-detailed-explaination

Idea

Consider how the corners of all rectangles appear in the large rectangle if there ' s a perfect rectangular cover.
Rule1: The local shape of the corner have to follow one of the three following patterns

• Corner of the large Rectangle (blue): It occurs only once among all rectangles
• T-junctions (green): It occurs twice among all rectangles
• Cross (red): It occurs four times among all rectangles

For each point being a corner of any rectangle, it should appear even times except the 4 corners of the large rectangle. So we can put those points to a hash map and remove them if they appear one more time.

At the end, we should only get 4 points.

Rule2: The large rectangle area should is equal to the sum of small rectangles

1  Public classSolution {2      Public BooleanIsrectanglecover (int[] rectangles) {3         if(rectangles==NULL|| rectangles.length==0 | | rectangles[0].length==0)return false;4         intsubrecareasum = 0;//sum of Subrectangle ' s area5         intx1 = Integer.max_value;//Large Rectangle bottom left x-axis6         inty1 = Integer.max_value;//Large Rectangle bottom left y-axis7         intx2 = integer.min_value;//Large Rectangle top right x-axis8         inty2 = Integer.min_value;//Large Rectangle top right Y-axis9         TenHashset<string> set =NewHashset<string> ();//Store points One          A          for(int[] rec:rectangles) { -             //Check if it has large rectangle ' s 4 points -X1 = math.min (x1, rec[0]); theY1 = math.min (y1, rec[1]); -x2 = Math.max (x2, rec[2]); -y2 = Math.max (y2, rec[3]); -              +             //calculate sum of Subrectangles -Subrecareasum + = (rec[2]-rec[0]) * (Rec[3]-rec[1]); +              A             //Store This rectangle ' s 4 points into HashSet atString P1 = integer.tostring (rec[0]) + "" + integer.tostring (rec[1]); -String P2 = integer.tostring (rec[0]) + "" + integer.tostring (rec[3]); -String p3 = integer.tostring (rec[2]) + "" + integer.tostring (rec[1]); -String P4 = integer.tostring (rec[2]) + "" + integer.tostring (rec[3]); -              -             if(!Set.add (p1)) Set.remove (p1); in             if(!Set.add (p2)) Set.remove (p2); -             if(!Set.add (p3)) Set.remove (p3); to             if(!Set.add (P4)) Set.remove (p4); +         } -          the         if(Set.size ()!=4 | |!set.contains (x1+ "" +y1) | |!set.contains (x1+ "" +y2) | |!set.contains (x2+ "" +y1) | |!set.contains (x2+ "" +y2)) *             return false; $         returnSubrecareasum = = (x2-x1) * (y2-y1);Panax Notoginseng     } -}

Leetcode:perfect Rectangle